Properties

Label 1350.2.e.l.451.2
Level $1350$
Weight $2$
Character 1350.451
Analytic conductor $10.780$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1350,2,Mod(451,1350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1350.451");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.e (of order \(3\), degree \(2\), not 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: \(10.7798042729\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 1350.451
Dual form 1350.2.e.l.901.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.68614 - 2.92048i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.68614 - 2.92048i) q^{7} -1.00000 q^{8} +(-2.18614 + 3.78651i) q^{11} +(-3.37228 - 5.84096i) q^{13} +(-1.68614 - 2.92048i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.62772 q^{17} -2.37228 q^{19} +(2.18614 + 3.78651i) q^{22} +(-0.686141 - 1.18843i) q^{23} -6.74456 q^{26} -3.37228 q^{28} +(0.686141 - 1.18843i) q^{29} +(-2.37228 - 4.10891i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.813859 + 1.40965i) q^{34} +4.00000 q^{37} +(-1.18614 + 2.05446i) q^{38} +(-1.50000 - 2.59808i) q^{41} +(-2.81386 + 4.87375i) q^{43} +4.37228 q^{44} -1.37228 q^{46} +(3.68614 - 6.38458i) q^{47} +(-2.18614 - 3.78651i) q^{49} +(-3.37228 + 5.84096i) q^{52} -11.4891 q^{53} +(-1.68614 + 2.92048i) q^{56} +(-0.686141 - 1.18843i) q^{58} +(2.18614 + 3.78651i) q^{59} +(4.05842 - 7.02939i) q^{61} -4.74456 q^{62} +1.00000 q^{64} +(-3.50000 - 6.06218i) q^{67} +(0.813859 + 1.40965i) q^{68} +6.00000 q^{71} -3.11684 q^{73} +(2.00000 - 3.46410i) q^{74} +(1.18614 + 2.05446i) q^{76} +(7.37228 + 12.7692i) q^{77} +(-1.00000 + 1.73205i) q^{79} -3.00000 q^{82} +(-3.68614 + 6.38458i) q^{83} +(2.81386 + 4.87375i) q^{86} +(2.18614 - 3.78651i) q^{88} -16.1168 q^{89} -22.7446 q^{91} +(-0.686141 + 1.18843i) q^{92} +(-3.68614 - 6.38458i) q^{94} +(-4.18614 + 7.25061i) q^{97} -4.37228 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} + q^{7} - 4 q^{8} - 3 q^{11} - 2 q^{13} - q^{14} - 2 q^{16} - 18 q^{17} + 2 q^{19} + 3 q^{22} + 3 q^{23} - 4 q^{26} - 2 q^{28} - 3 q^{29} + 2 q^{31} + 2 q^{32} - 9 q^{34} + 16 q^{37} + q^{38} - 6 q^{41} - 17 q^{43} + 6 q^{44} + 6 q^{46} + 9 q^{47} - 3 q^{49} - 2 q^{52} - q^{56} + 3 q^{58} + 3 q^{59} - q^{61} + 4 q^{62} + 4 q^{64} - 14 q^{67} + 9 q^{68} + 24 q^{71} + 22 q^{73} + 8 q^{74} - q^{76} + 18 q^{77} - 4 q^{79} - 12 q^{82} - 9 q^{83} + 17 q^{86} + 3 q^{88} - 30 q^{89} - 68 q^{91} + 3 q^{92} - 9 q^{94} - 11 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1027\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 1.68614 2.92048i 0.637301 1.10384i −0.348721 0.937226i \(-0.613384\pi\)
0.986023 0.166612i \(-0.0532826\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −2.18614 + 3.78651i −0.659146 + 1.14167i 0.321691 + 0.946845i \(0.395749\pi\)
−0.980837 + 0.194830i \(0.937584\pi\)
\(12\) 0 0
\(13\) −3.37228 5.84096i −0.935303 1.61999i −0.774094 0.633071i \(-0.781794\pi\)
−0.161209 0.986920i \(-0.551539\pi\)
\(14\) −1.68614 2.92048i −0.450640 0.780531i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.62772 −0.394780 −0.197390 0.980325i \(-0.563246\pi\)
−0.197390 + 0.980325i \(0.563246\pi\)
\(18\) 0 0
\(19\) −2.37228 −0.544239 −0.272119 0.962264i \(-0.587725\pi\)
−0.272119 + 0.962264i \(0.587725\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.18614 + 3.78651i 0.466087 + 0.807286i
\(23\) −0.686141 1.18843i −0.143070 0.247805i 0.785581 0.618759i \(-0.212364\pi\)
−0.928651 + 0.370954i \(0.879031\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −6.74456 −1.32272
\(27\) 0 0
\(28\) −3.37228 −0.637301
\(29\) 0.686141 1.18843i 0.127413 0.220686i −0.795261 0.606268i \(-0.792666\pi\)
0.922674 + 0.385582i \(0.125999\pi\)
\(30\) 0 0
\(31\) −2.37228 4.10891i −0.426074 0.737982i 0.570446 0.821335i \(-0.306770\pi\)
−0.996520 + 0.0833529i \(0.973437\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −0.813859 + 1.40965i −0.139576 + 0.241752i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) −1.18614 + 2.05446i −0.192417 + 0.333277i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) −2.81386 + 4.87375i −0.429110 + 0.743240i −0.996794 0.0800065i \(-0.974506\pi\)
0.567685 + 0.823246i \(0.307839\pi\)
\(44\) 4.37228 0.659146
\(45\) 0 0
\(46\) −1.37228 −0.202332
\(47\) 3.68614 6.38458i 0.537679 0.931287i −0.461350 0.887218i \(-0.652635\pi\)
0.999029 0.0440687i \(-0.0140321\pi\)
\(48\) 0 0
\(49\) −2.18614 3.78651i −0.312306 0.540930i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.37228 + 5.84096i −0.467651 + 0.809996i
\(53\) −11.4891 −1.57815 −0.789076 0.614295i \(-0.789440\pi\)
−0.789076 + 0.614295i \(0.789440\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.68614 + 2.92048i −0.225320 + 0.390266i
\(57\) 0 0
\(58\) −0.686141 1.18843i −0.0900947 0.156049i
\(59\) 2.18614 + 3.78651i 0.284611 + 0.492961i 0.972515 0.232841i \(-0.0748021\pi\)
−0.687904 + 0.725802i \(0.741469\pi\)
\(60\) 0 0
\(61\) 4.05842 7.02939i 0.519628 0.900022i −0.480112 0.877207i \(-0.659404\pi\)
0.999740 0.0228144i \(-0.00726267\pi\)
\(62\) −4.74456 −0.602560
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −3.50000 6.06218i −0.427593 0.740613i 0.569066 0.822292i \(-0.307305\pi\)
−0.996659 + 0.0816792i \(0.973972\pi\)
\(68\) 0.813859 + 1.40965i 0.0986949 + 0.170945i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −3.11684 −0.364799 −0.182399 0.983225i \(-0.558386\pi\)
−0.182399 + 0.983225i \(0.558386\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) 0 0
\(76\) 1.18614 + 2.05446i 0.136060 + 0.235662i
\(77\) 7.37228 + 12.7692i 0.840149 + 1.45518i
\(78\) 0 0
\(79\) −1.00000 + 1.73205i −0.112509 + 0.194871i −0.916781 0.399390i \(-0.869222\pi\)
0.804272 + 0.594261i \(0.202555\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.00000 −0.331295
\(83\) −3.68614 + 6.38458i −0.404607 + 0.700799i −0.994276 0.106846i \(-0.965925\pi\)
0.589669 + 0.807645i \(0.299258\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.81386 + 4.87375i 0.303426 + 0.525550i
\(87\) 0 0
\(88\) 2.18614 3.78651i 0.233043 0.403643i
\(89\) −16.1168 −1.70838 −0.854191 0.519959i \(-0.825947\pi\)
−0.854191 + 0.519959i \(0.825947\pi\)
\(90\) 0 0
\(91\) −22.7446 −2.38428
\(92\) −0.686141 + 1.18843i −0.0715351 + 0.123902i
\(93\) 0 0
\(94\) −3.68614 6.38458i −0.380196 0.658519i
\(95\) 0 0
\(96\) 0 0
\(97\) −4.18614 + 7.25061i −0.425038 + 0.736188i −0.996424 0.0844938i \(-0.973073\pi\)
0.571386 + 0.820682i \(0.306406\pi\)
\(98\) −4.37228 −0.441667
\(99\) 0 0
\(100\) 0 0
\(101\) 1.37228 2.37686i 0.136547 0.236507i −0.789640 0.613570i \(-0.789733\pi\)
0.926187 + 0.377064i \(0.123066\pi\)
\(102\) 0 0
\(103\) −8.00000 13.8564i −0.788263 1.36531i −0.927030 0.374987i \(-0.877647\pi\)
0.138767 0.990325i \(-0.455686\pi\)
\(104\) 3.37228 + 5.84096i 0.330679 + 0.572754i
\(105\) 0 0
\(106\) −5.74456 + 9.94987i −0.557961 + 0.966417i
\(107\) 8.48913 0.820675 0.410337 0.911934i \(-0.365411\pi\)
0.410337 + 0.911934i \(0.365411\pi\)
\(108\) 0 0
\(109\) 15.3723 1.47240 0.736199 0.676765i \(-0.236619\pi\)
0.736199 + 0.676765i \(0.236619\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.68614 + 2.92048i 0.159325 + 0.275960i
\(113\) −1.62772 2.81929i −0.153123 0.265217i 0.779251 0.626712i \(-0.215600\pi\)
−0.932374 + 0.361495i \(0.882266\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.37228 −0.127413
\(117\) 0 0
\(118\) 4.37228 0.402501
\(119\) −2.74456 + 4.75372i −0.251594 + 0.435773i
\(120\) 0 0
\(121\) −4.05842 7.02939i −0.368947 0.639036i
\(122\) −4.05842 7.02939i −0.367432 0.636411i
\(123\) 0 0
\(124\) −2.37228 + 4.10891i −0.213037 + 0.368991i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.11684 0.720253 0.360127 0.932903i \(-0.382733\pi\)
0.360127 + 0.932903i \(0.382733\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.37228 2.37686i −0.119897 0.207667i 0.799830 0.600227i \(-0.204923\pi\)
−0.919727 + 0.392560i \(0.871590\pi\)
\(132\) 0 0
\(133\) −4.00000 + 6.92820i −0.346844 + 0.600751i
\(134\) −7.00000 −0.604708
\(135\) 0 0
\(136\) 1.62772 0.139576
\(137\) 9.55842 16.5557i 0.816631 1.41445i −0.0915197 0.995803i \(-0.529172\pi\)
0.908151 0.418643i \(-0.137494\pi\)
\(138\) 0 0
\(139\) −0.441578 0.764836i −0.0374542 0.0648725i 0.846691 0.532085i \(-0.178591\pi\)
−0.884145 + 0.467213i \(0.845258\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) 29.4891 2.46600
\(144\) 0 0
\(145\) 0 0
\(146\) −1.55842 + 2.69927i −0.128976 + 0.223393i
\(147\) 0 0
\(148\) −2.00000 3.46410i −0.164399 0.284747i
\(149\) 0.941578 + 1.63086i 0.0771371 + 0.133605i 0.902014 0.431708i \(-0.142089\pi\)
−0.824877 + 0.565313i \(0.808755\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 2.37228 0.192417
\(153\) 0 0
\(154\) 14.7446 1.18815
\(155\) 0 0
\(156\) 0 0
\(157\) −3.37228 5.84096i −0.269137 0.466160i 0.699502 0.714631i \(-0.253405\pi\)
−0.968639 + 0.248471i \(0.920072\pi\)
\(158\) 1.00000 + 1.73205i 0.0795557 + 0.137795i
\(159\) 0 0
\(160\) 0 0
\(161\) −4.62772 −0.364715
\(162\) 0 0
\(163\) 21.4891 1.68316 0.841579 0.540134i \(-0.181626\pi\)
0.841579 + 0.540134i \(0.181626\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 0 0
\(166\) 3.68614 + 6.38458i 0.286100 + 0.495540i
\(167\) −6.68614 11.5807i −0.517389 0.896144i −0.999796 0.0201970i \(-0.993571\pi\)
0.482407 0.875947i \(-0.339763\pi\)
\(168\) 0 0
\(169\) −16.2446 + 28.1364i −1.24958 + 2.16434i
\(170\) 0 0
\(171\) 0 0
\(172\) 5.62772 0.429110
\(173\) −10.3723 + 17.9653i −0.788590 + 1.36588i 0.138241 + 0.990399i \(0.455855\pi\)
−0.926831 + 0.375479i \(0.877478\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.18614 3.78651i −0.164787 0.285419i
\(177\) 0 0
\(178\) −8.05842 + 13.9576i −0.604004 + 1.04617i
\(179\) 14.7446 1.10206 0.551030 0.834485i \(-0.314235\pi\)
0.551030 + 0.834485i \(0.314235\pi\)
\(180\) 0 0
\(181\) 20.8614 1.55062 0.775308 0.631583i \(-0.217595\pi\)
0.775308 + 0.631583i \(0.217595\pi\)
\(182\) −11.3723 + 19.6974i −0.842970 + 1.46007i
\(183\) 0 0
\(184\) 0.686141 + 1.18843i 0.0505830 + 0.0876123i
\(185\) 0 0
\(186\) 0 0
\(187\) 3.55842 6.16337i 0.260218 0.450710i
\(188\) −7.37228 −0.537679
\(189\) 0 0
\(190\) 0 0
\(191\) 8.74456 15.1460i 0.632734 1.09593i −0.354256 0.935148i \(-0.615266\pi\)
0.986990 0.160780i \(-0.0514008\pi\)
\(192\) 0 0
\(193\) 10.5584 + 18.2877i 0.760012 + 1.31638i 0.942844 + 0.333235i \(0.108140\pi\)
−0.182832 + 0.983144i \(0.558526\pi\)
\(194\) 4.18614 + 7.25061i 0.300547 + 0.520563i
\(195\) 0 0
\(196\) −2.18614 + 3.78651i −0.156153 + 0.270465i
\(197\) −5.48913 −0.391084 −0.195542 0.980695i \(-0.562647\pi\)
−0.195542 + 0.980695i \(0.562647\pi\)
\(198\) 0 0
\(199\) 13.4891 0.956219 0.478109 0.878300i \(-0.341322\pi\)
0.478109 + 0.878300i \(0.341322\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −1.37228 2.37686i −0.0965534 0.167235i
\(203\) −2.31386 4.00772i −0.162401 0.281287i
\(204\) 0 0
\(205\) 0 0
\(206\) −16.0000 −1.11477
\(207\) 0 0
\(208\) 6.74456 0.467651
\(209\) 5.18614 8.98266i 0.358733 0.621344i
\(210\) 0 0
\(211\) 9.37228 + 16.2333i 0.645214 + 1.11754i 0.984252 + 0.176771i \(0.0565653\pi\)
−0.339037 + 0.940773i \(0.610101\pi\)
\(212\) 5.74456 + 9.94987i 0.394538 + 0.683360i
\(213\) 0 0
\(214\) 4.24456 7.35180i 0.290152 0.502559i
\(215\) 0 0
\(216\) 0 0
\(217\) −16.0000 −1.08615
\(218\) 7.68614 13.3128i 0.520571 0.901656i
\(219\) 0 0
\(220\) 0 0
\(221\) 5.48913 + 9.50744i 0.369239 + 0.639540i
\(222\) 0 0
\(223\) 3.31386 5.73977i 0.221912 0.384364i −0.733476 0.679715i \(-0.762103\pi\)
0.955389 + 0.295351i \(0.0954368\pi\)
\(224\) 3.37228 0.225320
\(225\) 0 0
\(226\) −3.25544 −0.216548
\(227\) −9.55842 + 16.5557i −0.634415 + 1.09884i 0.352224 + 0.935916i \(0.385426\pi\)
−0.986639 + 0.162923i \(0.947908\pi\)
\(228\) 0 0
\(229\) −6.31386 10.9359i −0.417232 0.722666i 0.578428 0.815733i \(-0.303666\pi\)
−0.995660 + 0.0930670i \(0.970333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.686141 + 1.18843i −0.0450473 + 0.0780243i
\(233\) 7.11684 0.466240 0.233120 0.972448i \(-0.425107\pi\)
0.233120 + 0.972448i \(0.425107\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.18614 3.78651i 0.142306 0.246481i
\(237\) 0 0
\(238\) 2.74456 + 4.75372i 0.177904 + 0.308138i
\(239\) −1.62772 2.81929i −0.105288 0.182365i 0.808568 0.588403i \(-0.200243\pi\)
−0.913856 + 0.406038i \(0.866910\pi\)
\(240\) 0 0
\(241\) 6.24456 10.8159i 0.402248 0.696713i −0.591749 0.806122i \(-0.701562\pi\)
0.993997 + 0.109409i \(0.0348958\pi\)
\(242\) −8.11684 −0.521770
\(243\) 0 0
\(244\) −8.11684 −0.519628
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000 + 13.8564i 0.509028 + 0.881662i
\(248\) 2.37228 + 4.10891i 0.150640 + 0.260916i
\(249\) 0 0
\(250\) 0 0
\(251\) 24.6060 1.55312 0.776558 0.630046i \(-0.216964\pi\)
0.776558 + 0.630046i \(0.216964\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 4.05842 7.02939i 0.254648 0.441063i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.18614 3.78651i −0.136368 0.236196i 0.789751 0.613427i \(-0.210210\pi\)
−0.926119 + 0.377231i \(0.876876\pi\)
\(258\) 0 0
\(259\) 6.74456 11.6819i 0.419087 0.725880i
\(260\) 0 0
\(261\) 0 0
\(262\) −2.74456 −0.169560
\(263\) 8.74456 15.1460i 0.539213 0.933944i −0.459734 0.888057i \(-0.652055\pi\)
0.998947 0.0458872i \(-0.0146115\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 + 6.92820i 0.245256 + 0.424795i
\(267\) 0 0
\(268\) −3.50000 + 6.06218i −0.213797 + 0.370306i
\(269\) 1.37228 0.0836695 0.0418347 0.999125i \(-0.486680\pi\)
0.0418347 + 0.999125i \(0.486680\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0.813859 1.40965i 0.0493475 0.0854723i
\(273\) 0 0
\(274\) −9.55842 16.5557i −0.577445 1.00016i
\(275\) 0 0
\(276\) 0 0
\(277\) 8.37228 14.5012i 0.503042 0.871294i −0.496952 0.867778i \(-0.665548\pi\)
0.999994 0.00351574i \(-0.00111910\pi\)
\(278\) −0.883156 −0.0529682
\(279\) 0 0
\(280\) 0 0
\(281\) −0.686141 + 1.18843i −0.0409317 + 0.0708958i −0.885765 0.464133i \(-0.846366\pi\)
0.844834 + 0.535029i \(0.179699\pi\)
\(282\) 0 0
\(283\) −1.56930 2.71810i −0.0932850 0.161574i 0.815607 0.578607i \(-0.196403\pi\)
−0.908892 + 0.417033i \(0.863070\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0 0
\(286\) 14.7446 25.5383i 0.871864 1.51011i
\(287\) −10.1168 −0.597178
\(288\) 0 0
\(289\) −14.3505 −0.844149
\(290\) 0 0
\(291\) 0 0
\(292\) 1.55842 + 2.69927i 0.0911997 + 0.157963i
\(293\) −13.1168 22.7190i −0.766294 1.32726i −0.939560 0.342385i \(-0.888765\pi\)
0.173265 0.984875i \(-0.444568\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 1.88316 0.109088
\(299\) −4.62772 + 8.01544i −0.267628 + 0.463545i
\(300\) 0 0
\(301\) 9.48913 + 16.4356i 0.546944 + 0.947335i
\(302\) −5.00000 8.66025i −0.287718 0.498342i
\(303\) 0 0
\(304\) 1.18614 2.05446i 0.0680298 0.117831i
\(305\) 0 0
\(306\) 0 0
\(307\) −1.23369 −0.0704103 −0.0352051 0.999380i \(-0.511208\pi\)
−0.0352051 + 0.999380i \(0.511208\pi\)
\(308\) 7.37228 12.7692i 0.420075 0.727591i
\(309\) 0 0
\(310\) 0 0
\(311\) −10.3723 17.9653i −0.588158 1.01872i −0.994474 0.104987i \(-0.966520\pi\)
0.406315 0.913733i \(-0.366813\pi\)
\(312\) 0 0
\(313\) 1.81386 3.14170i 0.102525 0.177579i −0.810199 0.586155i \(-0.800641\pi\)
0.912724 + 0.408576i \(0.133974\pi\)
\(314\) −6.74456 −0.380618
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) −1.37228 + 2.37686i −0.0770750 + 0.133498i −0.901987 0.431764i \(-0.857891\pi\)
0.824912 + 0.565262i \(0.191225\pi\)
\(318\) 0 0
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) 0 0
\(321\) 0 0
\(322\) −2.31386 + 4.00772i −0.128946 + 0.223342i
\(323\) 3.86141 0.214854
\(324\) 0 0
\(325\) 0 0
\(326\) 10.7446 18.6101i 0.595086 1.03072i
\(327\) 0 0
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) −12.4307 21.5306i −0.685327 1.18702i
\(330\) 0 0
\(331\) −8.11684 + 14.0588i −0.446142 + 0.772741i −0.998131 0.0611107i \(-0.980536\pi\)
0.551989 + 0.833851i \(0.313869\pi\)
\(332\) 7.37228 0.404607
\(333\) 0 0
\(334\) −13.3723 −0.731699
\(335\) 0 0
\(336\) 0 0
\(337\) −1.18614 2.05446i −0.0646132 0.111913i 0.831909 0.554912i \(-0.187248\pi\)
−0.896522 + 0.442999i \(0.853915\pi\)
\(338\) 16.2446 + 28.1364i 0.883588 + 1.53042i
\(339\) 0 0
\(340\) 0 0
\(341\) 20.7446 1.12338
\(342\) 0 0
\(343\) 8.86141 0.478471
\(344\) 2.81386 4.87375i 0.151713 0.262775i
\(345\) 0 0
\(346\) 10.3723 + 17.9653i 0.557617 + 0.965821i
\(347\) 2.44158 + 4.22894i 0.131071 + 0.227021i 0.924090 0.382176i \(-0.124825\pi\)
−0.793019 + 0.609197i \(0.791492\pi\)
\(348\) 0 0
\(349\) −9.05842 + 15.6896i −0.484886 + 0.839848i −0.999849 0.0173648i \(-0.994472\pi\)
0.514963 + 0.857212i \(0.327806\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.37228 −0.233043
\(353\) 10.6753 18.4901i 0.568187 0.984129i −0.428558 0.903514i \(-0.640978\pi\)
0.996745 0.0806147i \(-0.0256883\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 8.05842 + 13.9576i 0.427096 + 0.739751i
\(357\) 0 0
\(358\) 7.37228 12.7692i 0.389637 0.674871i
\(359\) 17.4891 0.923041 0.461520 0.887130i \(-0.347304\pi\)
0.461520 + 0.887130i \(0.347304\pi\)
\(360\) 0 0
\(361\) −13.3723 −0.703804
\(362\) 10.4307 18.0665i 0.548226 0.949555i
\(363\) 0 0
\(364\) 11.3723 + 19.6974i 0.596070 + 1.03242i
\(365\) 0 0
\(366\) 0 0
\(367\) −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i \(-0.970461\pi\)
0.578101 + 0.815966i \(0.303794\pi\)
\(368\) 1.37228 0.0715351
\(369\) 0 0
\(370\) 0 0
\(371\) −19.3723 + 33.5538i −1.00576 + 1.74203i
\(372\) 0 0
\(373\) −7.74456 13.4140i −0.400998 0.694549i 0.592848 0.805314i \(-0.298003\pi\)
−0.993847 + 0.110765i \(0.964670\pi\)
\(374\) −3.55842 6.16337i −0.184002 0.318700i
\(375\) 0 0
\(376\) −3.68614 + 6.38458i −0.190098 + 0.329260i
\(377\) −9.25544 −0.476679
\(378\) 0 0
\(379\) 17.8614 0.917479 0.458739 0.888571i \(-0.348301\pi\)
0.458739 + 0.888571i \(0.348301\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −8.74456 15.1460i −0.447411 0.774938i
\(383\) 11.4891 + 19.8997i 0.587067 + 1.01683i 0.994614 + 0.103646i \(0.0330508\pi\)
−0.407547 + 0.913184i \(0.633616\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21.1168 1.07482
\(387\) 0 0
\(388\) 8.37228 0.425038
\(389\) −2.31386 + 4.00772i −0.117317 + 0.203200i −0.918704 0.394947i \(-0.870763\pi\)
0.801386 + 0.598147i \(0.204096\pi\)
\(390\) 0 0
\(391\) 1.11684 + 1.93443i 0.0564812 + 0.0978284i
\(392\) 2.18614 + 3.78651i 0.110417 + 0.191247i
\(393\) 0 0
\(394\) −2.74456 + 4.75372i −0.138269 + 0.239489i
\(395\) 0 0
\(396\) 0 0
\(397\) −22.7446 −1.14152 −0.570758 0.821118i \(-0.693351\pi\)
−0.570758 + 0.821118i \(0.693351\pi\)
\(398\) 6.74456 11.6819i 0.338074 0.585562i
\(399\) 0 0
\(400\) 0 0
\(401\) −0.558422 0.967215i −0.0278863 0.0483004i 0.851745 0.523956i \(-0.175544\pi\)
−0.879632 + 0.475655i \(0.842211\pi\)
\(402\) 0 0
\(403\) −16.0000 + 27.7128i −0.797017 + 1.38047i
\(404\) −2.74456 −0.136547
\(405\) 0 0
\(406\) −4.62772 −0.229670
\(407\) −8.74456 + 15.1460i −0.433452 + 0.750761i
\(408\) 0 0
\(409\) −8.93070 15.4684i −0.441595 0.764865i 0.556213 0.831040i \(-0.312254\pi\)
−0.997808 + 0.0661749i \(0.978920\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −8.00000 + 13.8564i −0.394132 + 0.682656i
\(413\) 14.7446 0.725532
\(414\) 0 0
\(415\) 0 0
\(416\) 3.37228 5.84096i 0.165340 0.286377i
\(417\) 0 0
\(418\) −5.18614 8.98266i −0.253662 0.439356i
\(419\) 12.8614 + 22.2766i 0.628321 + 1.08828i 0.987889 + 0.155165i \(0.0495908\pi\)
−0.359568 + 0.933119i \(0.617076\pi\)
\(420\) 0 0
\(421\) −15.2337 + 26.3855i −0.742445 + 1.28595i 0.208935 + 0.977930i \(0.433000\pi\)
−0.951379 + 0.308022i \(0.900333\pi\)
\(422\) 18.7446 0.912471
\(423\) 0 0
\(424\) 11.4891 0.557961
\(425\) 0 0
\(426\) 0 0
\(427\) −13.6861 23.7051i −0.662319 1.14717i
\(428\) −4.24456 7.35180i −0.205169 0.355363i
\(429\) 0 0
\(430\) 0 0
\(431\) −8.23369 −0.396603 −0.198301 0.980141i \(-0.563542\pi\)
−0.198301 + 0.980141i \(0.563542\pi\)
\(432\) 0 0
\(433\) −6.37228 −0.306232 −0.153116 0.988208i \(-0.548931\pi\)
−0.153116 + 0.988208i \(0.548931\pi\)
\(434\) −8.00000 + 13.8564i −0.384012 + 0.665129i
\(435\) 0 0
\(436\) −7.68614 13.3128i −0.368099 0.637567i
\(437\) 1.62772 + 2.81929i 0.0778643 + 0.134865i
\(438\) 0 0
\(439\) 9.11684 15.7908i 0.435123 0.753656i −0.562182 0.827013i \(-0.690038\pi\)
0.997306 + 0.0733577i \(0.0233715\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 10.9783 0.522182
\(443\) 1.75544 3.04051i 0.0834033 0.144459i −0.821306 0.570487i \(-0.806754\pi\)
0.904710 + 0.426029i \(0.140088\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −3.31386 5.73977i −0.156916 0.271786i
\(447\) 0 0
\(448\) 1.68614 2.92048i 0.0796627 0.137980i
\(449\) −9.86141 −0.465389 −0.232694 0.972550i \(-0.574754\pi\)
−0.232694 + 0.972550i \(0.574754\pi\)
\(450\) 0 0
\(451\) 13.1168 0.617648
\(452\) −1.62772 + 2.81929i −0.0765614 + 0.132608i
\(453\) 0 0
\(454\) 9.55842 + 16.5557i 0.448599 + 0.776996i
\(455\) 0 0
\(456\) 0 0
\(457\) 6.44158 11.1571i 0.301324 0.521909i −0.675112 0.737715i \(-0.735905\pi\)
0.976436 + 0.215806i \(0.0692380\pi\)
\(458\) −12.6277 −0.590055
\(459\) 0 0
\(460\) 0 0
\(461\) 0.941578 1.63086i 0.0438537 0.0759568i −0.843265 0.537497i \(-0.819370\pi\)
0.887119 + 0.461541i \(0.152703\pi\)
\(462\) 0 0
\(463\) 10.0000 + 17.3205i 0.464739 + 0.804952i 0.999190 0.0402476i \(-0.0128147\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) 0.686141 + 1.18843i 0.0318533 + 0.0551715i
\(465\) 0 0
\(466\) 3.55842 6.16337i 0.164841 0.285512i
\(467\) 43.1168 1.99521 0.997605 0.0691713i \(-0.0220355\pi\)
0.997605 + 0.0691713i \(0.0220355\pi\)
\(468\) 0 0
\(469\) −23.6060 −1.09002
\(470\) 0 0
\(471\) 0 0
\(472\) −2.18614 3.78651i −0.100625 0.174288i
\(473\) −12.3030 21.3094i −0.565692 0.979807i
\(474\) 0 0
\(475\) 0 0
\(476\) 5.48913 0.251594
\(477\) 0 0
\(478\) −3.25544 −0.148900
\(479\) −0.255437 + 0.442430i −0.0116712 + 0.0202152i −0.871802 0.489858i \(-0.837048\pi\)
0.860131 + 0.510074i \(0.170382\pi\)
\(480\) 0 0
\(481\) −13.4891 23.3639i −0.615051 1.06530i
\(482\) −6.24456 10.8159i −0.284432 0.492651i
\(483\) 0 0
\(484\) −4.05842 + 7.02939i −0.184474 + 0.319518i
\(485\) 0 0
\(486\) 0 0
\(487\) 12.7446 0.577511 0.288756 0.957403i \(-0.406758\pi\)
0.288756 + 0.957403i \(0.406758\pi\)
\(488\) −4.05842 + 7.02939i −0.183716 + 0.318206i
\(489\) 0 0
\(490\) 0 0
\(491\) −18.3030 31.7017i −0.826002 1.43068i −0.901151 0.433505i \(-0.857277\pi\)
0.0751489 0.997172i \(-0.476057\pi\)
\(492\) 0 0
\(493\) −1.11684 + 1.93443i −0.0503001 + 0.0871224i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) 4.74456 0.213037
\(497\) 10.1168 17.5229i 0.453802 0.786009i
\(498\) 0 0
\(499\) −7.55842 13.0916i −0.338361 0.586059i 0.645763 0.763538i \(-0.276539\pi\)
−0.984125 + 0.177479i \(0.943206\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 12.3030 21.3094i 0.549109 0.951085i
\(503\) −6.86141 −0.305935 −0.152967 0.988231i \(-0.548883\pi\)
−0.152967 + 0.988231i \(0.548883\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) 0 0
\(508\) −4.05842 7.02939i −0.180063 0.311879i
\(509\) −21.1753 36.6766i −0.938577 1.62566i −0.768127 0.640297i \(-0.778811\pi\)
−0.170450 0.985366i \(-0.554522\pi\)
\(510\) 0 0
\(511\) −5.25544 + 9.10268i −0.232487 + 0.402679i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −4.37228 −0.192853
\(515\) 0 0
\(516\) 0 0
\(517\) 16.1168 + 27.9152i 0.708818 + 1.22771i
\(518\) −6.74456 11.6819i −0.296339 0.513274i
\(519\) 0 0
\(520\) 0 0
\(521\) 6.76631 0.296438 0.148219 0.988955i \(-0.452646\pi\)
0.148219 + 0.988955i \(0.452646\pi\)
\(522\) 0 0
\(523\) −6.11684 −0.267471 −0.133735 0.991017i \(-0.542697\pi\)
−0.133735 + 0.991017i \(0.542697\pi\)
\(524\) −1.37228 + 2.37686i −0.0599484 + 0.103834i
\(525\) 0 0
\(526\) −8.74456 15.1460i −0.381281 0.660398i
\(527\) 3.86141 + 6.68815i 0.168206 + 0.291340i
\(528\) 0 0
\(529\) 10.5584 18.2877i 0.459062 0.795118i
\(530\) 0 0
\(531\) 0 0
\(532\) 8.00000 0.346844
\(533\) −10.1168 + 17.5229i −0.438209 + 0.759001i
\(534\) 0 0
\(535\) 0 0
\(536\) 3.50000 + 6.06218i 0.151177 + 0.261846i
\(537\) 0 0
\(538\) 0.686141 1.18843i 0.0295816 0.0512369i
\(539\) 19.1168 0.823421
\(540\) 0 0
\(541\) 27.3723 1.17683 0.588413 0.808560i \(-0.299753\pi\)
0.588413 + 0.808560i \(0.299753\pi\)
\(542\) 4.00000 6.92820i 0.171815 0.297592i
\(543\) 0 0
\(544\) −0.813859 1.40965i −0.0348939 0.0604381i
\(545\) 0 0
\(546\) 0 0
\(547\) −14.7337 + 25.5195i −0.629967 + 1.09113i 0.357591 + 0.933878i \(0.383598\pi\)
−0.987558 + 0.157256i \(0.949735\pi\)
\(548\) −19.1168 −0.816631
\(549\) 0 0
\(550\) 0 0
\(551\) −1.62772 + 2.81929i −0.0693431 + 0.120106i
\(552\) 0 0
\(553\) 3.37228 + 5.84096i 0.143404 + 0.248383i
\(554\) −8.37228 14.5012i −0.355704 0.616098i
\(555\) 0 0
\(556\) −0.441578 + 0.764836i −0.0187271 + 0.0324363i
\(557\) −44.2337 −1.87424 −0.937121 0.349005i \(-0.886520\pi\)
−0.937121 + 0.349005i \(0.886520\pi\)
\(558\) 0 0
\(559\) 37.9565 1.60539
\(560\) 0 0
\(561\) 0 0
\(562\) 0.686141 + 1.18843i 0.0289431 + 0.0501309i
\(563\) 20.3614 + 35.2670i 0.858131 + 1.48633i 0.873710 + 0.486448i \(0.161708\pi\)
−0.0155787 + 0.999879i \(0.504959\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −3.13859 −0.131925
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) −15.3030 + 26.5055i −0.641534 + 1.11117i 0.343556 + 0.939132i \(0.388369\pi\)
−0.985090 + 0.172038i \(0.944965\pi\)
\(570\) 0 0
\(571\) −4.30298 7.45299i −0.180074 0.311898i 0.761831 0.647775i \(-0.224300\pi\)
−0.941906 + 0.335878i \(0.890967\pi\)
\(572\) −14.7446 25.5383i −0.616501 1.06781i
\(573\) 0 0
\(574\) −5.05842 + 8.76144i −0.211134 + 0.365696i
\(575\) 0 0
\(576\) 0 0
\(577\) 41.1168 1.71172 0.855858 0.517210i \(-0.173030\pi\)
0.855858 + 0.517210i \(0.173030\pi\)
\(578\) −7.17527 + 12.4279i −0.298452 + 0.516934i
\(579\) 0 0
\(580\) 0 0
\(581\) 12.4307 + 21.5306i 0.515712 + 0.893240i
\(582\) 0 0
\(583\) 25.1168 43.5036i 1.04023 1.80174i
\(584\) 3.11684 0.128976
\(585\) 0 0
\(586\) −26.2337 −1.08370
\(587\) −13.5000 + 23.3827i −0.557205 + 0.965107i 0.440524 + 0.897741i \(0.354793\pi\)
−0.997728 + 0.0673658i \(0.978541\pi\)
\(588\) 0 0
\(589\) 5.62772 + 9.74749i 0.231886 + 0.401639i
\(590\) 0 0
\(591\) 0 0
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) −19.7228 −0.809919 −0.404959 0.914335i \(-0.632714\pi\)
−0.404959 + 0.914335i \(0.632714\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.941578 1.63086i 0.0385685 0.0668027i
\(597\) 0 0
\(598\) 4.62772 + 8.01544i 0.189241 + 0.327776i
\(599\) −1.88316 3.26172i −0.0769437 0.133270i 0.824986 0.565153i \(-0.191183\pi\)
−0.901930 + 0.431883i \(0.857849\pi\)
\(600\) 0 0
\(601\) 0.930703 1.61203i 0.0379642 0.0657559i −0.846419 0.532517i \(-0.821246\pi\)
0.884383 + 0.466762i \(0.154579\pi\)
\(602\) 18.9783 0.773496
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) 9.05842 + 15.6896i 0.367670 + 0.636823i 0.989201 0.146567i \(-0.0468223\pi\)
−0.621531 + 0.783390i \(0.713489\pi\)
\(608\) −1.18614 2.05446i −0.0481044 0.0833192i
\(609\) 0 0
\(610\) 0 0
\(611\) −49.7228 −2.01157
\(612\) 0 0
\(613\) −34.2337 −1.38269 −0.691343 0.722527i \(-0.742981\pi\)
−0.691343 + 0.722527i \(0.742981\pi\)
\(614\) −0.616844 + 1.06841i −0.0248938 + 0.0431173i
\(615\) 0 0
\(616\) −7.37228 12.7692i −0.297038 0.514484i
\(617\) 2.44158 + 4.22894i 0.0982942 + 0.170251i 0.910979 0.412453i \(-0.135328\pi\)
−0.812684 + 0.582704i \(0.801995\pi\)
\(618\) 0 0
\(619\) 10.4416 18.0853i 0.419682 0.726911i −0.576225 0.817291i \(-0.695475\pi\)
0.995907 + 0.0903798i \(0.0288081\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −20.7446 −0.831781
\(623\) −27.1753 + 47.0689i −1.08875 + 1.88578i
\(624\) 0 0
\(625\) 0 0
\(626\) −1.81386 3.14170i −0.0724964 0.125567i
\(627\) 0 0
\(628\) −3.37228 + 5.84096i −0.134569 + 0.233080i
\(629\) −6.51087 −0.259606
\(630\) 0 0
\(631\) −23.7228 −0.944390 −0.472195 0.881494i \(-0.656538\pi\)
−0.472195 + 0.881494i \(0.656538\pi\)
\(632\) 1.00000 1.73205i 0.0397779 0.0688973i
\(633\) 0 0
\(634\) 1.37228 + 2.37686i 0.0545003 + 0.0943972i
\(635\) 0 0
\(636\) 0 0
\(637\) −14.7446 + 25.5383i −0.584201 + 1.01187i
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) 0 0
\(641\) −19.5000 + 33.7750i −0.770204 + 1.33403i 0.167247 + 0.985915i \(0.446512\pi\)
−0.937451 + 0.348117i \(0.886821\pi\)
\(642\) 0 0
\(643\) 5.50000 + 9.52628i 0.216899 + 0.375680i 0.953858 0.300257i \(-0.0970725\pi\)
−0.736959 + 0.675937i \(0.763739\pi\)
\(644\) 2.31386 + 4.00772i 0.0911788 + 0.157926i
\(645\) 0 0
\(646\) 1.93070 3.34408i 0.0759625 0.131571i
\(647\) −39.0951 −1.53699 −0.768493 0.639858i \(-0.778993\pi\)
−0.768493 + 0.639858i \(0.778993\pi\)
\(648\) 0 0
\(649\) −19.1168 −0.750402
\(650\) 0 0
\(651\) 0 0
\(652\) −10.7446 18.6101i −0.420790 0.728829i
\(653\) −9.86141 17.0805i −0.385907 0.668410i 0.605988 0.795474i \(-0.292778\pi\)
−0.991895 + 0.127064i \(0.959445\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.00000 0.117130
\(657\) 0 0
\(658\) −24.8614 −0.969199
\(659\) 8.74456 15.1460i 0.340640 0.590005i −0.643912 0.765100i \(-0.722690\pi\)
0.984552 + 0.175094i \(0.0560230\pi\)
\(660\) 0 0
\(661\) 6.11684 + 10.5947i 0.237918 + 0.412085i 0.960117 0.279600i \(-0.0902018\pi\)
−0.722199 + 0.691685i \(0.756868\pi\)
\(662\) 8.11684 + 14.0588i 0.315470 + 0.546410i
\(663\) 0 0
\(664\) 3.68614 6.38458i 0.143050 0.247770i
\(665\) 0 0
\(666\) 0 0
\(667\) −1.88316 −0.0729161
\(668\) −6.68614 + 11.5807i −0.258695 + 0.448072i
\(669\) 0 0
\(670\) 0 0
\(671\) 17.7446 + 30.7345i 0.685021 + 1.18649i
\(672\) 0 0
\(673\) −5.00000 + 8.66025i −0.192736 + 0.333828i −0.946156 0.323711i \(-0.895069\pi\)
0.753420 + 0.657539i \(0.228403\pi\)
\(674\) −2.37228 −0.0913769
\(675\) 0 0
\(676\) 32.4891 1.24958
\(677\) −6.86141 + 11.8843i −0.263705 + 0.456751i −0.967224 0.253926i \(-0.918278\pi\)
0.703518 + 0.710677i \(0.251611\pi\)
\(678\) 0 0
\(679\) 14.1168 + 24.4511i 0.541755 + 0.938347i
\(680\) 0 0
\(681\) 0 0
\(682\) 10.3723 17.9653i 0.397175 0.687928i
\(683\) −30.0951 −1.15156 −0.575778 0.817606i \(-0.695301\pi\)
−0.575778 + 0.817606i \(0.695301\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 4.43070 7.67420i 0.169165 0.293002i
\(687\) 0 0
\(688\) −2.81386 4.87375i −0.107277 0.185810i
\(689\) 38.7446 + 67.1076i 1.47605 + 2.55659i
\(690\) 0 0
\(691\) 18.1168 31.3793i 0.689197 1.19372i −0.282901 0.959149i \(-0.591297\pi\)
0.972098 0.234575i \(-0.0753700\pi\)
\(692\) 20.7446 0.788590
\(693\) 0 0
\(694\) 4.88316 0.185362
\(695\) 0 0
\(696\) 0 0
\(697\) 2.44158 + 4.22894i 0.0924814 + 0.160182i
\(698\) 9.05842 + 15.6896i 0.342866 + 0.593862i
\(699\) 0 0
\(700\) 0 0
\(701\) −42.8614 −1.61885 −0.809426 0.587221i \(-0.800222\pi\)
−0.809426 + 0.587221i \(0.800222\pi\)
\(702\) 0 0
\(703\) −9.48913 −0.357889
\(704\) −2.18614 + 3.78651i −0.0823933 + 0.142709i
\(705\) 0 0
\(706\) −10.6753 18.4901i −0.401769 0.695884i
\(707\) −4.62772 8.01544i −0.174043 0.301452i
\(708\) 0 0
\(709\) −1.43070 + 2.47805i −0.0537312 + 0.0930652i −0.891640 0.452745i \(-0.850445\pi\)
0.837909 + 0.545810i \(0.183778\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 16.1168 0.604004
\(713\) −3.25544 + 5.63858i −0.121917 + 0.211167i
\(714\) 0 0
\(715\) 0 0
\(716\) −7.37228 12.7692i −0.275515 0.477206i
\(717\) 0 0
\(718\) 8.74456 15.1460i 0.326344 0.565245i
\(719\) 3.76631 0.140460 0.0702299 0.997531i \(-0.477627\pi\)
0.0702299 + 0.997531i \(0.477627\pi\)
\(720\) 0 0
\(721\) −53.9565 −2.00945
\(722\) −6.68614 + 11.5807i −0.248832 + 0.430990i
\(723\) 0 0
\(724\) −10.4307 18.0665i −0.387654 0.671436i
\(725\) 0 0
\(726\) 0 0
\(727\) 9.05842 15.6896i 0.335958 0.581897i −0.647710 0.761887i \(-0.724273\pi\)
0.983668 + 0.179990i \(0.0576066\pi\)
\(728\) 22.7446 0.842970
\(729\) 0 0
\(730\) 0 0
\(731\) 4.58017 7.93309i 0.169404 0.293416i
\(732\) 0 0
\(733\) −0.116844 0.202380i −0.00431573 0.00747506i 0.863859 0.503733i \(-0.168040\pi\)
−0.868175 + 0.496258i \(0.834707\pi\)
\(734\) 8.00000 + 13.8564i 0.295285 + 0.511449i
\(735\) 0 0
\(736\) 0.686141 1.18843i 0.0252915 0.0438061i
\(737\) 30.6060 1.12739
\(738\) 0 0
\(739\) −41.1168 −1.51251 −0.756254 0.654278i \(-0.772972\pi\)
−0.756254 + 0.654278i \(0.772972\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 19.3723 + 33.5538i 0.711179 + 1.23180i
\(743\) −3.94158 6.82701i −0.144602 0.250459i 0.784622 0.619974i \(-0.212857\pi\)
−0.929225 + 0.369516i \(0.879524\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −15.4891 −0.567097
\(747\) 0 0
\(748\) −7.11684 −0.260218
\(749\) 14.3139 24.7923i 0.523017 0.905892i
\(750\) 0 0
\(751\) −8.11684 14.0588i −0.296188 0.513012i 0.679073 0.734071i \(-0.262382\pi\)
−0.975261 + 0.221059i \(0.929049\pi\)
\(752\) 3.68614 + 6.38458i 0.134420 + 0.232822i
\(753\) 0 0
\(754\) −4.62772 + 8.01544i −0.168532 + 0.291905i
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 8.93070 15.4684i 0.324378 0.561839i
\(759\) 0 0
\(760\) 0 0
\(761\) −25.5475 44.2496i −0.926098 1.60405i −0.789786 0.613383i \(-0.789808\pi\)
−0.136312 0.990666i \(-0.543525\pi\)
\(762\) 0 0
\(763\) 25.9198 44.8945i 0.938361 1.62529i
\(764\) −17.4891 −0.632734
\(765\) 0 0
\(766\) 22.9783 0.830238
\(767\) 14.7446 25.5383i 0.532395 0.922136i
\(768\) 0 0
\(769\) 23.4307 + 40.5832i 0.844933 + 1.46347i 0.885680 + 0.464297i \(0.153693\pi\)
−0.0407468 + 0.999170i \(0.512974\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.5584 18.2877i 0.380006 0.658190i
\(773\) 3.25544 0.117090 0.0585450 0.998285i \(-0.481354\pi\)
0.0585450 + 0.998285i \(0.481354\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 4.18614 7.25061i 0.150274 0.260282i
\(777\) 0 0
\(778\) 2.31386 + 4.00772i 0.0829559 + 0.143684i
\(779\) 3.55842 + 6.16337i 0.127494 + 0.220826i
\(780\) 0 0
\(781\) −13.1168 + 22.7190i −0.469358 + 0.812951i
\(782\) 2.23369 0.0798765
\(783\) 0 0
\(784\) 4.37228 0.156153
\(785\) 0 0
\(786\) 0 0
\(787\) −14.0000 24.2487i −0.499046 0.864373i 0.500953 0.865474i \(-0.332983\pi\)
−0.999999 + 0.00110111i \(0.999650\pi\)
\(788\) 2.74456 + 4.75372i 0.0977710 + 0.169344i