Properties

Label 1350.2.e.l.901.2
Level $1350$
Weight $2$
Character 1350.901
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 901.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 1350.901
Dual form 1350.2.e.l.451.2

$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

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

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 0.986023 + 0.166612i \(0.0532826\pi\)
−0.348721 + 0.937226i \(0.613384\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −2.18614 3.78651i −0.659146 1.14167i −0.980837 0.194830i \(-0.937584\pi\)
0.321691 0.946845i \(-0.395749\pi\)
\(12\) 0 0
\(13\) −3.37228 + 5.84096i −0.935303 + 1.61999i −0.161209 + 0.986920i \(0.551539\pi\)
−0.774094 + 0.633071i \(0.781794\pi\)
\(14\) −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 −0.928651 0.370954i \(-0.879031\pi\)
0.785581 + 0.618759i \(0.212364\pi\)
\(24\) 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 0.922674 0.385582i \(-0.125999\pi\)
−0.795261 + 0.606268i \(0.792666\pi\)
\(30\) 0 0
\(31\) −2.37228 + 4.10891i −0.426074 + 0.737982i −0.996520 0.0833529i \(-0.973437\pi\)
0.570446 + 0.821335i \(0.306770\pi\)
\(32\) 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 −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) 0 0
\(43\) −2.81386 4.87375i −0.429110 0.743240i 0.567685 0.823246i \(-0.307839\pi\)
−0.996794 + 0.0800065i \(0.974506\pi\)
\(44\) 4.37228 0.659146
\(45\) 0 0
\(46\) −1.37228 −0.202332
\(47\) 3.68614 + 6.38458i 0.537679 + 0.931287i 0.999029 + 0.0440687i \(0.0140321\pi\)
−0.461350 + 0.887218i \(0.652635\pi\)
\(48\) 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 −0.687904 0.725802i \(-0.741469\pi\)
0.972515 + 0.232841i \(0.0748021\pi\)
\(60\) 0 0
\(61\) 4.05842 + 7.02939i 0.519628 + 0.900022i 0.999740 + 0.0228144i \(0.00726267\pi\)
−0.480112 + 0.877207i \(0.659404\pi\)
\(62\) −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 −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) 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 0.804272 0.594261i \(-0.202555\pi\)
−0.916781 + 0.399390i \(0.869222\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.00000 −0.331295
\(83\) −3.68614 6.38458i −0.404607 0.700799i 0.589669 0.807645i \(-0.299258\pi\)
−0.994276 + 0.106846i \(0.965925\pi\)
\(84\) 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 0.571386 0.820682i \(-0.306406\pi\)
−0.996424 + 0.0844938i \(0.973073\pi\)
\(98\) −4.37228 −0.441667
\(99\) 0 0
\(100\) 0 0
\(101\) 1.37228 + 2.37686i 0.136547 + 0.236507i 0.926187 0.377064i \(-0.123066\pi\)
−0.789640 + 0.613570i \(0.789733\pi\)
\(102\) 0 0
\(103\) −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i \(0.455686\pi\)
−0.927030 + 0.374987i \(0.877647\pi\)
\(104\) 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 −0.932374 0.361495i \(-0.882266\pi\)
0.779251 + 0.626712i \(0.215600\pi\)
\(114\) 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 −0.919727 0.392560i \(-0.871590\pi\)
0.799830 + 0.600227i \(0.204923\pi\)
\(132\) 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 0.908151 + 0.418643i \(0.137494\pi\)
−0.0915197 + 0.995803i \(0.529172\pi\)
\(138\) 0 0
\(139\) −0.441578 + 0.764836i −0.0374542 + 0.0648725i −0.884145 0.467213i \(-0.845258\pi\)
0.846691 + 0.532085i \(0.178591\pi\)
\(140\) 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 −0.824877 0.565313i \(-0.808755\pi\)
0.902014 + 0.431708i \(0.142089\pi\)
\(150\) 0 0
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) 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 −0.968639 0.248471i \(-0.920072\pi\)
0.699502 + 0.714631i \(0.253405\pi\)
\(158\) 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 0.482407 + 0.875947i \(0.339763\pi\)
−0.999796 + 0.0201970i \(0.993571\pi\)
\(168\) 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 −0.926831 0.375479i \(-0.877478\pi\)
0.138241 0.990399i \(-0.455855\pi\)
\(174\) 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 0.986990 + 0.160780i \(0.0514008\pi\)
−0.354256 + 0.935148i \(0.615266\pi\)
\(192\) 0 0
\(193\) 10.5584 18.2877i 0.760012 1.31638i −0.182832 0.983144i \(-0.558526\pi\)
0.942844 0.333235i \(-0.108140\pi\)
\(194\) 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 −0.339037 0.940773i \(-0.610101\pi\)
0.984252 0.176771i \(-0.0565653\pi\)
\(212\) 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 0.955389 0.295351i \(-0.0954368\pi\)
−0.733476 + 0.679715i \(0.762103\pi\)
\(224\) 3.37228 0.225320
\(225\) 0 0
\(226\) −3.25544 −0.216548
\(227\) −9.55842 16.5557i −0.634415 1.09884i −0.986639 0.162923i \(-0.947908\pi\)
0.352224 0.935916i \(-0.385426\pi\)
\(228\) 0 0
\(229\) −6.31386 + 10.9359i −0.417232 + 0.722666i −0.995660 0.0930670i \(-0.970333\pi\)
0.578428 + 0.815733i \(0.303666\pi\)
\(230\) 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 −0.913856 0.406038i \(-0.866910\pi\)
0.808568 + 0.588403i \(0.200243\pi\)
\(240\) 0 0
\(241\) 6.24456 + 10.8159i 0.402248 + 0.696713i 0.993997 0.109409i \(-0.0348958\pi\)
−0.591749 + 0.806122i \(0.701562\pi\)
\(242\) −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 −0.926119 0.377231i \(-0.876876\pi\)
0.789751 + 0.613427i \(0.210210\pi\)
\(258\) 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 0.998947 + 0.0458872i \(0.0146115\pi\)
−0.459734 + 0.888057i \(0.652055\pi\)
\(264\) 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 0.999994 + 0.00351574i \(0.00111910\pi\)
−0.496952 + 0.867778i \(0.665548\pi\)
\(278\) −0.883156 −0.0529682
\(279\) 0 0
\(280\) 0 0
\(281\) −0.686141 1.18843i −0.0409317 0.0708958i 0.844834 0.535029i \(-0.179699\pi\)
−0.885765 + 0.464133i \(0.846366\pi\)
\(282\) 0 0
\(283\) −1.56930 + 2.71810i −0.0932850 + 0.161574i −0.908892 0.417033i \(-0.863070\pi\)
0.815607 + 0.578607i \(0.196403\pi\)
\(284\) −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 0.173265 + 0.984875i \(0.444568\pi\)
−0.939560 + 0.342385i \(0.888765\pi\)
\(294\) 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 0.406315 + 0.913733i \(0.366813\pi\)
−0.994474 + 0.104987i \(0.966520\pi\)
\(312\) 0 0
\(313\) 1.81386 + 3.14170i 0.102525 + 0.177579i 0.912724 0.408576i \(-0.133974\pi\)
−0.810199 + 0.586155i \(0.800641\pi\)
\(314\) −6.74456 −0.380618
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) −1.37228 2.37686i −0.0770750 0.133498i 0.824912 0.565262i \(-0.191225\pi\)
−0.901987 + 0.431764i \(0.857891\pi\)
\(318\) 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 0.551989 0.833851i \(-0.313869\pi\)
−0.998131 + 0.0611107i \(0.980536\pi\)
\(332\) 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 −0.896522 0.442999i \(-0.853915\pi\)
0.831909 + 0.554912i \(0.187248\pi\)
\(338\) 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 −0.793019 0.609197i \(-0.791492\pi\)
0.924090 + 0.382176i \(0.124825\pi\)
\(348\) 0 0
\(349\) −9.05842 15.6896i −0.484886 0.839848i 0.514963 0.857212i \(-0.327806\pi\)
−0.999849 + 0.0173648i \(0.994472\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.37228 −0.233043
\(353\) 10.6753 + 18.4901i 0.568187 + 0.984129i 0.996745 + 0.0806147i \(0.0256883\pi\)
−0.428558 + 0.903514i \(0.640978\pi\)
\(354\) 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 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) 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 −0.993847 0.110765i \(-0.964670\pi\)
0.592848 + 0.805314i \(0.298003\pi\)
\(374\) −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 −0.407547 0.913184i \(-0.633616\pi\)
0.994614 0.103646i \(-0.0330508\pi\)
\(384\) 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 0.801386 0.598147i \(-0.204096\pi\)
−0.918704 + 0.394947i \(0.870763\pi\)
\(390\) 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 −0.879632 0.475655i \(-0.842211\pi\)
0.851745 + 0.523956i \(0.175544\pi\)
\(402\) 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 −0.997808 0.0661749i \(-0.978920\pi\)
0.556213 + 0.831040i \(0.312254\pi\)
\(410\) 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 −0.359568 0.933119i \(-0.617076\pi\)
0.987889 0.155165i \(-0.0495908\pi\)
\(420\) 0 0
\(421\) −15.2337 26.3855i −0.742445 1.28595i −0.951379 0.308022i \(-0.900333\pi\)
0.208935 0.977930i \(-0.433000\pi\)
\(422\) 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 0.997306 0.0733577i \(-0.0233715\pi\)
−0.562182 + 0.827013i \(0.690038\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 10.9783 0.522182
\(443\) 1.75544 + 3.04051i 0.0834033 + 0.144459i 0.904710 0.426029i \(-0.140088\pi\)
−0.821306 + 0.570487i \(0.806754\pi\)
\(444\) 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 0.976436 0.215806i \(-0.0692380\pi\)
−0.675112 + 0.737715i \(0.735905\pi\)
\(458\) −12.6277 −0.590055
\(459\) 0 0
\(460\) 0 0
\(461\) 0.941578 + 1.63086i 0.0438537 + 0.0759568i 0.887119 0.461541i \(-0.152703\pi\)
−0.843265 + 0.537497i \(0.819370\pi\)
\(462\) 0 0
\(463\) 10.0000 17.3205i 0.464739 0.804952i −0.534450 0.845200i \(-0.679481\pi\)
0.999190 + 0.0402476i \(0.0128147\pi\)
\(464\) 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 0.860131 0.510074i \(-0.170382\pi\)
−0.871802 + 0.489858i \(0.837048\pi\)
\(480\) 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 0.0751489 + 0.997172i \(0.476057\pi\)
−0.901151 + 0.433505i \(0.857277\pi\)
\(492\) 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 −0.984125 0.177479i \(-0.943206\pi\)
0.645763 + 0.763538i \(0.276539\pi\)
\(500\) 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 −0.170450 + 0.985366i \(0.554522\pi\)
−0.768127 + 0.640297i \(0.778811\pi\)
\(510\) 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 −0.987558 0.157256i \(-0.949735\pi\)
0.357591 0.933878i \(-0.383598\pi\)
\(548\) −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 −0.0155787 0.999879i \(-0.504959\pi\)
0.873710 0.486448i \(-0.161708\pi\)
\(564\) 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 −0.985090 0.172038i \(-0.944965\pi\)
0.343556 0.939132i \(-0.388369\pi\)
\(570\) 0 0
\(571\) −4.30298 + 7.45299i −0.180074 + 0.311898i −0.941906 0.335878i \(-0.890967\pi\)
0.761831 + 0.647775i \(0.224300\pi\)
\(572\) −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 −0.997728 0.0673658i \(-0.978541\pi\)
0.440524 0.897741i \(-0.354793\pi\)
\(588\) 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 −0.901930 0.431883i \(-0.857849\pi\)
0.824986 + 0.565153i \(0.191183\pi\)
\(600\) 0 0
\(601\) 0.930703 + 1.61203i 0.0379642 + 0.0657559i 0.884383 0.466762i \(-0.154579\pi\)
−0.846419 + 0.532517i \(0.821246\pi\)
\(602\) 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 −0.621531 0.783390i \(-0.713489\pi\)
0.989201 + 0.146567i \(0.0468223\pi\)
\(608\) −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 −0.812684 0.582704i \(-0.801995\pi\)
0.910979 + 0.412453i \(0.135328\pi\)
\(618\) 0 0
\(619\) 10.4416 + 18.0853i 0.419682 + 0.726911i 0.995907 0.0903798i \(-0.0288081\pi\)
−0.576225 + 0.817291i \(0.695475\pi\)
\(620\) 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 −0.937451 0.348117i \(-0.886821\pi\)
0.167247 0.985915i \(-0.446512\pi\)
\(642\) 0 0
\(643\) 5.50000 9.52628i 0.216899 0.375680i −0.736959 0.675937i \(-0.763739\pi\)
0.953858 + 0.300257i \(0.0970725\pi\)
\(644\) 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 −0.991895 0.127064i \(-0.959445\pi\)
0.605988 + 0.795474i \(0.292778\pi\)
\(654\) 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 0.984552 0.175094i \(-0.0560230\pi\)
−0.643912 + 0.765100i \(0.722690\pi\)
\(660\) 0 0
\(661\) 6.11684 10.5947i 0.237918 0.412085i −0.722199 0.691685i \(-0.756868\pi\)
0.960117 + 0.279600i \(0.0902018\pi\)
\(662\) 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 0.753420 0.657539i \(-0.228403\pi\)
−0.946156 + 0.323711i \(0.895069\pi\)
\(674\) −2.37228 −0.0913769
\(675\) 0 0
\(676\) 32.4891 1.24958
\(677\) −6.86141 11.8843i −0.263705 0.456751i 0.703518 0.710677i \(-0.251611\pi\)
−0.967224 + 0.253926i \(0.918278\pi\)
\(678\) 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 0.972098 + 0.234575i \(0.0753700\pi\)
−0.282901 + 0.959149i \(0.591297\pi\)
\(692\) 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 0.837909 0.545810i \(-0.183778\pi\)
−0.891640 + 0.452745i \(0.850445\pi\)
\(710\) 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 0.983668 0.179990i \(-0.0576066\pi\)
−0.647710 + 0.761887i \(0.724273\pi\)
\(728\) 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 −0.868175 0.496258i \(-0.834707\pi\)
0.863859 + 0.503733i \(0.168040\pi\)
\(734\) 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 −0.929225 0.369516i \(-0.879524\pi\)
0.784622 + 0.619974i \(0.212857\pi\)
\(744\) 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 −0.975261 0.221059i \(-0.929049\pi\)
0.679073 + 0.734071i \(0.262382\pi\)
\(752\) 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 −0.136312 + 0.990666i \(0.543525\pi\)
−0.789786 + 0.613383i \(0.789808\pi\)
\(762\) 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 −0.0407468 0.999170i \(-0.512974\pi\)
0.885680 0.464297i \(-0.153693\pi\)
\(770\) 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 −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) 2.74456 4.75372i 0.0977710 0.169344i
\(789\)