Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [550,2,Mod(201,550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(550, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("550.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.h (of order \(5\), degree \(4\), 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: | \(4.39177211117\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 201.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 550.201 |
Dual form | 550.2.h.c.301.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/550\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | −0.500000 | − | 1.53884i | −0.288675 | − | 0.888451i | −0.985273 | − | 0.170989i | \(-0.945304\pi\) |
0.696598 | − | 0.717462i | \(-0.254696\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.30902 | + | 0.951057i | 0.534404 | + | 0.388267i | ||||
\(7\) | −0.690983 | + | 2.12663i | −0.261167 | + | 0.803789i | 0.731385 | + | 0.681965i | \(0.238874\pi\) |
−0.992552 | + | 0.121824i | \(0.961126\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 0.309017 | − | 0.224514i | 0.103006 | − | 0.0748380i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | + | 0.726543i | 0.975711 | + | 0.219061i | ||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | −0.190983 | + | 0.138757i | −0.0529692 | + | 0.0384843i | −0.613955 | − | 0.789341i | \(-0.710422\pi\) |
0.560986 | + | 0.827826i | \(0.310422\pi\) | |||||||
\(14\) | −0.690983 | − | 2.12663i | −0.184673 | − | 0.568365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 0.309017 | + | 0.224514i | 0.0749476 | + | 0.0544526i | 0.624628 | − | 0.780922i | \(-0.285251\pi\) |
−0.549681 | + | 0.835375i | \(0.685251\pi\) | |||||||
\(18\) | −0.118034 | + | 0.363271i | −0.0278209 | + | 0.0856239i | ||||
\(19\) | 0.809017 | + | 2.48990i | 0.185601 | + | 0.571222i | 0.999958 | − | 0.00914245i | \(-0.00291017\pi\) |
−0.814357 | + | 0.580364i | \(0.802910\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.61803 | 0.789520 | ||||||||
\(22\) | −3.04508 | + | 1.31433i | −0.649214 | + | 0.280216i | ||||
\(23\) | 3.85410 | 0.803636 | 0.401818 | − | 0.915720i | \(-0.368378\pi\) | ||||
0.401818 | + | 0.915720i | \(0.368378\pi\) | |||||||
\(24\) | 1.30902 | − | 0.951057i | 0.267202 | − | 0.194134i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0729490 | − | 0.224514i | 0.0143065 | − | 0.0440308i | ||||
\(27\) | −4.42705 | − | 3.21644i | −0.851986 | − | 0.619004i | ||||
\(28\) | 1.80902 | + | 1.31433i | 0.341872 | + | 0.248385i | ||||
\(29\) | −0.163119 | + | 0.502029i | −0.0302904 | + | 0.0932244i | −0.965059 | − | 0.262033i | \(-0.915607\pi\) |
0.934768 | + | 0.355258i | \(0.115607\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.28115 | − | 6.01661i | 1.48734 | − | 1.08062i | 0.512241 | − | 0.858842i | \(-0.328816\pi\) |
0.975098 | − | 0.221773i | \(-0.0711844\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.500000 | − | 5.34307i | −0.0870388 | − | 0.930109i | ||||
\(34\) | −0.381966 | −0.0655066 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.118034 | − | 0.363271i | −0.0196723 | − | 0.0605452i | ||||
\(37\) | 2.73607 | − | 8.42075i | 0.449807 | − | 1.38436i | −0.427318 | − | 0.904101i | \(-0.640542\pi\) |
0.877125 | − | 0.480262i | \(-0.159458\pi\) | |||||||
\(38\) | −2.11803 | − | 1.53884i | −0.343590 | − | 0.249633i | ||||
\(39\) | 0.309017 | + | 0.224514i | 0.0494823 | + | 0.0359510i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.14590 | − | 3.52671i | −0.178959 | − | 0.550780i | 0.820833 | − | 0.571168i | \(-0.193510\pi\) |
−0.999792 | + | 0.0203886i | \(0.993510\pi\) | |||||||
\(42\) | −2.92705 | + | 2.12663i | −0.451654 | + | 0.328146i | ||||
\(43\) | 9.47214 | 1.44449 | 0.722244 | − | 0.691639i | \(-0.243111\pi\) | ||||
0.722244 | + | 0.691639i | \(0.243111\pi\) | |||||||
\(44\) | 1.69098 | − | 2.85317i | 0.254925 | − | 0.430131i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.11803 | + | 2.26538i | −0.459729 | + | 0.334013i | ||||
\(47\) | −0.0729490 | − | 0.224514i | −0.0106407 | − | 0.0327487i | 0.945595 | − | 0.325346i | \(-0.105481\pi\) |
−0.956236 | + | 0.292597i | \(0.905481\pi\) | |||||||
\(48\) | −0.500000 | + | 1.53884i | −0.0721688 | + | 0.222113i | ||||
\(49\) | 1.61803 | + | 1.17557i | 0.231148 | + | 0.167939i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.190983 | − | 0.587785i | 0.0267430 | − | 0.0823064i | ||||
\(52\) | 0.0729490 | + | 0.224514i | 0.0101162 | + | 0.0311345i | ||||
\(53\) | 1.11803 | − | 0.812299i | 0.153574 | − | 0.111578i | −0.508345 | − | 0.861154i | \(-0.669742\pi\) |
0.661919 | + | 0.749576i | \(0.269742\pi\) | |||||||
\(54\) | 5.47214 | 0.744663 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 3.42705 | − | 2.48990i | 0.453924 | − | 0.329795i | ||||
\(58\) | −0.163119 | − | 0.502029i | −0.0214186 | − | 0.0659196i | ||||
\(59\) | −3.54508 | + | 10.9106i | −0.461531 | + | 1.42045i | 0.401763 | + | 0.915744i | \(0.368398\pi\) |
−0.863294 | + | 0.504702i | \(0.831602\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.80902 | − | 1.31433i | −0.231621 | − | 0.168282i | 0.465921 | − | 0.884826i | \(-0.345723\pi\) |
−0.697542 | + | 0.716544i | \(0.745723\pi\) | |||||||
\(62\) | −3.16312 | + | 9.73508i | −0.401717 | + | 1.23636i | ||||
\(63\) | 0.263932 | + | 0.812299i | 0.0332523 | + | 0.102340i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.54508 | + | 4.02874i | 0.436370 | + | 0.495904i | ||||
\(67\) | 9.32624 | 1.13938 | 0.569691 | − | 0.821859i | \(-0.307063\pi\) | ||||
0.569691 | + | 0.821859i | \(0.307063\pi\) | |||||||
\(68\) | 0.309017 | − | 0.224514i | 0.0374738 | − | 0.0272263i | ||||
\(69\) | −1.92705 | − | 5.93085i | −0.231990 | − | 0.713991i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.92705 | − | 5.75934i | −0.940768 | − | 0.683508i | 0.00783751 | − | 0.999969i | \(-0.497505\pi\) |
−0.948605 | + | 0.316461i | \(0.897505\pi\) | |||||||
\(72\) | 0.309017 | + | 0.224514i | 0.0364180 | + | 0.0264592i | ||||
\(73\) | −2.51722 | + | 7.74721i | −0.294618 | + | 0.906742i | 0.688731 | + | 0.725017i | \(0.258168\pi\) |
−0.983349 | + | 0.181725i | \(0.941832\pi\) | |||||||
\(74\) | 2.73607 | + | 8.42075i | 0.318061 | + | 0.978892i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.61803 | 0.300309 | ||||||||
\(77\) | −3.78115 | + | 6.37988i | −0.430902 | + | 0.727055i | ||||
\(78\) | −0.381966 | −0.0432491 | ||||||||
\(79\) | 9.66312 | − | 7.02067i | 1.08719 | − | 0.789887i | 0.108264 | − | 0.994122i | \(-0.465471\pi\) |
0.978922 | + | 0.204235i | \(0.0654708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.38197 | + | 7.33094i | −0.264663 | + | 0.814549i | ||||
\(82\) | 3.00000 | + | 2.17963i | 0.331295 | + | 0.240700i | ||||
\(83\) | 7.28115 | + | 5.29007i | 0.799210 | + | 0.580660i | 0.910682 | − | 0.413107i | \(-0.135557\pi\) |
−0.111472 | + | 0.993768i | \(0.535557\pi\) | |||||||
\(84\) | 1.11803 | − | 3.44095i | 0.121988 | − | 0.375439i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.66312 | + | 5.56758i | −0.826335 | + | 0.600368i | ||||
\(87\) | 0.854102 | 0.0915693 | ||||||||
\(88\) | 0.309017 | + | 3.30220i | 0.0329413 | + | 0.352015i | ||||
\(89\) | −13.1803 | −1.39711 | −0.698557 | − | 0.715555i | \(-0.746174\pi\) | ||||
−0.698557 | + | 0.715555i | \(0.746174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.163119 | − | 0.502029i | −0.0170995 | − | 0.0526269i | ||||
\(92\) | 1.19098 | − | 3.66547i | 0.124169 | − | 0.382152i | ||||
\(93\) | −13.3992 | − | 9.73508i | −1.38943 | − | 1.00948i | ||||
\(94\) | 0.190983 | + | 0.138757i | 0.0196984 | + | 0.0143117i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | − | 1.53884i | −0.0510310 | − | 0.157057i | ||||
\(97\) | 9.70820 | − | 7.05342i | 0.985719 | − | 0.716167i | 0.0267394 | − | 0.999642i | \(-0.491488\pi\) |
0.958979 | + | 0.283476i | \(0.0914876\pi\) | |||||||
\(98\) | −2.00000 | −0.202031 | ||||||||
\(99\) | 1.16312 | − | 0.502029i | 0.116898 | − | 0.0504558i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.1353 | + | 10.9964i | −1.50601 | + | 1.09418i | −0.538107 | + | 0.842877i | \(0.680860\pi\) |
−0.967908 | + | 0.251307i | \(0.919140\pi\) | |||||||
\(102\) | 0.190983 | + | 0.587785i | 0.0189101 | + | 0.0581994i | ||||
\(103\) | −5.21885 | + | 16.0620i | −0.514228 | + | 1.58263i | 0.270453 | + | 0.962733i | \(0.412826\pi\) |
−0.784682 | + | 0.619899i | \(0.787174\pi\) | |||||||
\(104\) | −0.190983 | − | 0.138757i | −0.0187274 | − | 0.0136063i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.427051 | + | 1.31433i | −0.0414789 | + | 0.127659i | ||||
\(107\) | 2.52786 | + | 7.77997i | 0.244378 | + | 0.752118i | 0.995738 | + | 0.0922255i | \(0.0293981\pi\) |
−0.751360 | + | 0.659892i | \(0.770602\pi\) | |||||||
\(108\) | −4.42705 | + | 3.21644i | −0.425993 | + | 0.309502i | ||||
\(109\) | −11.6180 | −1.11281 | −0.556403 | − | 0.830913i | \(-0.687819\pi\) | ||||
−0.556403 | + | 0.830913i | \(0.687819\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.3262 | −1.35979 | ||||||||
\(112\) | 1.80902 | − | 1.31433i | 0.170936 | − | 0.124192i | ||||
\(113\) | −4.54508 | − | 13.9883i | −0.427566 | − | 1.31591i | −0.900516 | − | 0.434823i | \(-0.856811\pi\) |
0.472950 | − | 0.881089i | \(-0.343189\pi\) | |||||||
\(114\) | −1.30902 | + | 4.02874i | −0.122601 | + | 0.377326i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.427051 | + | 0.310271i | 0.0396507 | + | 0.0288079i | ||||
\(117\) | −0.0278640 | + | 0.0857567i | −0.00257603 | + | 0.00792821i | ||||
\(118\) | −3.54508 | − | 10.9106i | −0.326352 | − | 1.00441i | ||||
\(119\) | −0.690983 | + | 0.502029i | −0.0633423 | + | 0.0460209i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.94427 | + | 4.70228i | 0.904025 | + | 0.427480i | ||||
\(122\) | 2.23607 | 0.202444 | ||||||||
\(123\) | −4.85410 | + | 3.52671i | −0.437680 | + | 0.317993i | ||||
\(124\) | −3.16312 | − | 9.73508i | −0.284056 | − | 0.874236i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.690983 | − | 0.502029i | −0.0615577 | − | 0.0447243i | ||||
\(127\) | −2.35410 | − | 1.71036i | −0.208893 | − | 0.151769i | 0.478420 | − | 0.878131i | \(-0.341210\pi\) |
−0.687313 | + | 0.726362i | \(0.741210\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | −4.73607 | − | 14.5761i | −0.416988 | − | 1.28336i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1459 | 0.973822 | 0.486911 | − | 0.873452i | \(-0.338124\pi\) | ||||
0.486911 | + | 0.873452i | \(0.338124\pi\) | |||||||
\(132\) | −5.23607 | − | 1.17557i | −0.455741 | − | 0.102320i | ||||
\(133\) | −5.85410 | −0.507615 | ||||||||
\(134\) | −7.54508 | + | 5.48183i | −0.651796 | + | 0.473558i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.118034 | + | 0.363271i | −0.0101213 | + | 0.0311503i | ||||
\(137\) | −12.7533 | − | 9.26581i | −1.08959 | − | 0.791631i | −0.110258 | − | 0.993903i | \(-0.535168\pi\) |
−0.979329 | + | 0.202272i | \(0.935168\pi\) | |||||||
\(138\) | 5.04508 | + | 3.66547i | 0.429466 | + | 0.312025i | ||||
\(139\) | −0.881966 | + | 2.71441i | −0.0748074 | + | 0.230233i | −0.981468 | − | 0.191628i | \(-0.938623\pi\) |
0.906660 | + | 0.421862i | \(0.138623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.309017 | + | 0.224514i | −0.0260239 | + | 0.0189075i | ||||
\(142\) | 9.79837 | 0.822261 | ||||||||
\(143\) | −0.718847 | + | 0.310271i | −0.0601130 | + | 0.0259461i | ||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.51722 | − | 7.74721i | −0.208327 | − | 0.641164i | ||||
\(147\) | 1.00000 | − | 3.07768i | 0.0824786 | − | 0.253843i | ||||
\(148\) | −7.16312 | − | 5.20431i | −0.588805 | − | 0.427792i | ||||
\(149\) | 8.66312 | + | 6.29412i | 0.709710 | + | 0.515635i | 0.883080 | − | 0.469222i | \(-0.155466\pi\) |
−0.173370 | + | 0.984857i | \(0.555466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.88197 | − | 18.1028i | −0.478668 | − | 1.47319i | −0.840947 | − | 0.541118i | \(-0.818001\pi\) |
0.362279 | − | 0.932070i | \(-0.381999\pi\) | |||||||
\(152\) | −2.11803 | + | 1.53884i | −0.171795 | + | 0.124817i | ||||
\(153\) | 0.145898 | 0.0117952 | ||||||||
\(154\) | −0.690983 | − | 7.38394i | −0.0556810 | − | 0.595015i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.309017 | − | 0.224514i | 0.0247412 | − | 0.0179755i | ||||
\(157\) | 2.09017 | + | 6.43288i | 0.166814 | + | 0.513400i | 0.999165 | − | 0.0408481i | \(-0.0130060\pi\) |
−0.832352 | + | 0.554248i | \(0.813006\pi\) | |||||||
\(158\) | −3.69098 | + | 11.3597i | −0.293639 | + | 0.903727i | ||||
\(159\) | −1.80902 | − | 1.31433i | −0.143464 | − | 0.104233i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.66312 | + | 8.19624i | −0.209883 | + | 0.645954i | ||||
\(162\) | −2.38197 | − | 7.33094i | −0.187145 | − | 0.575973i | ||||
\(163\) | −0.145898 | + | 0.106001i | −0.0114276 | + | 0.00830265i | −0.593484 | − | 0.804845i | \(-0.702248\pi\) |
0.582057 | + | 0.813148i | \(0.302248\pi\) | |||||||
\(164\) | −3.70820 | −0.289562 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00000 | −0.698535 | ||||||||
\(167\) | 1.80902 | − | 1.31433i | 0.139986 | − | 0.101706i | −0.515588 | − | 0.856836i | \(-0.672427\pi\) |
0.655574 | + | 0.755131i | \(0.272427\pi\) | |||||||
\(168\) | 1.11803 | + | 3.44095i | 0.0862582 | + | 0.265475i | ||||
\(169\) | −4.00000 | + | 12.3107i | −0.307692 | + | 0.946980i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.809017 | + | 0.587785i | 0.0618671 | + | 0.0449491i | ||||
\(172\) | 2.92705 | − | 9.00854i | 0.223186 | − | 0.686894i | ||||
\(173\) | −4.11803 | − | 12.6740i | −0.313088 | − | 0.963587i | −0.976534 | − | 0.215362i | \(-0.930907\pi\) |
0.663446 | − | 0.748224i | \(-0.269093\pi\) | |||||||
\(174\) | −0.690983 | + | 0.502029i | −0.0523833 | + | 0.0380587i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.19098 | − | 2.48990i | −0.165152 | − | 0.187683i | ||||
\(177\) | 18.5623 | 1.39523 | ||||||||
\(178\) | 10.6631 | − | 7.74721i | 0.799235 | − | 0.580678i | ||||
\(179\) | 4.52786 | + | 13.9353i | 0.338428 | + | 1.04158i | 0.965009 | + | 0.262219i | \(0.0844541\pi\) |
−0.626580 | + | 0.779357i | \(0.715546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.70820 | + | 4.14725i | 0.424287 | + | 0.308263i | 0.779361 | − | 0.626576i | \(-0.215544\pi\) |
−0.355073 | + | 0.934839i | \(0.615544\pi\) | |||||||
\(182\) | 0.427051 | + | 0.310271i | 0.0316551 | + | 0.0229988i | ||||
\(183\) | −1.11803 | + | 3.44095i | −0.0826475 | + | 0.254363i | ||||
\(184\) | 1.19098 | + | 3.66547i | 0.0878004 | + | 0.270222i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.5623 | 1.21441 | ||||||||
\(187\) | 0.836881 | + | 0.951057i | 0.0611988 | + | 0.0695481i | ||||
\(188\) | −0.236068 | −0.0172170 | ||||||||
\(189\) | 9.89919 | − | 7.19218i | 0.720060 | − | 0.523154i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.13525 | + | 18.8824i | −0.443931 | + | 1.36628i | 0.439720 | + | 0.898135i | \(0.355078\pi\) |
−0.883651 | + | 0.468146i | \(0.844922\pi\) | |||||||
\(192\) | 1.30902 | + | 0.951057i | 0.0944702 | + | 0.0686366i | ||||
\(193\) | −1.97214 | − | 1.43284i | −0.141957 | − | 0.103138i | 0.514540 | − | 0.857466i | \(-0.327963\pi\) |
−0.656497 | + | 0.754328i | \(0.727963\pi\) | |||||||
\(194\) | −3.70820 | + | 11.4127i | −0.266234 | + | 0.819383i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.61803 | − | 1.17557i | 0.115574 | − | 0.0839693i | ||||
\(197\) | −27.5967 | −1.96619 | −0.983093 | − | 0.183105i | \(-0.941385\pi\) | ||||
−0.983093 | + | 0.183105i | \(0.941385\pi\) | |||||||
\(198\) | −0.645898 | + | 1.08981i | −0.0459020 | + | 0.0774497i | ||||
\(199\) | −1.29180 | −0.0915730 | −0.0457865 | − | 0.998951i | \(-0.514579\pi\) | ||||
−0.0457865 | + | 0.998951i | \(0.514579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.66312 | − | 14.3516i | −0.328911 | − | 1.01228i | ||||
\(202\) | 5.78115 | − | 17.7926i | 0.406761 | − | 1.25188i | ||||
\(203\) | −0.954915 | − | 0.693786i | −0.0670219 | − | 0.0486943i | ||||
\(204\) | −0.500000 | − | 0.363271i | −0.0350070 | − | 0.0254341i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.21885 | − | 16.0620i | −0.363614 | − | 1.11909i | ||||
\(207\) | 1.19098 | − | 0.865300i | 0.0827790 | − | 0.0601425i | ||||
\(208\) | 0.236068 | 0.0163684 | ||||||||
\(209\) | 0.809017 | + | 8.64527i | 0.0559609 | + | 0.598006i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7361 | + | 8.52675i | −0.807944 | + | 0.587006i | −0.913234 | − | 0.407436i | \(-0.866423\pi\) |
0.105290 | + | 0.994442i | \(0.466423\pi\) | |||||||
\(212\) | −0.427051 | − | 1.31433i | −0.0293300 | − | 0.0902684i | ||||
\(213\) | −4.89919 | + | 15.0781i | −0.335687 | + | 1.03314i | ||||
\(214\) | −6.61803 | − | 4.80828i | −0.452399 | − | 0.328687i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.69098 | − | 5.20431i | 0.115057 | − | 0.354108i | ||||
\(217\) | 7.07295 | + | 21.7683i | 0.480143 | + | 1.47773i | ||||
\(218\) | 9.39919 | − | 6.82891i | 0.636593 | − | 0.462512i | ||||
\(219\) | 13.1803 | 0.890645 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0901699 | −0.00606549 | ||||||||
\(222\) | 11.5902 | − | 8.42075i | 0.777881 | − | 0.565164i | ||||
\(223\) | −0.635255 | − | 1.95511i | −0.0425398 | − | 0.130924i | 0.927531 | − | 0.373746i | \(-0.121927\pi\) |
−0.970071 | + | 0.242822i | \(0.921927\pi\) | |||||||
\(224\) | −0.690983 | + | 2.12663i | −0.0461682 | + | 0.142091i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.8992 | + | 8.64527i | 0.791522 | + | 0.575074i | ||||
\(227\) | −6.10081 | + | 18.7764i | −0.404925 | + | 1.24623i | 0.516033 | + | 0.856569i | \(0.327408\pi\) |
−0.920958 | + | 0.389663i | \(0.872592\pi\) | |||||||
\(228\) | −1.30902 | − | 4.02874i | −0.0866918 | − | 0.266810i | ||||
\(229\) | 12.5172 | − | 9.09429i | 0.827161 | − | 0.600968i | −0.0915935 | − | 0.995796i | \(-0.529196\pi\) |
0.918755 | + | 0.394829i | \(0.129196\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.7082 | + | 2.62866i | 0.770343 | + | 0.172953i | ||||
\(232\) | −0.527864 | −0.0346560 | ||||||||
\(233\) | 16.4443 | − | 11.9475i | 1.07730 | − | 0.782704i | 0.100090 | − | 0.994978i | \(-0.468087\pi\) |
0.977210 | + | 0.212274i | \(0.0680870\pi\) | |||||||
\(234\) | −0.0278640 | − | 0.0857567i | −0.00182153 | − | 0.00560609i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.28115 | + | 6.74315i | 0.604152 | + | 0.438942i | ||||
\(237\) | −15.6353 | − | 11.3597i | −1.01562 | − | 0.737890i | ||||
\(238\) | 0.263932 | − | 0.812299i | 0.0171082 | − | 0.0526535i | ||||
\(239\) | −5.39919 | − | 16.6170i | −0.349244 | − | 1.07486i | −0.959272 | − | 0.282484i | \(-0.908842\pi\) |
0.610028 | − | 0.792380i | \(-0.291158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | −10.8090 | + | 2.04087i | −0.694830 | + | 0.131192i | ||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | −1.80902 | + | 1.31433i | −0.115810 | + | 0.0841412i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.85410 | − | 5.70634i | 0.118213 | − | 0.363823i | ||||
\(247\) | −0.500000 | − | 0.363271i | −0.0318142 | − | 0.0231144i | ||||
\(248\) | 8.28115 | + | 6.01661i | 0.525854 | + | 0.382055i | ||||
\(249\) | 4.50000 | − | 13.8496i | 0.285176 | − | 0.877681i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.88197 | + | 2.82041i | −0.245028 | + | 0.178023i | −0.703520 | − | 0.710675i | \(-0.748390\pi\) |
0.458493 | + | 0.888698i | \(0.348390\pi\) | |||||||
\(252\) | 0.854102 | 0.0538034 | ||||||||
\(253\) | 12.4721 | + | 2.80017i | 0.784116 | + | 0.176045i | ||||
\(254\) | 2.90983 | 0.182579 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −4.28115 | + | 13.1760i | −0.267051 | + | 0.821898i | 0.724163 | + | 0.689629i | \(0.242226\pi\) |
−0.991214 | + | 0.132269i | \(0.957774\pi\) | |||||||
\(258\) | 12.3992 | + | 9.00854i | 0.771940 | + | 0.560847i | ||||
\(259\) | 16.0172 | + | 11.6372i | 0.995262 | + | 0.723100i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0623059 | + | 0.191758i | 0.00385664 | + | 0.0118695i | ||||
\(262\) | −9.01722 | + | 6.55139i | −0.557086 | + | 0.404747i | ||||
\(263\) | 16.0902 | 0.992162 | 0.496081 | − | 0.868276i | \(-0.334772\pi\) | ||||
0.496081 | + | 0.868276i | \(0.334772\pi\) | |||||||
\(264\) | 4.92705 | − | 2.12663i | 0.303239 | − | 0.130885i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.73607 | − | 3.44095i | 0.290387 | − | 0.210978i | ||||
\(267\) | 6.59017 | + | 20.2825i | 0.403312 | + | 1.24127i | ||||
\(268\) | 2.88197 | − | 8.86978i | 0.176044 | − | 0.541808i | ||||
\(269\) | −8.01722 | − | 5.82485i | −0.488819 | − | 0.355147i | 0.315911 | − | 0.948789i | \(-0.397690\pi\) |
−0.804730 | + | 0.593641i | \(0.797690\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.64590 | − | 26.6093i | 0.525201 | − | 1.61640i | −0.238717 | − | 0.971089i | \(-0.576727\pi\) |
0.763918 | − | 0.645313i | \(-0.223273\pi\) | |||||||
\(272\) | −0.118034 | − | 0.363271i | −0.00715686 | − | 0.0220266i | ||||
\(273\) | −0.690983 | + | 0.502029i | −0.0418202 | + | 0.0303841i | ||||
\(274\) | 15.7639 | 0.952334 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.23607 | −0.375367 | ||||||||
\(277\) | −15.5623 | + | 11.3067i | −0.935048 | + | 0.679352i | −0.947224 | − | 0.320573i | \(-0.896124\pi\) |
0.0121753 | + | 0.999926i | \(0.496124\pi\) | |||||||
\(278\) | −0.881966 | − | 2.71441i | −0.0528968 | − | 0.162800i | ||||
\(279\) | 1.20820 | − | 3.71847i | 0.0723333 | − | 0.222619i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7082 | + | 13.5923i | 1.11604 | + | 0.810849i | 0.983604 | − | 0.180343i | \(-0.0577207\pi\) |
0.132434 | + | 0.991192i | \(0.457721\pi\) | |||||||
\(282\) | 0.118034 | − | 0.363271i | 0.00702882 | − | 0.0216325i | ||||
\(283\) | 6.79837 | + | 20.9232i | 0.404121 | + | 1.24376i | 0.921627 | + | 0.388078i | \(0.126861\pi\) |
−0.517505 | + | 0.855680i | \(0.673139\pi\) | |||||||
\(284\) | −7.92705 | + | 5.75934i | −0.470384 | + | 0.341754i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.399187 | − | 0.673542i | 0.0236044 | − | 0.0398274i | ||||
\(287\) | 8.29180 | 0.489449 | ||||||||
\(288\) | 0.309017 | − | 0.224514i | 0.0182090 | − | 0.0132296i | ||||
\(289\) | −5.20820 | − | 16.0292i | −0.306365 | − | 0.942894i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.7082 | − | 11.4127i | −0.920831 | − | 0.669023i | ||||
\(292\) | 6.59017 | + | 4.78804i | 0.385661 | + | 0.280199i | ||||
\(293\) | 3.24671 | − | 9.99235i | 0.189675 | − | 0.583759i | −0.810323 | − | 0.585984i | \(-0.800708\pi\) |
0.999998 | + | 0.00222470i | \(0.000708144\pi\) | |||||||
\(294\) | 1.00000 | + | 3.07768i | 0.0583212 | + | 0.179494i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.85410 | 0.514634 | ||||||||
\(297\) | −11.9894 | − | 13.6251i | −0.695693 | − | 0.790606i | ||||
\(298\) | −10.7082 | −0.620310 | ||||||||
\(299\) | −0.736068 | + | 0.534785i | −0.0425679 | + | 0.0309274i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.54508 | + | 20.1437i | −0.377252 | + | 1.16106i | ||||
\(302\) | 15.3992 | + | 11.1882i | 0.886124 | + | 0.643807i | ||||
\(303\) | 24.4894 | + | 17.7926i | 1.40688 | + | 1.02216i | ||||
\(304\) | 0.809017 | − | 2.48990i | 0.0464003 | − | 0.142805i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.118034 | + | 0.0857567i | −0.00674755 | + | 0.00490238i | ||||
\(307\) | −28.7984 | −1.64361 | −0.821805 | − | 0.569769i | \(-0.807033\pi\) | ||||
−0.821805 | + | 0.569769i | \(0.807033\pi\) | |||||||
\(308\) | 4.89919 | + | 5.56758i | 0.279157 | + | 0.317242i | ||||
\(309\) | 27.3262 | 1.55454 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.30902 | + | 4.02874i | 0.0742275 | + | 0.228449i | 0.981286 | − | 0.192556i | \(-0.0616776\pi\) |
−0.907058 | + | 0.421005i | \(0.861678\pi\) | |||||||
\(312\) | −0.118034 | + | 0.363271i | −0.00668236 | + | 0.0205662i | ||||
\(313\) | 0.809017 | + | 0.587785i | 0.0457283 | + | 0.0332236i | 0.610415 | − | 0.792082i | \(-0.291003\pi\) |
−0.564686 | + | 0.825306i | \(0.691003\pi\) | |||||||
\(314\) | −5.47214 | − | 3.97574i | −0.308810 | − | 0.224364i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.69098 | − | 11.3597i | −0.207634 | − | 0.639032i | ||||
\(317\) | 2.26393 | − | 1.64484i | 0.127155 | − | 0.0923836i | −0.522390 | − | 0.852707i | \(-0.674959\pi\) |
0.649545 | + | 0.760323i | \(0.274959\pi\) | |||||||
\(318\) | 2.23607 | 0.125392 | ||||||||
\(319\) | −0.892609 | + | 1.50609i | −0.0499765 | + | 0.0843246i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.7082 | − | 7.77997i | 0.597674 | − | 0.434235i | ||||
\(322\) | −2.66312 | − | 8.19624i | −0.148410 | − | 0.456758i | ||||
\(323\) | −0.309017 | + | 0.951057i | −0.0171942 | + | 0.0529182i | ||||
\(324\) | 6.23607 | + | 4.53077i | 0.346448 | + | 0.251709i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.0557281 | − | 0.171513i | 0.00308649 | − | 0.00949925i | ||||
\(327\) | 5.80902 | + | 17.8783i | 0.321239 | + | 0.988673i | ||||
\(328\) | 3.00000 | − | 2.17963i | 0.165647 | − | 0.120350i | ||||
\(329\) | 0.527864 | 0.0291021 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9443 | −0.931341 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(332\) | 7.28115 | − | 5.29007i | 0.399605 | − | 0.290330i | ||||
\(333\) | −1.04508 | − | 3.21644i | −0.0572703 | − | 0.176260i | ||||
\(334\) | −0.690983 | + | 2.12663i | −0.0378089 | + | 0.116364i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.92705 | − | 2.12663i | −0.159684 | − | 0.116017i | ||||
\(337\) | 9.30902 | − | 28.6502i | 0.507094 | − | 1.56068i | −0.290126 | − | 0.956988i | \(-0.593697\pi\) |
0.797221 | − | 0.603688i | \(-0.206303\pi\) | |||||||
\(338\) | −4.00000 | − | 12.3107i | −0.217571 | − | 0.669616i | ||||
\(339\) | −19.2533 | + | 13.9883i | −1.04570 | + | 0.759742i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.1697 | − | 13.4535i | 1.68793 | − | 0.728550i | ||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −16.2812 | + | 11.8290i | −0.879100 | + | 0.638703i | ||||
\(344\) | 2.92705 | + | 9.00854i | 0.157816 | + | 0.485708i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.7812 | + | 7.83297i | 0.579598 | + | 0.421103i | ||||
\(347\) | −15.2533 | − | 11.0822i | −0.818839 | − | 0.594922i | 0.0975404 | − | 0.995232i | \(-0.468902\pi\) |
−0.916380 | + | 0.400310i | \(0.868902\pi\) | |||||||
\(348\) | 0.263932 | − | 0.812299i | 0.0141482 | − | 0.0435438i | ||||
\(349\) | −7.29180 | − | 22.4418i | −0.390321 | − | 1.20128i | −0.932546 | − | 0.361051i | \(-0.882418\pi\) |
0.542225 | − | 0.840233i | \(-0.317582\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.29180 | 0.0689510 | ||||||||
\(352\) | 3.23607 | + | 0.726543i | 0.172483 | + | 0.0387248i | ||||
\(353\) | −4.43769 | −0.236195 | −0.118097 | − | 0.993002i | \(-0.537679\pi\) | ||||
−0.118097 | + | 0.993002i | \(0.537679\pi\) | |||||||
\(354\) | −15.0172 | + | 10.9106i | −0.798156 | + | 0.579894i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.07295 | + | 12.5352i | −0.215866 | + | 0.664367i | ||||
\(357\) | 1.11803 | + | 0.812299i | 0.0591726 | + | 0.0429914i | ||||
\(358\) | −11.8541 | − | 8.61251i | −0.626509 | − | 0.455185i | ||||
\(359\) | 0.291796 | − | 0.898056i | 0.0154004 | − | 0.0473976i | −0.943061 | − | 0.332620i | \(-0.892067\pi\) |
0.958461 | + | 0.285222i | \(0.0920674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.82624 | − | 7.13918i | 0.517170 | − | 0.375746i | ||||
\(362\) | −7.05573 | −0.370841 | ||||||||
\(363\) | 2.26393 | − | 17.6538i | 0.118826 | − | 0.926584i | ||||
\(364\) | −0.527864 | −0.0276676 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.11803 | − | 3.44095i | −0.0584406 | − | 0.179862i | ||||
\(367\) | 1.65248 | − | 5.08580i | 0.0862585 | − | 0.265476i | −0.898619 | − | 0.438731i | \(-0.855428\pi\) |
0.984877 | + | 0.173254i | \(0.0554282\pi\) | |||||||
\(368\) | −3.11803 | − | 2.26538i | −0.162539 | − | 0.118091i | ||||
\(369\) | −1.14590 | − | 0.832544i | −0.0596531 | − | 0.0433405i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.954915 | + | 2.93893i | 0.0495767 | + | 0.152581i | ||||
\(372\) | −13.3992 | + | 9.73508i | −0.694715 | + | 0.504740i | ||||
\(373\) | 2.38197 | 0.123334 | 0.0616668 | − | 0.998097i | \(-0.480358\pi\) | ||||
0.0616668 | + | 0.998097i | \(0.480358\pi\) | |||||||
\(374\) | −1.23607 | − | 0.277515i | −0.0639156 | − | 0.0143499i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.190983 | − | 0.138757i | 0.00984920 | − | 0.00715586i | ||||
\(377\) | −0.0385072 | − | 0.118513i | −0.00198322 | − | 0.00610372i | ||||
\(378\) | −3.78115 | + | 11.6372i | −0.194482 | + | 0.598553i | ||||
\(379\) | 4.78115 | + | 3.47371i | 0.245591 | + | 0.178433i | 0.703771 | − | 0.710427i | \(-0.251498\pi\) |
−0.458179 | + | 0.888860i | \(0.651498\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.45492 | + | 4.47777i | −0.0745376 | + | 0.229403i | ||||
\(382\) | −6.13525 | − | 18.8824i | −0.313907 | − | 0.966106i | ||||
\(383\) | 1.61803 | − | 1.17557i | 0.0826777 | − | 0.0600688i | −0.545679 | − | 0.837995i | \(-0.683728\pi\) |
0.628356 | + | 0.777926i | \(0.283728\pi\) | |||||||
\(384\) | −1.61803 | −0.0825700 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.43769 | 0.124075 | ||||||||
\(387\) | 2.92705 | − | 2.12663i | 0.148790 | − | 0.108103i | ||||
\(388\) | −3.70820 | − | 11.4127i | −0.188256 | − | 0.579391i | ||||
\(389\) | 0.545085 | − | 1.67760i | 0.0276369 | − | 0.0850576i | −0.936287 | − | 0.351237i | \(-0.885761\pi\) |
0.963924 | + | 0.266179i | \(0.0857612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.19098 | + | 0.865300i | 0.0602306 | + | 0.0437601i | ||||
\(392\) | −0.618034 | + | 1.90211i | −0.0312154 | + | 0.0960712i | ||||
\(393\) | −5.57295 | − | 17.1518i | −0.281118 | − | 0.865193i | ||||
\(394\) | 22.3262 | − | 16.2210i | 1.12478 | − | 0.817200i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.118034 | − | 1.26133i | −0.00593143 | − | 0.0633841i | ||||
\(397\) | −17.4721 | −0.876901 | −0.438451 | − | 0.898755i | \(-0.644473\pi\) | ||||
−0.438451 | + | 0.898755i | \(0.644473\pi\) | |||||||
\(398\) | 1.04508 | − | 0.759299i | 0.0523854 | − | 0.0380602i | ||||
\(399\) | 2.92705 | + | 9.00854i | 0.146536 | + | 0.450991i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.54508 | + | 1.12257i | 0.0771579 | + | 0.0560585i | 0.625695 | − | 0.780067i | \(-0.284815\pi\) |
−0.548538 | + | 0.836126i | \(0.684815\pi\) | |||||||
\(402\) | 12.2082 | + | 8.86978i | 0.608890 | + | 0.442384i | ||||
\(403\) | −0.746711 | + | 2.29814i | −0.0371963 | + | 0.114479i | ||||
\(404\) | 5.78115 | + | 17.7926i | 0.287623 | + | 0.885213i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.18034 | 0.0585793 | ||||||||
\(407\) | 14.9721 | − | 25.2623i | 0.742141 | − | 1.25220i | ||||
\(408\) | 0.618034 | 0.0305972 | ||||||||
\(409\) | −14.9721 | + | 10.8779i | −0.740324 | + | 0.537877i | −0.892813 | − | 0.450428i | \(-0.851271\pi\) |
0.152488 | + | 0.988305i | \(0.451271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.88197 | + | 24.2582i | −0.388789 | + | 1.19657i | ||||
\(412\) | 13.6631 | + | 9.92684i | 0.673134 | + | 0.489060i | ||||
\(413\) | −20.7533 | − | 15.0781i | −1.02120 | − | 0.741947i | ||||
\(414\) | −0.454915 | + | 1.40008i | −0.0223579 | + | 0.0688104i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.190983 | + | 0.138757i | −0.00936371 | + | 0.00680314i | ||||
\(417\) | 4.61803 | 0.226146 | ||||||||
\(418\) | −5.73607 | − | 6.51864i | −0.280560 | − | 0.318837i | ||||
\(419\) | −31.1803 | −1.52326 | −0.761630 | − | 0.648013i | \(-0.775600\pi\) | ||||
−0.761630 | + | 0.648013i | \(0.775600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.46149 | − | 16.8087i | −0.266177 | − | 0.819208i | −0.991420 | − | 0.130715i | \(-0.958273\pi\) |
0.725243 | − | 0.688493i | \(-0.241727\pi\) | |||||||
\(422\) | 4.48278 | − | 13.7966i | 0.218218 | − | 0.671607i | ||||
\(423\) | −0.0729490 | − | 0.0530006i | −0.00354690 | − | 0.00257698i | ||||
\(424\) | 1.11803 | + | 0.812299i | 0.0542965 | + | 0.0394487i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.89919 | − | 15.0781i | −0.237366 | − | 0.730539i | ||||
\(427\) | 4.04508 | − | 2.93893i | 0.195755 | − | 0.142225i | ||||
\(428\) | 8.18034 | 0.395412 | ||||||||
\(429\) | 0.836881 | + | 0.951057i | 0.0404050 | + | 0.0459174i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.80902 | + | 3.49396i | −0.231642 | + | 0.168298i | −0.697552 | − | 0.716534i | \(-0.745727\pi\) |
0.465909 | + | 0.884832i | \(0.345727\pi\) | |||||||
\(432\) | 1.69098 | + | 5.20431i | 0.0813575 | + | 0.250393i | ||||
\(433\) | −2.61803 | + | 8.05748i | −0.125815 | + | 0.387218i | −0.994049 | − | 0.108937i | \(-0.965255\pi\) |
0.868234 | + | 0.496155i | \(0.165255\pi\) | |||||||
\(434\) | −18.5172 | − | 13.4535i | −0.888855 | − | 0.645791i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.59017 | + | 11.0494i | −0.171938 | + | 0.529171i | ||||
\(437\) | 3.11803 | + | 9.59632i | 0.149156 | + | 0.459054i | ||||
\(438\) | −10.6631 | + | 7.74721i | −0.509504 | + | 0.370176i | ||||
\(439\) | 22.7082 | 1.08380 | 0.541902 | − | 0.840442i | \(-0.317704\pi\) | ||||
0.541902 | + | 0.840442i | \(0.317704\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.763932 | 0.0363777 | ||||||||
\(442\) | 0.0729490 | − | 0.0530006i | 0.00346983 | − | 0.00252098i | ||||
\(443\) | −9.42705 | − | 29.0135i | −0.447893 | − | 1.37847i | −0.879280 | − | 0.476305i | \(-0.841976\pi\) |
0.431387 | − | 0.902167i | \(-0.358024\pi\) | |||||||
\(444\) | −4.42705 | + | 13.6251i | −0.210099 | + | 0.646617i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.66312 | + | 1.20833i | 0.0787510 | + | 0.0572159i | ||||
\(447\) | 5.35410 | − | 16.4782i | 0.253240 | − | 0.779394i | ||||
\(448\) | −0.690983 | − | 2.12663i | −0.0326459 | − | 0.100474i | ||||
\(449\) | −13.1803 | + | 9.57608i | −0.622019 | + | 0.451923i | −0.853626 | − | 0.520886i | \(-0.825602\pi\) |
0.231607 | + | 0.972809i | \(0.425602\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.14590 | − | 12.2452i | −0.0539582 | − | 0.576605i | ||||
\(452\) | −14.7082 | −0.691816 | ||||||||
\(453\) | −24.9164 | + | 18.1028i | −1.17067 | + | 0.850545i | ||||
\(454\) | −6.10081 | − | 18.7764i | −0.286325 | − | 0.881219i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.42705 | + | 2.48990i | 0.160486 | + | 0.116600i | ||||
\(457\) | 9.80902 | + | 7.12667i | 0.458846 | + | 0.333371i | 0.793079 | − | 0.609119i | \(-0.208477\pi\) |
−0.334232 | + | 0.942491i | \(0.608477\pi\) | |||||||
\(458\) | −4.78115 | + | 14.7149i | −0.223409 | + | 0.687581i | ||||
\(459\) | −0.645898 | − | 1.98787i | −0.0301479 | − | 0.0927858i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.4164 | −1.69608 | −0.848041 | − | 0.529931i | \(-0.822218\pi\) | ||||
−0.848041 | + | 0.529931i | \(0.822218\pi\) | |||||||
\(462\) | −11.0172 | + | 4.75528i | −0.512568 | + | 0.221236i | ||||
\(463\) | −38.5967 | −1.79374 | −0.896871 | − | 0.442291i | \(-0.854166\pi\) | ||||
−0.896871 | + | 0.442291i | \(0.854166\pi\) | |||||||
\(464\) | 0.427051 | − | 0.310271i | 0.0198253 | − | 0.0144040i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.28115 | + | 19.3314i | −0.290969 | + | 0.895510i | ||||
\(467\) | 26.0344 | + | 18.9151i | 1.20473 | + | 0.875288i | 0.994742 | − | 0.102416i | \(-0.0326573\pi\) |
0.209989 | + | 0.977704i | \(0.432657\pi\) | |||||||
\(468\) | 0.0729490 | + | 0.0530006i | 0.00337207 | + | 0.00244995i | ||||
\(469\) | −6.44427 | + | 19.8334i | −0.297569 | + | 0.915823i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.85410 | − | 6.43288i | 0.407975 | − | 0.296412i | ||||
\(472\) | −11.4721 | −0.528048 | ||||||||
\(473\) | 30.6525 | + | 6.88191i | 1.40940 | + | 0.316431i | ||||
\(474\) | 19.3262 | 0.887684 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.263932 | + | 0.812299i | 0.0120973 | + | 0.0372317i | ||||
\(477\) | 0.163119 | − | 0.502029i | 0.00746870 | − | 0.0229863i | ||||
\(478\) | 14.1353 | + | 10.2699i | 0.646532 | + | 0.469733i | ||||
\(479\) | −8.04508 | − | 5.84510i | −0.367589 | − | 0.267069i | 0.388621 | − | 0.921398i | \(-0.372951\pi\) |
−0.756211 | + | 0.654328i | \(0.772951\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.645898 | + | 1.98787i | 0.0294504 | + | 0.0906391i | ||||
\(482\) | −14.5623 | + | 10.5801i | −0.663295 | + | 0.481912i | ||||
\(483\) | 13.9443 | 0.634486 | ||||||||
\(484\) | 7.54508 | − | 8.00448i | 0.342958 | − | 0.363840i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.19098 | − | 2.31838i | 0.144746 | − | 0.105164i | ||||
\(487\) | −3.36475 | − | 10.3556i | −0.152471 | − | 0.469258i | 0.845425 | − | 0.534095i | \(-0.179347\pi\) |
−0.997896 | + | 0.0648366i | \(0.979347\pi\) | |||||||
\(488\) | 0.690983 | − | 2.12663i | 0.0312793 | − | 0.0962679i | ||||
\(489\) | 0.236068 | + | 0.171513i | 0.0106754 | + | 0.00775611i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.76393 | − | 11.5842i | 0.169864 | − | 0.522787i | −0.829498 | − | 0.558510i | \(-0.811373\pi\) |
0.999362 | + | 0.0357226i | \(0.0113733\pi\) | |||||||
\(492\) | 1.85410 | + | 5.70634i | 0.0835894 | + | 0.257262i | ||||
\(493\) | −0.163119 | + | 0.118513i | −0.00734651 | + | 0.00533755i | ||||
\(494\) | 0.618034 | 0.0278067 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.2361 | −0.459613 | ||||||||
\(497\) | 17.7254 | − | 12.8783i | 0.795094 | − | 0.577670i | ||||
\(498\) | 4.50000 | + | 13.8496i | 0.201650 | + | 0.620614i | ||||
\(499\) | 4.77458 | − | 14.6946i | 0.213739 | − | 0.657822i | −0.785501 | − | 0.618860i | \(-0.787595\pi\) |
0.999241 | − | 0.0389621i | \(-0.0124052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.92705 | − | 2.12663i | −0.130771 | − | 0.0950107i | ||||
\(502\) | 1.48278 | − | 4.56352i | 0.0661797 | − | 0.203680i | ||||
\(503\) | 9.73607 | + | 29.9645i | 0.434110 | + | 1.33605i | 0.893996 | + | 0.448075i | \(0.147890\pi\) |
−0.459886 | + | 0.887978i | \(0.652110\pi\) | |||||||
\(504\) | −0.690983 | + | 0.502029i | −0.0307788 | + | 0.0223621i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.7361 | + | 5.06555i | −0.521732 | + | 0.225191i | ||||
\(507\) | 20.9443 | 0.930168 | ||||||||
\(508\) | −2.35410 | + | 1.71036i | −0.104446 | + | 0.0758847i | ||||
\(509\) | 3.17376 | + | 9.76784i | 0.140675 | + | 0.432952i | 0.996429 | − | 0.0844297i | \(-0.0269069\pi\) |
−0.855755 | + | 0.517381i | \(0.826907\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.7361 | − | 10.7064i | −0.651885 | − | 0.473622i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | 4.42705 | − | 13.6251i | 0.195459 | − | 0.601561i | ||||
\(514\) | −4.28115 | − | 13.1760i | −0.188834 | − | 0.581170i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15.3262 | −0.674700 | ||||||||
\(517\) | −0.0729490 | − | 0.779543i | −0.00320829 | − | 0.0342843i | ||||
\(518\) | −19.7984 | −0.869891 | ||||||||
\(519\) | −17.4443 | + | 12.6740i | −0.765719 | + | 0.556327i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.10081 | + | 9.54332i | −0.135849 | + | 0.418100i | −0.995721 | − | 0.0924091i | \(-0.970543\pi\) |
0.859872 | + | 0.510510i | \(0.170543\pi\) | |||||||
\(522\) | −0.163119 | − | 0.118513i | −0.00713952 | − | 0.00518717i | ||||
\(523\) | −22.2533 | − | 16.1680i | −0.973068 | − | 0.706976i | −0.0169196 | − | 0.999857i | \(-0.505386\pi\) |
−0.956149 | + | 0.292881i | \(0.905386\pi\) | |||||||
\(524\) | 3.44427 | − | 10.6004i | 0.150464 | − | 0.463080i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.0172 | + | 9.45756i | −0.567578 | + | 0.412369i | ||||
\(527\) | 3.90983 | 0.170315 | ||||||||
\(528\) | −2.73607 | + | 4.61653i | −0.119072 | + | 0.200908i | ||||
\(529\) | −8.14590 | −0.354169 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.35410 | + | 4.16750i | 0.0587630 | + | 0.180854i | ||||
\(532\) | −1.80902 | + | 5.56758i | −0.0784308 | + | 0.241385i | ||||
\(533\) | 0.708204 | + | 0.514540i | 0.0306757 | + | 0.0222872i | ||||
\(534\) | −17.2533 | − | 12.5352i | −0.746623 | − | 0.542453i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.88197 | + | 8.86978i | 0.124482 | + | 0.383116i | ||||
\(537\) | 19.1803 | − | 13.9353i | 0.827693 | − | 0.601354i | ||||
\(538\) | 9.90983 | 0.427243 | ||||||||
\(539\) | 4.38197 | + | 4.97980i | 0.188745 | + | 0.214495i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.0066 | + | 18.8949i | −1.11811 | + | 0.812355i | −0.983922 | − | 0.178601i | \(-0.942843\pi\) |
−0.134189 | + | 0.990956i | \(0.542843\pi\) | |||||||
\(542\) | 8.64590 | + | 26.6093i | 0.371373 | + | 1.14297i | ||||
\(543\) | 3.52786 | − | 10.8576i | 0.151395 | − | 0.465946i | ||||
\(544\) | 0.309017 | + | 0.224514i | 0.0132490 | + | 0.00962596i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.263932 | − | 0.812299i | 0.0112952 | − | 0.0347632i | ||||
\(547\) | 5.54508 | + | 17.0660i | 0.237091 | + | 0.729690i | 0.996837 | + | 0.0794708i | \(0.0253230\pi\) |
−0.759746 | + | 0.650219i | \(0.774677\pi\) | |||||||
\(548\) | −12.7533 | + | 9.26581i | −0.544794 | + | 0.395816i | ||||
\(549\) | −0.854102 | −0.0364522 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.38197 | −0.0588737 | ||||||||
\(552\) | 5.04508 | − | 3.66547i | 0.214733 | − | 0.156013i | ||||
\(553\) | 8.25329 | + | 25.4010i | 0.350966 | + | 1.08016i | ||||
\(554\) | 5.94427 | − | 18.2946i | 0.252548 | − | 0.777263i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.30902 | + | 1.67760i | 0.0979241 | + | 0.0711460i | ||||
\(557\) | −1.81966 | + | 5.60034i | −0.0771015 | + | 0.237294i | −0.982177 | − | 0.187956i | \(-0.939814\pi\) |
0.905076 | + | 0.425250i | \(0.139814\pi\) | |||||||
\(558\) | 1.20820 | + | 3.71847i | 0.0511474 | + | 0.157415i | ||||
\(559\) | −1.80902 | + | 1.31433i | −0.0765133 | + | 0.0555901i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.04508 | − | 1.76336i | 0.0441235 | − | 0.0744489i | ||||
\(562\) | −23.1246 | −0.975453 | ||||||||
\(563\) | −14.2533 | + | 10.3556i | −0.600705 | + | 0.436437i | −0.846129 | − | 0.532978i | \(-0.821073\pi\) |
0.245424 | + | 0.969416i | \(0.421073\pi\) | |||||||
\(564\) | 0.118034 | + | 0.363271i | 0.00497013 | + | 0.0152965i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.7984 | − | 12.9313i | −0.748121 | − | 0.543542i | ||||
\(567\) | −13.9443 | − | 10.1311i | −0.585604 | − | 0.425466i | ||||
\(568\) | 3.02786 | − | 9.31881i | 0.127046 | − | 0.391008i | ||||
\(569\) | −0.645898 | − | 1.98787i | −0.0270775 | − | 0.0833358i | 0.936605 | − | 0.350388i | \(-0.113950\pi\) |
−0.963682 | + | 0.267052i | \(0.913950\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.52786 | −0.356880 | −0.178440 | − | 0.983951i | \(-0.557105\pi\) | ||||
−0.178440 | + | 0.983951i | \(0.557105\pi\) | |||||||
\(572\) | 0.0729490 | + | 0.779543i | 0.00305015 | + | 0.0325943i | ||||
\(573\) | 32.1246 | 1.34202 | ||||||||
\(574\) | −6.70820 | + | 4.87380i | −0.279995 | + | 0.203428i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.118034 | + | 0.363271i | −0.00491808 | + | 0.0151363i | ||||
\(577\) | 17.6074 | + | 12.7925i | 0.733005 | + | 0.532560i | 0.890513 | − | 0.454958i | \(-0.150346\pi\) |
−0.157507 | + | 0.987518i | \(0.550346\pi\) | |||||||
\(578\) | 13.6353 | + | 9.90659i | 0.567152 | + | 0.412060i | ||||
\(579\) | −1.21885 | + | 3.75123i | −0.0506536 | + | 0.155896i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.2812 | + | 11.8290i | −0.675456 | + | 0.490748i | ||||
\(582\) | 19.4164 | 0.804836 | ||||||||
\(583\) | 4.20820 | − | 1.81636i | 0.174286 | − | 0.0752258i | ||||
\(584\) | −8.14590 | −0.337080 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.24671 | + | 9.99235i | 0.134120 | + | 0.412780i | ||||
\(587\) | 5.01064 | − | 15.4212i | 0.206811 | − | 0.636500i | −0.792823 | − | 0.609452i | \(-0.791389\pi\) |
0.999634 | − | 0.0270477i | \(-0.00861060\pi\) | |||||||
\(588\) | −2.61803 | − | 1.90211i | −0.107966 | − | 0.0784418i | ||||
\(589\) | 21.6803 | + | 15.7517i | 0.893323 | + | 0.649037i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.7984 | + | 42.4670i | 0.567589 | + | 1.74686i | ||||
\(592\) | −7.16312 | + | 5.20431i | −0.294402 | + | 0.213896i | ||||
\(593\) | −42.3951 | −1.74096 | −0.870479 | − | 0.492205i | \(-0.836191\pi\) | ||||
−0.870479 | + | 0.492205i | \(0.836191\pi\) | |||||||
\(594\) | 17.7082 | + | 3.97574i | 0.726576 | + | 0.163127i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.66312 | − | 6.29412i | 0.354855 | − | 0.257817i | ||||
\(597\) | 0.645898 | + | 1.98787i | 0.0264348 | + | 0.0813581i | ||||
\(598\) | 0.281153 | − | 0.865300i | 0.0114972 | − | 0.0353847i | ||||
\(599\) | −2.47214 | − | 1.79611i | −0.101009 | − | 0.0733871i | 0.536134 | − | 0.844133i | \(-0.319884\pi\) |
−0.637143 | + | 0.770745i | \(0.719884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.02786 | + | 6.24112i | −0.0827183 | + | 0.254581i | −0.983859 | − | 0.178946i | \(-0.942731\pi\) |
0.901141 | + | 0.433527i | \(0.142731\pi\) | |||||||
\(602\) | −6.54508 | − | 20.1437i | −0.266758 | − | 0.820996i | ||||
\(603\) | 2.88197 | − | 2.09387i | 0.117363 | − | 0.0852690i | ||||
\(604\) | −19.0344 | −0.774500 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −30.2705 | −1.22966 | ||||||||
\(607\) | −10.8262 | + | 7.86572i | −0.439423 | + | 0.319260i | −0.785406 | − | 0.618981i | \(-0.787546\pi\) |
0.345982 | + | 0.938241i | \(0.387546\pi\) | |||||||
\(608\) | 0.809017 | + | 2.48990i | 0.0328100 | + | 0.100979i | ||||
\(609\) | −0.590170 | + | 1.81636i | −0.0239149 | + | 0.0736025i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0450850 | + | 0.0327561i | 0.00182394 | + | 0.00132517i | ||||
\(612\) | 0.0450850 | − | 0.138757i | 0.00182245 | − | 0.00560893i | ||||
\(613\) | −2.21885 | − | 6.82891i | −0.0896184 | − | 0.275817i | 0.896195 | − | 0.443659i | \(-0.146320\pi\) |
−0.985814 | + | 0.167842i | \(0.946320\pi\) | |||||||
\(614\) | 23.2984 | − | 16.9273i | 0.940246 | − | 0.683129i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.23607 | − | 1.62460i | −0.291549 | − | 0.0654569i | ||||
\(617\) | 25.7984 | 1.03860 | 0.519302 | − | 0.854591i | \(-0.326192\pi\) | ||||
0.519302 | + | 0.854591i | \(0.326192\pi\) | |||||||
\(618\) | −22.1074 | + | 16.0620i | −0.889290 | + | 0.646107i | ||||
\(619\) | −8.10739 | − | 24.9520i | −0.325864 | − | 1.00290i | −0.971049 | − | 0.238879i | \(-0.923220\pi\) |
0.645186 | − | 0.764026i | \(-0.276780\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.0623 | − | 12.3965i | −0.684687 | − | 0.497454i | ||||
\(622\) | −3.42705 | − | 2.48990i | −0.137412 | − | 0.0998358i | ||||
\(623\) | 9.10739 | − | 28.0297i | 0.364880 | − | 1.12298i | ||||
\(624\) | −0.118034 | − | 0.363271i | −0.00472514 | − | 0.0145425i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.00000 | −0.0399680 | ||||||||
\(627\) | 12.8992 | − | 5.56758i | 0.515144 | − | 0.222348i | ||||
\(628\) | 6.76393 | 0.269910 | ||||||||
\(629\) | 2.73607 | − | 1.98787i | 0.109094 | − | 0.0792616i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.07295 | + | 6.37988i | −0.0825228 | + | 0.253979i | −0.983802 | − | 0.179260i | \(-0.942630\pi\) |
0.901279 | + | 0.433239i | \(0.142630\pi\) | |||||||
\(632\) | 9.66312 | + | 7.02067i | 0.384378 | + | 0.279267i | ||||
\(633\) | 18.9894 | + | 13.7966i | 0.754759 | + | 0.548365i | ||||
\(634\) | −0.864745 | + | 2.66141i | −0.0343434 | + | 0.105698i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.80902 | + | 1.31433i | −0.0717322 | + | 0.0521165i | ||||
\(637\) | −0.472136 | −0.0187067 | ||||||||
\(638\) | −0.163119 | − | 1.74311i | −0.00645794 | − | 0.0690104i | ||||
\(639\) | −3.74265 | −0.148057 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.0000 | − | 40.0099i | −0.513469 | − | 1.58030i | −0.786050 | − | 0.618163i | \(-0.787877\pi\) |
0.272581 | − | 0.962133i | \(-0.412123\pi\) | |||||||
\(642\) | −4.09017 | + | 12.5882i | −0.161426 | + | 0.496819i | ||||
\(643\) | 11.4271 | + | 8.30224i | 0.450639 | + | 0.327408i | 0.789848 | − | 0.613303i | \(-0.210159\pi\) |
−0.339209 | + | 0.940711i | \(0.610159\pi\) | |||||||
\(644\) | 6.97214 | + | 5.06555i | 0.274741 | + | 0.199611i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.309017 | − | 0.951057i | −0.0121581 | − | 0.0374188i | ||||
\(647\) | 0.854102 | − | 0.620541i | 0.0335782 | − | 0.0243960i | −0.570870 | − | 0.821041i | \(-0.693394\pi\) |
0.604448 | + | 0.796645i | \(0.293394\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | −19.3992 | + | 32.7319i | −0.761485 | + | 1.28484i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.9615 | − | 21.7683i | 1.17428 | − | 0.853167i | ||||
\(652\) | 0.0557281 | + | 0.171513i | 0.00218248 | + | 0.00671698i | ||||
\(653\) | −3.23607 | + | 9.95959i | −0.126637 | + | 0.389749i | −0.994196 | − | 0.107586i | \(-0.965688\pi\) |
0.867559 | + | 0.497335i | \(0.165688\pi\) | |||||||
\(654\) | −15.2082 | − | 11.0494i | −0.594688 | − | 0.432066i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.14590 | + | 3.52671i | −0.0447398 | + | 0.137695i | ||||
\(657\) | 0.961493 | + | 2.95917i | 0.0375114 | + | 0.115448i | ||||
\(658\) | −0.427051 | + | 0.310271i | −0.0166482 | + | 0.0120956i | ||||
\(659\) | 43.4508 | 1.69260 | 0.846302 | − | 0.532703i | \(-0.178824\pi\) | ||||
0.846302 | + | 0.532703i | \(0.178824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5967 | 1.07339 | 0.536695 | − | 0.843777i | \(-0.319673\pi\) | ||||
0.536695 | + | 0.843777i | \(0.319673\pi\) | |||||||
\(662\) | 13.7082 | − | 9.95959i | 0.532784 | − | 0.387091i | ||||
\(663\) | 0.0450850 | + | 0.138757i | 0.00175096 | + | 0.00538889i | ||||
\(664\) | −2.78115 | + | 8.55951i | −0.107930 | + | 0.332173i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.73607 | + | 1.98787i | 0.106020 | + | 0.0770284i | ||||
\(667\) | −0.628677 | + | 1.93487i | −0.0243425 | + | 0.0749184i | ||||
\(668\) | −0.690983 | − | 2.12663i | −0.0267349 | − | 0.0822817i | ||||
\(669\) | −2.69098 | + | 1.95511i | −0.104039 | + | 0.0755891i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.89919 | − | 5.56758i | −0.189131 | − | 0.214934i | ||||
\(672\) | 3.61803 | 0.139569 | ||||||||
\(673\) | 9.37132 | − | 6.80866i | 0.361238 | − | 0.262455i | −0.392330 | − | 0.919824i | \(-0.628331\pi\) |
0.753568 | + | 0.657370i | \(0.228331\pi\) | |||||||
\(674\) | 9.30902 | + | 28.6502i | 0.358570 | + | 1.10356i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.4721 | + | 7.60845i | 0.402774 | + | 0.292633i | ||||
\(677\) | −8.76393 | − | 6.36737i | −0.336825 | − | 0.244718i | 0.406496 | − | 0.913653i | \(-0.366751\pi\) |
−0.743321 | + | 0.668935i | \(0.766751\pi\) | |||||||
\(678\) | 7.35410 | − | 22.6336i | 0.282433 | − | 0.869238i | ||||
\(679\) | 8.29180 | + | 25.5195i | 0.318210 | + | 0.979349i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.9443 | 1.22411 | ||||||||
\(682\) | −17.3090 | + | 29.2052i | −0.662797 | + | 1.11833i | ||||
\(683\) | 6.11146 | 0.233848 | 0.116924 | − | 0.993141i | \(-0.462697\pi\) | ||||
0.116924 | + | 0.993141i | \(0.462697\pi\) | |||||||
\(684\) | 0.809017 | − | 0.587785i | 0.0309335 | − | 0.0224745i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.21885 | − | 19.1396i | 0.237437 | − | 0.730755i | ||||
\(687\) | −20.2533 | − | 14.7149i | −0.772711 | − | 0.561408i | ||||
\(688\) | −7.66312 | − | 5.56758i | −0.292154 | − | 0.212262i | ||||
\(689\) | −0.100813 | + | 0.310271i | −0.00384067 | + | 0.0118204i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.2984 | − | 23.4661i | 1.22869 | − | 0.892694i | 0.231897 | − | 0.972740i | \(-0.425507\pi\) |
0.996791 | + | 0.0800463i | \(0.0255068\pi\) | |||||||
\(692\) | −13.3262 | −0.506588 | ||||||||
\(693\) | 0.263932 | + | 2.82041i | 0.0100259 | + | 0.107139i | ||||
\(694\) | 18.8541 | 0.715692 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.263932 | + | 0.812299i | 0.0100043 | + | 0.0307901i | ||||
\(697\) | 0.437694 | − | 1.34708i | 0.0165788 | − | 0.0510244i | ||||
\(698\) | 19.0902 | + | 13.8698i | 0.722574 | + | 0.524980i | ||||
\(699\) | −26.6074 | − | 19.3314i | −1.00638 | − | 0.731181i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.89919 | − | 12.0005i | −0.147270 | − | 0.453251i | 0.850026 | − | 0.526741i | \(-0.176586\pi\) |
−0.997296 | + | 0.0734900i | \(0.976586\pi\) | |||||||
\(702\) | −1.04508 | + | 0.759299i | −0.0394442 | + | 0.0286579i | ||||
\(703\) | 23.1803 | 0.874263 | ||||||||
\(704\) | −3.04508 | + | 1.31433i | −0.114766 | + | 0.0495356i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.59017 | − | 2.60841i | 0.135118 | − | 0.0981688i | ||||
\(707\) | −12.9271 | − | 39.7854i | −0.486172 | − | 1.49628i | ||||
\(708\) | 5.73607 | − | 17.6538i | 0.215575 | − | 0.663471i | ||||
\(709\) | 37.3156 | + | 27.1114i | 1.40142 | + | 1.01819i | 0.994501 | + | 0.104723i | \(0.0333955\pi\) |
0.406915 | + | 0.913466i | \(0.366604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.40983 | − | 4.33901i | 0.0528728 | − | 0.162726i | ||||
\(712\) | −4.07295 | − | 12.5352i | −0.152640 | − | 0.469778i | ||||
\(713\) | 31.9164 | − | 23.1886i | 1.19528 | − | 0.868421i | ||||
\(714\) | −1.38197 | −0.0517188 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.6525 | 0.547589 | ||||||||
\(717\) | −22.8713 | + | 16.6170i | −0.854145 | + | 0.620573i | ||||
\(718\) | 0.291796 | + | 0.898056i | 0.0108897 | + | 0.0335152i | ||||
\(719\) | 6.16312 | − | 18.9681i | 0.229846 | − | 0.707392i | −0.767918 | − | 0.640548i | \(-0.778707\pi\) |
0.997763 | − | 0.0668436i | \(-0.0212929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.5517 | − | 22.1971i | −1.13780 | − | 0.826663i | ||||
\(722\) | −3.75329 | + | 11.5514i | −0.139683 | + | 0.429900i | ||||
\(723\) | −9.00000 | − | 27.6992i | −0.334714 | − | 1.03014i | ||||
\(724\) | 5.70820 | − | 4.14725i | 0.212144 | − | 0.154131i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.54508 | + | 15.6129i | 0.317138 | + | 0.579450i | ||||
\(727\) | −13.8197 | −0.512543 | −0.256271 | − | 0.966605i | \(-0.582494\pi\) | ||||
−0.256271 | + | 0.966605i | \(0.582494\pi\) | |||||||
\(728\) | 0.427051 | − | 0.310271i | 0.0158276 | − | 0.0114994i | ||||
\(729\) | 9.11803 | + | 28.0624i | 0.337705 | + | 1.03935i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.92705 | + | 2.12663i | 0.108261 | + | 0.0786561i | ||||
\(732\) | 2.92705 | + | 2.12663i | 0.108187 | + | 0.0786024i | ||||
\(733\) | −6.74671 | + | 20.7642i | −0.249195 | + | 0.766945i | 0.745723 | + | 0.666257i | \(0.232104\pi\) |
−0.994918 | + | 0.100688i | \(0.967896\pi\) | |||||||
\(734\) | 1.65248 | + | 5.08580i | 0.0609940 | + | 0.187720i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.85410 | 0.142064 | ||||||||
\(737\) | 30.1803 | + | 6.77591i | 1.11171 | + | 0.249594i | ||||
\(738\) | 1.41641 | 0.0521387 | ||||||||
\(739\) | −7.85410 | + | 5.70634i | −0.288918 | + | 0.209911i | −0.722798 | − | 0.691060i | \(-0.757144\pi\) |
0.433880 | + | 0.900971i | \(0.357144\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.309017 | + | 0.951057i | −0.0113520 | + | 0.0349379i | ||||
\(742\) | −2.50000 | − | 1.81636i | −0.0917779 | − | 0.0666805i | ||||
\(743\) | −34.4058 | − | 24.9973i | −1.26223 | − | 0.917060i | −0.263360 | − | 0.964698i | \(-0.584831\pi\) |
−0.998865 | + | 0.0476373i | \(0.984831\pi\) | |||||||
\(744\) | 5.11803 | − | 15.7517i | 0.187636 | − | 0.577485i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.92705 | + | 1.40008i | −0.0705543 | + | 0.0512607i | ||||
\(747\) | 3.43769 | 0.125779 | ||||||||
\(748\) | 1.16312 | − | 0.502029i | 0.0425278 | − | 0.0183560i | ||||
\(749\) | −18.2918 | −0.668368 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.31559 | + | 25.5928i | 0.303440 | + | 0.933893i | 0.980255 | + | 0.197740i | \(0.0633600\pi\) |
−0.676814 | + | 0.736154i | \(0.736640\pi\) | |||||||
\(752\) | −0.0729490 | + | 0.224514i | −0.00266018 | + | 0.00818718i | ||||
\(753\) | 6.28115 | + | 4.56352i | 0.228898 | + | 0.166304i | ||||
\(754\) | 0.100813 | + | 0.0732450i | 0.00367140 | + | 0.00266742i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.78115 | − | 11.6372i | −0.137519 | − | 0.423241i | ||||
\(757\) | 12.3090 | − | 8.94302i | 0.447379 | − | 0.325040i | −0.341181 | − | 0.939998i | \(-0.610827\pi\) |
0.788560 | + | 0.614958i | \(0.210827\pi\) | |||||||
\(758\) | −5.90983 | −0.214655 | ||||||||
\(759\) | −1.92705 | − | 20.5927i | −0.0699475 | − | 0.747469i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2254 | − | 12.5150i | 0.624421 | − | 0.453669i | −0.230042 | − | 0.973181i | \(-0.573886\pi\) |
0.854463 | + | 0.519512i | \(0.173886\pi\) | |||||||
\(762\) | −1.45492 | − | 4.47777i | −0.0527060 | − | 0.162212i | ||||
\(763\) | 8.02786 | − | 24.7072i | 0.290628 | − | 0.894462i | ||||
\(764\) | 16.0623 | + | 11.6699i | 0.581114 | + | 0.422204i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.618034 | + | 1.90211i | −0.0223305 | + | 0.0687261i | ||||
\(767\) | −0.836881 | − | 2.57565i | −0.0302180 | − | 0.0930015i | ||||
\(768\) | 1.30902 | − | 0.951057i | 0.0472351 | − | 0.0343183i | ||||
\(769\) | −42.2361 | −1.52307 | −0.761536 | − | 0.648123i | \(-0.775554\pi\) | ||||
−0.761536 | + | 0.648123i | \(0.775554\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4164 | 0.807307 | ||||||||
\(772\) | −1.97214 | + | 1.43284i | −0.0709787 | + | 0.0515691i | ||||
\(773\) | 12.7984 | + | 39.3893i | 0.460326 | + | 1.41674i | 0.864767 | + | 0.502173i | \(0.167466\pi\) |
−0.404442 | + | 0.914564i | \(0.632534\pi\) | |||||||
\(774\) | −1.11803 | + | 3.44095i | −0.0401869 | + | 0.123683i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.70820 | + | 7.05342i | 0.348504 | + | 0.253203i | ||||
\(777\) | 9.89919 | − | 30.4666i | 0.355131 | − | 1.09298i | ||||
\(778\) | 0.545085 | + | 1.67760i | 0.0195422 | + | 0.0601448i | ||||
\(779\) | 7.85410 | − | 5.70634i | 0.281402 | − | 0.204451i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.4681 | − | 24.3970i | −0.768188 | − | 0.872992i | ||||
\(782\) | −1.47214 | −0.0526435 | ||||||||
\(783\) | 2.33688 | − | 1.69784i | 0.0835133 | − | 0.0606760i | ||||
\(784\) | −0.618034 | − | 1.90211i | −0.0220726 | − | 0.0679326i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.5902 | + | 10.6004i | 0.520414 | + | 0.378103i | ||||
\(787\) | −14.5623 | − | 10.5801i | −0.519090 | − | 0.377141i | 0.297171 | − | 0.954824i | \(-0.403957\pi\) |
−0.816261 | + | 0.577683i | \(0.803957\pi\) | |||||||
\(788\) | −8.52786 | + | 26.2461i | −0.303793 | + | 0.934977i | ||||
\(789\) | −8.04508 | − | 24.7602i | −0.286413 | − | 0.881487i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.8885 | 1.16938 | ||||||||
\(792\) | 0.836881 | + | 0.951057i | 0.0297373 | + | 0.0337943i | ||||
\(793\) | 0.527864 | 0.0187450 | ||||||||
\(794\) | 14.1353 | − | 10.2699i | 0.501641 | − | 0.364464i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.399187 | + | 1.22857i | −0.0141488 | + | 0.0435455i | ||||
\(797\) | −40.4615 | − | 29.3970i | −1.43322 | − | 1.04129i | −0.989406 | − | 0.145176i | \(-0.953625\pi\) |
−0.443814 | − | 0.896119i | \(-0.646375\pi\) | |||||||
\(798\) | −7.66312 | − | 5.56758i | −0.271271 | − | 0.197090i | ||||
\(799\) | 0.0278640 | − | 0.0857567i | 0.000985759 | − | 0.00303385i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.07295 | + | 2.95917i | −0.143911 | + | 0.104557i | ||||
\(802\) | −1.90983 | −0.0674384 | ||||||||
\(803\) | −13.7746 | + | 23.2416i | −0.486094 | + | 0.820179i | ||||
\(804\) | −15.0902 | −0.532189 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.746711 | − | 2.29814i | −0.0263018 | − | 0.0809485i | ||||
\(807\) | −4.95492 | + | 15.2497i | −0.174421 | + | 0.536813i | ||||
\(808\) | −15.1353 | − | 10.9964i | −0.532456 | − | 0.386852i | ||||
\(809\) | −26.7533 | − | 19.4374i | −0.940596 | − | 0.683383i | 0.00796840 | − | 0.999968i | \(-0.497464\pi\) |
−0.948564 | + | 0.316586i | \(0.897464\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.21885 | + | 12.9843i | 0.148144 | + | 0.455940i | 0.997402 | − | 0.0720383i | \(-0.0229504\pi\) |
−0.849258 | + | 0.527978i | \(0.822950\pi\) | |||||||
\(812\) | −0.954915 | + | 0.693786i | −0.0335109 | + | 0.0243471i | ||||
\(813\) | −45.2705 | −1.58771 | ||||||||
\(814\) | 2.73607 | + | 29.2380i | 0.0958991 | + | 1.02479i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.500000 | + | 0.363271i | −0.0175035 | + | 0.0127170i | ||||
\(817\) | 7.66312 | + | 23.5847i | 0.268099 | + | 0.825123i | ||||
\(818\) | 5.71885 | − | 17.6008i | 0.199955 | − | 0.615398i | ||||
\(819\) | −0.163119 | − | 0.118513i | −0.00569984 | − | 0.00414117i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.1631 | + | 37.4342i | −0.424496 | + | 1.30646i | 0.478980 | + | 0.877826i | \(0.341006\pi\) |
−0.903476 | + | 0.428638i | \(0.858994\pi\) | |||||||
\(822\) | −7.88197 | − | 24.2582i | −0.274915 | − | 0.846102i | ||||
\(823\) | −1.79180 | + | 1.30182i | −0.0624581 | + | 0.0453785i | −0.618576 | − | 0.785725i | \(-0.712290\pi\) |
0.556118 | + | 0.831103i | \(0.312290\pi\) | |||||||
\(824\) | −16.8885 | −0.588340 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.6525 | 0.892564 | ||||||||
\(827\) | −18.3713 | + | 13.3475i | −0.638833 | + | 0.464140i | −0.859449 | − | 0.511221i | \(-0.829193\pi\) |
0.220616 | + | 0.975361i | \(0.429193\pi\) | |||||||
\(828\) | −0.454915 | − | 1.40008i | −0.0158094 | − | 0.0486563i | ||||
\(829\) | 11.4377 | − | 35.2016i | 0.397248 | − | 1.22260i | −0.529950 | − | 0.848029i | \(-0.677789\pi\) |
0.927197 | − | 0.374573i | \(-0.122211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.1803 | + | 18.2946i | 0.873496 | + | 0.634632i | ||||
\(832\) | 0.0729490 | − | 0.224514i | 0.00252905 | − | 0.00778362i | ||||
\(833\) | 0.236068 | + | 0.726543i | 0.00817927 | + | 0.0251732i | ||||
\(834\) | −3.73607 | + | 2.71441i | −0.129369 | + | 0.0939924i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.47214 | + | 1.90211i | 0.293015 | + | 0.0657860i | ||||
\(837\) | −56.0132 | −1.93610 | ||||||||
\(838\) | 25.2254 | − | 18.3273i | 0.871398 | − | 0.633108i | ||||
\(839\) | −9.03851 | − | 27.8177i | −0.312044 | − | 0.960372i | −0.976954 | − | 0.213449i | \(-0.931530\pi\) |
0.664910 | − | 0.746923i | \(-0.268470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2361 | + | 16.8820i | 0.801244 | + | 0.582138i | ||||
\(842\) | 14.2984 | + | 10.3884i | 0.492755 | + | 0.358007i | ||||
\(843\) | 11.5623 | − | 35.5851i | 0.398227 | − | 1.22562i | ||||
\(844\) | 4.48278 | + | 13.7966i | 0.154304 | + | 0.474898i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.0901699 | 0.00310011 | ||||||||
\(847\) | −16.8713 | + | 17.8986i | −0.579706 | + | 0.615002i | ||||
\(848\) | −1.38197 | −0.0474569 | ||||||||
\(849\) | 28.7984 | − | 20.9232i | 0.988358 | − | 0.718084i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5451 | − | 32.4544i | 0.361481 | − | 1.11252i | ||||
\(852\) | 12.8262 | + | 9.31881i | 0.439420 | + | 0.319257i | ||||
\(853\) | 2.70820 | + | 1.96763i | 0.0927271 | + | 0.0673702i | 0.633183 | − | 0.774002i | \(-0.281748\pi\) |
−0.540456 | + | 0.841372i | \(0.681748\pi\) | |||||||
\(854\) | −1.54508 | + | 4.75528i | −0.0528717 | + | 0.162722i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.61803 | + | 4.80828i | −0.226200 | + | 0.164344i | ||||
\(857\) | 25.2705 | 0.863224 | 0.431612 | − | 0.902059i | \(-0.357945\pi\) | ||||
0.431612 | + | 0.902059i | \(0.357945\pi\) | |||||||
\(858\) | −1.23607 | − | 0.277515i | −0.0421987 | − | 0.00947419i | ||||
\(859\) | −1.18034 | −0.0402727 | −0.0201363 | − | 0.999797i | \(-0.506410\pi\) | ||||
−0.0201363 | + | 0.999797i | \(0.506410\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.14590 | − | 12.7598i | −0.141292 | − | 0.434852i | ||||
\(862\) | 1.83688 | − | 5.65334i | 0.0625644 | − | 0.192553i | ||||
\(863\) | −0.899187 | − | 0.653298i | −0.0306087 | − | 0.0222385i | 0.572376 | − | 0.819991i | \(-0.306022\pi\) |
−0.602984 | + | 0.797753i | \(0.706022\pi\) | |||||||
\(864\) | −4.42705 | − | 3.21644i | −0.150611 | − | 0.109426i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.61803 | − | 8.05748i | −0.0889644 | − | 0.273804i | ||||
\(867\) | −22.0623 | + | 16.0292i | −0.749275 | + | 0.544380i | ||||
\(868\) | 22.8885 | 0.776888 | ||||||||
\(869\) | 36.3713 | − | 15.6987i | 1.23381 | − | 0.532542i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.78115 | + | 1.29408i | −0.0603521 | + | 0.0438483i | ||||
\(872\) | −3.59017 | − | 11.0494i | −0.121578 | − | 0.374180i | ||||
\(873\) | 1.41641 | − | 4.35926i | 0.0479381 | − | 0.147538i | ||||
\(874\) | −8.16312 | − | 5.93085i | −0.276122 | − | 0.200614i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.07295 | − | 12.5352i | 0.137612 | − | 0.423527i | ||||
\(877\) | 11.6738 | + | 35.9281i | 0.394195 | + | 1.21321i | 0.929587 | + | 0.368603i | \(0.120164\pi\) |
−0.535392 | + | 0.844604i | \(0.679836\pi\) | |||||||
\(878\) | −18.3713 | + | 13.3475i | −0.620002 | + | 0.450458i | ||||
\(879\) | −17.0000 | −0.573396 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.67376 | 0.258536 | 0.129268 | − | 0.991610i | \(-0.458737\pi\) | ||||
0.129268 | + | 0.991610i | \(0.458737\pi\) | |||||||
\(882\) | −0.618034 | + | 0.449028i | −0.0208103 | + | 0.0151196i | ||||
\(883\) | 12.0344 | + | 37.0382i | 0.404991 | + | 1.24643i | 0.920903 | + | 0.389793i | \(0.127453\pi\) |
−0.515911 | + | 0.856642i | \(0.672547\pi\) | |||||||
\(884\) | −0.0278640 | + | 0.0857567i | −0.000937169 | + | 0.00288431i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.6803 | + | 17.9313i | 0.829152 | + | 0.602414i | ||||
\(887\) | −12.4443 | + | 38.2995i | −0.417838 | + | 1.28597i | 0.491850 | + | 0.870680i | \(0.336321\pi\) |
−0.909688 | + | 0.415293i | \(0.863679\pi\) | |||||||
\(888\) | −4.42705 | − | 13.6251i | −0.148562 | − | 0.457227i | ||||
\(889\) | 5.26393 | − | 3.82447i | 0.176547 | − | 0.128269i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.0344 | + | 21.9928i | −0.436670 | + | 0.736787i | ||||
\(892\) | −2.05573 | −0.0688309 | ||||||||
\(893\) | 0.500000 | − | 0.363271i | 0.0167319 | − | 0.0121564i | ||||
\(894\) | 5.35410 | + | 16.4782i | 0.179068 | + | 0.551115i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.80902 | + | 1.31433i | 0.0604350 | + | 0.0439086i | ||||
\(897\) | 1.19098 | + | 0.865300i | 0.0397658 | + | 0.0288915i | ||||
\(898\) | 5.03444 | − | 15.4944i | 0.168002 | − | 0.517055i | ||||
\(899\) | 1.66970 | + | 5.13880i | 0.0556875 | + | 0.171389i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.527864 | 0.0175857 | ||||||||
\(902\) | 8.12461 | + | 9.23305i | 0.270520 | + | 0.307427i | ||||
\(903\) | 34.2705 | 1.14045 | ||||||||
\(904\) | 11.8992 | − | 8.64527i | 0.395761 | − | 0.287537i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.51722 | − | 29.2910i | 0.316188 | − | 0.973128i | ||||
\(907\) | −32.0344 | − | 23.2744i | −1.06369 | − | 0.772813i | −0.0889194 | − | 0.996039i | \(-0.528341\pi\) |
−0.974767 | + | 0.223226i | \(0.928341\pi\) | |||||||
\(908\) | 15.9721 | + | 11.6044i | 0.530054 | + | 0.385107i | ||||
\(909\) | −2.20820 | + | 6.79615i | −0.0732415 | + | 0.225414i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.2361 | − | 7.43694i | 0.339136 | − | 0.246397i | −0.405161 | − | 0.914245i | \(-0.632785\pi\) |
0.744297 | + | 0.667849i | \(0.232785\pi\) | |||||||
\(912\) | −4.23607 | −0.140270 | ||||||||
\(913\) | 19.7188 | + | 22.4091i | 0.652599 | + | 0.741632i | ||||
\(914\) | −12.1246 | −0.401047 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.78115 | − | 14.7149i | −0.157974 | − | 0.486193i | ||||
\(917\) | −7.70163 | + | 23.7032i | −0.254330 | + | 0.782748i | ||||
\(918\) | 1.69098 | + | 1.22857i | 0.0558108 | + | 0.0405489i | ||||
\(919\) | 17.2082 | + | 12.5025i | 0.567646 | + | 0.412419i | 0.834249 | − | 0.551387i | \(-0.185901\pi\) |
−0.266603 | + | 0.963806i | \(0.585901\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.3992 | + | 44.3161i | 0.474469 | + | 1.46027i | ||||
\(922\) | 29.4615 | − | 21.4050i | 0.970263 | − | 0.704937i | ||||
\(923\) | 2.31308 | 0.0761360 | ||||||||
\(924\) | 6.11803 | − | 10.3229i | 0.201269 | − | 0.339597i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.2254 | − | 22.6866i | 1.02613 | − | 0.745528i | ||||
\(927\) | 1.99342 | + | 6.13512i | 0.0654726 | + | 0.201504i | ||||
\(928\) | −0.163119 | + | 0.502029i | −0.00535464 | + | 0.0164799i | ||||
\(929\) | 18.9443 | + | 13.7638i | 0.621541 | + | 0.451576i | 0.853460 | − | 0.521159i | \(-0.174500\pi\) |
−0.231918 | + | 0.972735i | \(0.574500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.61803 | + | 4.97980i | −0.0530289 | + | 0.163206i | ||||
\(932\) | −6.28115 | − | 19.3314i | −0.205746 | − | 0.633221i | ||||
\(933\) | 5.54508 | − | 4.02874i | 0.181538 | − | 0.131895i | ||||
\(934\) | −32.1803 | −1.05297 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.0901699 | −0.00294730 | ||||||||
\(937\) | −19.1353 | + | 13.9026i | −0.625122 | + | 0.454177i | −0.854707 | − | 0.519111i | \(-0.826263\pi\) |
0.229585 | + | 0.973289i | \(0.426263\pi\) | |||||||
\(938\) | −6.44427 | − | 19.8334i | −0.210413 | − | 0.647584i | ||||
\(939\) | 0.500000 | − | 1.53884i | 0.0163169 | − | 0.0502182i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.5172 | − | 14.9066i | −0.668842 | − | 0.485942i | 0.200795 | − | 0.979633i | \(-0.435647\pi\) |
−0.869637 | + | 0.493691i | \(0.835647\pi\) | |||||||
\(942\) | −3.38197 | + | 10.4086i | −0.110190 | + | 0.339131i | ||||
\(943\) | −4.41641 | − | 13.5923i | −0.143818 | − | 0.442626i | ||||
\(944\) | 9.28115 | − | 6.74315i | 0.302076 | − | 0.219471i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.8435 | + | 12.4495i | −0.937782 | + | 0.404768i | ||||
\(947\) | 18.0000 | 0.584921 | 0.292461 | − | 0.956278i | \(-0.405526\pi\) | ||||
0.292461 | + | 0.956278i | \(0.405526\pi\) | |||||||
\(948\) | −15.6353 | + | 11.3597i | −0.507809 | + | 0.368945i | ||||
\(949\) | −0.594235 | − | 1.82887i | −0.0192897 | − | 0.0593676i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.66312 | − | 2.66141i | −0.118785 | − | 0.0863022i | ||||
\(952\) | −0.690983 | − | 0.502029i | −0.0223949 | − | 0.0162708i | ||||
\(953\) | −12.7082 | + | 39.1118i | −0.411659 | + | 1.26696i | 0.503546 | + | 0.863968i | \(0.332028\pi\) |
−0.915205 | + | 0.402988i | \(0.867972\pi\) | |||||||
\(954\) | 0.163119 | + | 0.502029i | 0.00528117 | + | 0.0162538i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17.4721 | −0.565089 | ||||||||
\(957\) | 2.76393 | + | 0.620541i | 0.0893452 | + | 0.0200593i | ||||
\(958\) | 9.94427 | 0.321285 | ||||||||
\(959\) | 28.5172 | − | 20.7190i | 0.920869 | − | 0.669051i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.7984 | − | 70.1662i | 0.735431 | − | 2.26343i | ||||
\(962\) | −1.69098 | − | 1.22857i | −0.0545195 | − | 0.0396107i | ||||
\(963\) | 2.52786 | + | 1.83660i | 0.0814593 | + | 0.0591836i | ||||
\(964\) | 5.56231 | − | 17.1190i | 0.179150 | − | 0.551366i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.2812 | + | 8.19624i | −0.362965 | + | 0.263710i | ||||
\(967\) | 20.0557 | 0.644949 | 0.322474 | − | 0.946578i | \(-0.395485\pi\) | ||||
0.322474 | + | 0.946578i | \(0.395485\pi\) | |||||||
\(968\) | −1.39919 | + | 10.9106i | −0.0449716 | + | 0.350682i | ||||
\(969\) | 1.61803 | 0.0519787 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.6140 | + | 48.0549i | 0.501076 | + | 1.54215i | 0.807269 | + | 0.590184i | \(0.200945\pi\) |
−0.306193 | + | 0.951970i | \(0.599055\pi\) | |||||||
\(972\) | −1.21885 | + | 3.75123i | −0.0390945 | + | 0.120321i | ||||
\(973\) | −5.16312 | − | 3.75123i | −0.165522 | − | 0.120259i | ||||
\(974\) | 8.80902 | + | 6.40013i | 0.282259 | + | 0.205073i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.690983 | + | 2.12663i | 0.0221178 | + | 0.0680717i | ||||
\(977\) | 6.87132 | − | 4.99231i | 0.219833 | − | 0.159718i | −0.472418 | − | 0.881374i | \(-0.656619\pi\) |
0.692252 | + | 0.721656i | \(0.256619\pi\) | |||||||
\(978\) | −0.291796 | −0.00933061 | ||||||||
\(979\) | −42.6525 | − | 9.57608i | −1.36318 | − | 0.306053i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.59017 | + | 2.60841i | −0.114625 | + | 0.0832802i | ||||
\(982\) | 3.76393 | + | 11.5842i | 0.120112 | + | 0.369666i | ||||
\(983\) | 8.52786 | − | 26.2461i | 0.271997 | − | 0.837120i | −0.718002 | − | 0.696041i | \(-0.754943\pi\) |
0.989998 | − | 0.141078i | \(-0.0450569\pi\) | |||||||
\(984\) | −4.85410 | − | 3.52671i | −0.154743 | − | 0.112427i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.0623059 | − | 0.191758i | 0.00198422 | − | 0.00610681i | ||||
\(987\) | −0.263932 | − | 0.812299i | −0.00840105 | − | 0.0258558i | ||||
\(988\) | −0.500000 | + | 0.363271i | −0.0159071 | + | 0.0115572i | ||||
\(989\) | 36.5066 | 1.16084 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.11146 | −0.0670726 | −0.0335363 | − | 0.999437i | \(-0.510677\pi\) | ||||
−0.0335363 | + | 0.999437i | \(0.510677\pi\) | |||||||
\(992\) | 8.28115 | − | 6.01661i | 0.262927 | − | 0.191028i | ||||
\(993\) | 8.47214 | + | 26.0746i | 0.268855 | + | 0.827451i | ||||
\(994\) | −6.77051 | + | 20.8375i | −0.214748 | + | 0.660925i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.7812 | − | 8.55951i | −0.373300 | − | 0.271218i | ||||
\(997\) | −8.93363 | + | 27.4949i | −0.282931 | + | 0.870772i | 0.704080 | + | 0.710120i | \(0.251359\pi\) |
−0.987011 | + | 0.160651i | \(0.948641\pi\) | |||||||
\(998\) | 4.77458 | + | 14.6946i | 0.151137 | + | 0.465150i | ||||
\(999\) | −39.1976 | + | 28.4787i | −1.24016 | + | 0.901026i |
(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 | 550.2.h.c.201.1 | ✓ | 4 | |
5.2 | odd | 4 | 550.2.ba.e.399.1 | 8 | |||
5.3 | odd | 4 | 550.2.ba.e.399.2 | 8 | |||
5.4 | even | 2 | 550.2.h.g.201.1 | yes | 4 | ||
11.2 | odd | 10 | 6050.2.a.bx.1.1 | 2 | |||
11.4 | even | 5 | inner | 550.2.h.c.301.1 | yes | 4 | |
11.9 | even | 5 | 6050.2.a.co.1.1 | 2 | |||
55.4 | even | 10 | 550.2.h.g.301.1 | yes | 4 | ||
55.9 | even | 10 | 6050.2.a.ca.1.2 | 2 | |||
55.24 | odd | 10 | 6050.2.a.cr.1.2 | 2 | |||
55.37 | odd | 20 | 550.2.ba.e.499.2 | 8 | |||
55.48 | odd | 20 | 550.2.ba.e.499.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
550.2.h.c.201.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
550.2.h.c.301.1 | yes | 4 | 11.4 | even | 5 | inner | |
550.2.h.g.201.1 | yes | 4 | 5.4 | even | 2 | ||
550.2.h.g.301.1 | yes | 4 | 55.4 | even | 10 | ||
550.2.ba.e.399.1 | 8 | 5.2 | odd | 4 | |||
550.2.ba.e.399.2 | 8 | 5.3 | odd | 4 | |||
550.2.ba.e.499.1 | 8 | 55.48 | odd | 20 | |||
550.2.ba.e.499.2 | 8 | 55.37 | odd | 20 | |||
6050.2.a.bx.1.1 | 2 | 11.2 | odd | 10 | |||
6050.2.a.ca.1.2 | 2 | 55.9 | even | 10 | |||
6050.2.a.co.1.1 | 2 | 11.9 | even | 5 | |||
6050.2.a.cr.1.2 | 2 | 55.24 | odd | 10 |