Properties

Label 2646.2.h.m.667.2
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.m.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.44949 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.44949 q^{5} -1.00000 q^{8} +(0.724745 + 1.25529i) q^{10} -2.00000 q^{11} +(-2.44949 - 4.24264i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-1.27526 + 2.20881i) q^{19} +(-0.724745 + 1.25529i) q^{20} +(-1.00000 - 1.73205i) q^{22} +1.00000 q^{23} -2.89898 q^{25} +(2.44949 - 4.24264i) q^{26} +(-3.44949 + 5.97469i) q^{29} +(-3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(-5.89898 + 10.2173i) q^{37} -2.55051 q^{38} -1.44949 q^{40} +(4.89898 + 8.48528i) q^{41} +(-3.44949 + 5.97469i) q^{43} +(1.00000 - 1.73205i) q^{44} +(0.500000 + 0.866025i) q^{46} +(4.89898 + 8.48528i) q^{47} +(-1.44949 - 2.51059i) q^{50} +4.89898 q^{52} +(-5.44949 - 9.43879i) q^{53} -2.89898 q^{55} -6.89898 q^{58} +(-1.00000 + 1.73205i) q^{59} +(-3.27526 - 5.67291i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-3.55051 - 6.14966i) q^{65} +(6.44949 - 11.1708i) q^{67} -2.00000 q^{68} -0.101021 q^{71} +(3.44949 + 5.97469i) q^{73} -11.7980 q^{74} +(-1.27526 - 2.20881i) q^{76} +(0.949490 + 1.64456i) q^{79} +(-0.724745 - 1.25529i) q^{80} +(-4.89898 + 8.48528i) q^{82} +(1.00000 - 1.73205i) q^{83} +(1.44949 + 2.51059i) q^{85} -6.89898 q^{86} +2.00000 q^{88} +(-8.44949 + 14.6349i) q^{89} +(-0.500000 + 0.866025i) q^{92} +(-4.89898 + 8.48528i) q^{94} +(-1.84847 + 3.20164i) q^{95} +(-1.44949 + 2.51059i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 4 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 4 q^{8} - 2 q^{10} - 8 q^{11} - 2 q^{16} + 4 q^{17} - 10 q^{19} + 2 q^{20} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{29} - 12 q^{31} + 2 q^{32} - 4 q^{34} - 4 q^{37} - 20 q^{38} + 4 q^{40} - 4 q^{43} + 4 q^{44} + 2 q^{46} + 4 q^{50} - 12 q^{53} + 8 q^{55} - 8 q^{58} - 4 q^{59} - 18 q^{61} - 24 q^{62} + 4 q^{64} - 24 q^{65} + 16 q^{67} - 8 q^{68} - 20 q^{71} + 4 q^{73} - 8 q^{74} - 10 q^{76} - 6 q^{79} + 2 q^{80} + 4 q^{83} - 4 q^{85} - 8 q^{86} + 8 q^{88} - 24 q^{89} - 2 q^{92} + 22 q^{95} + 4 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

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
\(5\) 1.44949 0.648232 0.324116 0.946017i \(-0.394933\pi\)
0.324116 + 0.946017i \(0.394933\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.724745 + 1.25529i 0.229184 + 0.396959i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −2.44949 4.24264i −0.679366 1.17670i −0.975172 0.221449i \(-0.928921\pi\)
0.295806 0.955248i \(-0.404412\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) −1.27526 + 2.20881i −0.292564 + 0.506735i −0.974415 0.224756i \(-0.927842\pi\)
0.681852 + 0.731491i \(0.261175\pi\)
\(20\) −0.724745 + 1.25529i −0.162058 + 0.280692i
\(21\) 0 0
\(22\) −1.00000 1.73205i −0.213201 0.369274i
\(23\) 1.00000 0.208514 0.104257 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 0 0
\(25\) −2.89898 −0.579796
\(26\) 2.44949 4.24264i 0.480384 0.832050i
\(27\) 0 0
\(28\) 0 0
\(29\) −3.44949 + 5.97469i −0.640554 + 1.10947i 0.344755 + 0.938693i \(0.387962\pi\)
−0.985309 + 0.170780i \(0.945371\pi\)
\(30\) 0 0
\(31\) −3.00000 + 5.19615i −0.538816 + 0.933257i 0.460152 + 0.887840i \(0.347795\pi\)
−0.998968 + 0.0454165i \(0.985539\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.00000 + 1.73205i −0.171499 + 0.297044i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.89898 + 10.2173i −0.969786 + 1.67972i −0.273621 + 0.961838i \(0.588221\pi\)
−0.696165 + 0.717881i \(0.745112\pi\)
\(38\) −2.55051 −0.413747
\(39\) 0 0
\(40\) −1.44949 −0.229184
\(41\) 4.89898 + 8.48528i 0.765092 + 1.32518i 0.940198 + 0.340629i \(0.110640\pi\)
−0.175106 + 0.984550i \(0.556027\pi\)
\(42\) 0 0
\(43\) −3.44949 + 5.97469i −0.526042 + 0.911132i 0.473497 + 0.880795i \(0.342991\pi\)
−0.999540 + 0.0303367i \(0.990342\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) 0 0
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) 4.89898 + 8.48528i 0.714590 + 1.23771i 0.963118 + 0.269081i \(0.0867199\pi\)
−0.248528 + 0.968625i \(0.579947\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.44949 2.51059i −0.204989 0.355051i
\(51\) 0 0
\(52\) 4.89898 0.679366
\(53\) −5.44949 9.43879i −0.748545 1.29652i −0.948520 0.316717i \(-0.897419\pi\)
0.199975 0.979801i \(-0.435914\pi\)
\(54\) 0 0
\(55\) −2.89898 −0.390898
\(56\) 0 0
\(57\) 0 0
\(58\) −6.89898 −0.905880
\(59\) −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i \(-0.874892\pi\)
0.793560 + 0.608492i \(0.208225\pi\)
\(60\) 0 0
\(61\) −3.27526 5.67291i −0.419353 0.726341i 0.576521 0.817082i \(-0.304410\pi\)
−0.995875 + 0.0907408i \(0.971077\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.55051 6.14966i −0.440387 0.762772i
\(66\) 0 0
\(67\) 6.44949 11.1708i 0.787931 1.36474i −0.139302 0.990250i \(-0.544486\pi\)
0.927233 0.374486i \(-0.122181\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0 0
\(70\) 0 0
\(71\) −0.101021 −0.0119889 −0.00599446 0.999982i \(-0.501908\pi\)
−0.00599446 + 0.999982i \(0.501908\pi\)
\(72\) 0 0
\(73\) 3.44949 + 5.97469i 0.403732 + 0.699285i 0.994173 0.107796i \(-0.0343794\pi\)
−0.590441 + 0.807081i \(0.701046\pi\)
\(74\) −11.7980 −1.37148
\(75\) 0 0
\(76\) −1.27526 2.20881i −0.146282 0.253368i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.949490 + 1.64456i 0.106826 + 0.185028i 0.914483 0.404625i \(-0.132598\pi\)
−0.807657 + 0.589653i \(0.799265\pi\)
\(80\) −0.724745 1.25529i −0.0810289 0.140346i
\(81\) 0 0
\(82\) −4.89898 + 8.48528i −0.541002 + 0.937043i
\(83\) 1.00000 1.73205i 0.109764 0.190117i −0.805910 0.592037i \(-0.798324\pi\)
0.915675 + 0.401920i \(0.131657\pi\)
\(84\) 0 0
\(85\) 1.44949 + 2.51059i 0.157219 + 0.272312i
\(86\) −6.89898 −0.743936
\(87\) 0 0
\(88\) 2.00000 0.213201
\(89\) −8.44949 + 14.6349i −0.895644 + 1.55130i −0.0626387 + 0.998036i \(0.519952\pi\)
−0.833005 + 0.553265i \(0.813382\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.500000 + 0.866025i −0.0521286 + 0.0902894i
\(93\) 0 0
\(94\) −4.89898 + 8.48528i −0.505291 + 0.875190i
\(95\) −1.84847 + 3.20164i −0.189649 + 0.328482i
\(96\) 0 0
\(97\) −1.44949 + 2.51059i −0.147173 + 0.254912i −0.930182 0.367099i \(-0.880351\pi\)
0.783008 + 0.622011i \(0.213684\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.44949 2.51059i 0.144949 0.251059i
\(101\) 17.2474 1.71619 0.858093 0.513495i \(-0.171649\pi\)
0.858093 + 0.513495i \(0.171649\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 2.44949 + 4.24264i 0.240192 + 0.416025i
\(105\) 0 0
\(106\) 5.44949 9.43879i 0.529301 0.916777i
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) −6.34847 10.9959i −0.608073 1.05321i −0.991558 0.129666i \(-0.958609\pi\)
0.383485 0.923547i \(-0.374724\pi\)
\(110\) −1.44949 2.51059i −0.138203 0.239375i
\(111\) 0 0
\(112\) 0 0
\(113\) −3.05051 5.28364i −0.286968 0.497043i 0.686117 0.727492i \(-0.259314\pi\)
−0.973084 + 0.230449i \(0.925981\pi\)
\(114\) 0 0
\(115\) 1.44949 0.135166
\(116\) −3.44949 5.97469i −0.320277 0.554736i
\(117\) 0 0
\(118\) −2.00000 −0.184115
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 3.27526 5.67291i 0.296528 0.513601i
\(123\) 0 0
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) −11.4495 −1.02407
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 3.55051 6.14966i 0.311400 0.539361i
\(131\) 8.55051 0.747062 0.373531 0.927618i \(-0.378147\pi\)
0.373531 + 0.927618i \(0.378147\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.8990 1.11430
\(135\) 0 0
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −7.79796 −0.666225 −0.333112 0.942887i \(-0.608099\pi\)
−0.333112 + 0.942887i \(0.608099\pi\)
\(138\) 0 0
\(139\) −2.27526 3.94086i −0.192985 0.334259i 0.753253 0.657730i \(-0.228483\pi\)
−0.946238 + 0.323471i \(0.895150\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.0505103 0.0874863i −0.00423873 0.00734169i
\(143\) 4.89898 + 8.48528i 0.409673 + 0.709575i
\(144\) 0 0
\(145\) −5.00000 + 8.66025i −0.415227 + 0.719195i
\(146\) −3.44949 + 5.97469i −0.285482 + 0.494469i
\(147\) 0 0
\(148\) −5.89898 10.2173i −0.484893 0.839860i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −5.00000 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) 1.27526 2.20881i 0.103437 0.179158i
\(153\) 0 0
\(154\) 0 0
\(155\) −4.34847 + 7.53177i −0.349277 + 0.604966i
\(156\) 0 0
\(157\) 4.17423 7.22999i 0.333140 0.577016i −0.649986 0.759947i \(-0.725225\pi\)
0.983126 + 0.182931i \(0.0585584\pi\)
\(158\) −0.949490 + 1.64456i −0.0755373 + 0.130835i
\(159\) 0 0
\(160\) 0.724745 1.25529i 0.0572961 0.0992398i
\(161\) 0 0
\(162\) 0 0
\(163\) 9.89898 17.1455i 0.775348 1.34294i −0.159251 0.987238i \(-0.550908\pi\)
0.934599 0.355704i \(-0.115759\pi\)
\(164\) −9.79796 −0.765092
\(165\) 0 0
\(166\) 2.00000 0.155230
\(167\) −5.34847 9.26382i −0.413877 0.716856i 0.581433 0.813594i \(-0.302492\pi\)
−0.995310 + 0.0967384i \(0.969159\pi\)
\(168\) 0 0
\(169\) −5.50000 + 9.52628i −0.423077 + 0.732791i
\(170\) −1.44949 + 2.51059i −0.111171 + 0.192553i
\(171\) 0 0
\(172\) −3.44949 5.97469i −0.263021 0.455566i
\(173\) −1.55051 2.68556i −0.117883 0.204180i 0.801045 0.598604i \(-0.204277\pi\)
−0.918929 + 0.394424i \(0.870944\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 + 1.73205i 0.0753778 + 0.130558i
\(177\) 0 0
\(178\) −16.8990 −1.26663
\(179\) 10.3485 + 17.9241i 0.773481 + 1.33971i 0.935644 + 0.352944i \(0.114819\pi\)
−0.162163 + 0.986764i \(0.551847\pi\)
\(180\) 0 0
\(181\) −10.3485 −0.769196 −0.384598 0.923084i \(-0.625660\pi\)
−0.384598 + 0.923084i \(0.625660\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.00000 −0.0737210
\(185\) −8.55051 + 14.8099i −0.628646 + 1.08885i
\(186\) 0 0
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) −9.79796 −0.714590
\(189\) 0 0
\(190\) −3.69694 −0.268204
\(191\) 2.05051 + 3.55159i 0.148370 + 0.256984i 0.930625 0.365974i \(-0.119264\pi\)
−0.782255 + 0.622958i \(0.785931\pi\)
\(192\) 0 0
\(193\) 8.94949 15.5010i 0.644198 1.11578i −0.340288 0.940321i \(-0.610524\pi\)
0.984486 0.175463i \(-0.0561422\pi\)
\(194\) −2.89898 −0.208135
\(195\) 0 0
\(196\) 0 0
\(197\) −16.6969 −1.18961 −0.594804 0.803871i \(-0.702770\pi\)
−0.594804 + 0.803871i \(0.702770\pi\)
\(198\) 0 0
\(199\) 1.44949 + 2.51059i 0.102752 + 0.177971i 0.912817 0.408368i \(-0.133902\pi\)
−0.810066 + 0.586339i \(0.800569\pi\)
\(200\) 2.89898 0.204989
\(201\) 0 0
\(202\) 8.62372 + 14.9367i 0.606763 + 1.05094i
\(203\) 0 0
\(204\) 0 0
\(205\) 7.10102 + 12.2993i 0.495957 + 0.859022i
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 0 0
\(208\) −2.44949 + 4.24264i −0.169842 + 0.294174i
\(209\) 2.55051 4.41761i 0.176422 0.305573i
\(210\) 0 0
\(211\) −6.44949 11.1708i −0.444001 0.769033i 0.553981 0.832529i \(-0.313108\pi\)
−0.997982 + 0.0634968i \(0.979775\pi\)
\(212\) 10.8990 0.748545
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) −5.00000 + 8.66025i −0.340997 + 0.590624i
\(216\) 0 0
\(217\) 0 0
\(218\) 6.34847 10.9959i 0.429973 0.744734i
\(219\) 0 0
\(220\) 1.44949 2.51059i 0.0977246 0.169264i
\(221\) 4.89898 8.48528i 0.329541 0.570782i
\(222\) 0 0
\(223\) 5.55051 9.61377i 0.371690 0.643785i −0.618136 0.786071i \(-0.712112\pi\)
0.989826 + 0.142286i \(0.0454452\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3.05051 5.28364i 0.202917 0.351462i
\(227\) 5.44949 0.361695 0.180848 0.983511i \(-0.442116\pi\)
0.180848 + 0.983511i \(0.442116\pi\)
\(228\) 0 0
\(229\) 1.24745 0.0824337 0.0412169 0.999150i \(-0.486877\pi\)
0.0412169 + 0.999150i \(0.486877\pi\)
\(230\) 0.724745 + 1.25529i 0.0477883 + 0.0827717i
\(231\) 0 0
\(232\) 3.44949 5.97469i 0.226470 0.392258i
\(233\) −3.50000 + 6.06218i −0.229293 + 0.397146i −0.957599 0.288106i \(-0.906975\pi\)
0.728306 + 0.685252i \(0.240308\pi\)
\(234\) 0 0
\(235\) 7.10102 + 12.2993i 0.463220 + 0.802320i
\(236\) −1.00000 1.73205i −0.0650945 0.112747i
\(237\) 0 0
\(238\) 0 0
\(239\) 3.39898 + 5.88721i 0.219862 + 0.380812i 0.954766 0.297360i \(-0.0961061\pi\)
−0.734904 + 0.678171i \(0.762773\pi\)
\(240\) 0 0
\(241\) 0.898979 0.0579084 0.0289542 0.999581i \(-0.490782\pi\)
0.0289542 + 0.999581i \(0.490782\pi\)
\(242\) −3.50000 6.06218i −0.224989 0.389692i
\(243\) 0 0
\(244\) 6.55051 0.419353
\(245\) 0 0
\(246\) 0 0
\(247\) 12.4949 0.795031
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) 0 0
\(250\) −5.72474 9.91555i −0.362065 0.627114i
\(251\) −17.4495 −1.10140 −0.550701 0.834703i \(-0.685640\pi\)
−0.550701 + 0.834703i \(0.685640\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) −1.50000 2.59808i −0.0941184 0.163018i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.20204 −0.511629 −0.255815 0.966726i \(-0.582344\pi\)
−0.255815 + 0.966726i \(0.582344\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7.10102 0.440387
\(261\) 0 0
\(262\) 4.27526 + 7.40496i 0.264126 + 0.457480i
\(263\) −25.8990 −1.59700 −0.798500 0.601995i \(-0.794373\pi\)
−0.798500 + 0.601995i \(0.794373\pi\)
\(264\) 0 0
\(265\) −7.89898 13.6814i −0.485230 0.840444i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.44949 + 11.1708i 0.393965 + 0.682368i
\(269\) −9.17423 15.8902i −0.559363 0.968845i −0.997550 0.0699611i \(-0.977712\pi\)
0.438187 0.898884i \(-0.355621\pi\)
\(270\) 0 0
\(271\) −3.55051 + 6.14966i −0.215678 + 0.373565i −0.953482 0.301450i \(-0.902530\pi\)
0.737804 + 0.675015i \(0.235863\pi\)
\(272\) 1.00000 1.73205i 0.0606339 0.105021i
\(273\) 0 0
\(274\) −3.89898 6.75323i −0.235546 0.407978i
\(275\) 5.79796 0.349630
\(276\) 0 0
\(277\) −18.6969 −1.12339 −0.561695 0.827344i \(-0.689851\pi\)
−0.561695 + 0.827344i \(0.689851\pi\)
\(278\) 2.27526 3.94086i 0.136461 0.236357i
\(279\) 0 0
\(280\) 0 0
\(281\) −9.50000 + 16.4545i −0.566722 + 0.981592i 0.430165 + 0.902750i \(0.358455\pi\)
−0.996887 + 0.0788417i \(0.974878\pi\)
\(282\) 0 0
\(283\) 12.7247 22.0399i 0.756408 1.31014i −0.188264 0.982118i \(-0.560286\pi\)
0.944672 0.328018i \(-0.106381\pi\)
\(284\) 0.0505103 0.0874863i 0.00299723 0.00519136i
\(285\) 0 0
\(286\) −4.89898 + 8.48528i −0.289683 + 0.501745i
\(287\) 0 0
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −10.0000 −0.587220
\(291\) 0 0
\(292\) −6.89898 −0.403732
\(293\) 1.37628 + 2.38378i 0.0804029 + 0.139262i 0.903423 0.428750i \(-0.141046\pi\)
−0.823020 + 0.568012i \(0.807713\pi\)
\(294\) 0 0
\(295\) −1.44949 + 2.51059i −0.0843926 + 0.146172i
\(296\) 5.89898 10.2173i 0.342871 0.593870i
\(297\) 0 0
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) −2.44949 4.24264i −0.141658 0.245358i
\(300\) 0 0
\(301\) 0 0
\(302\) −2.50000 4.33013i −0.143859 0.249171i
\(303\) 0 0
\(304\) 2.55051 0.146282
\(305\) −4.74745 8.22282i −0.271838 0.470837i
\(306\) 0 0
\(307\) 25.2474 1.44095 0.720474 0.693482i \(-0.243924\pi\)
0.720474 + 0.693482i \(0.243924\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −8.69694 −0.493953
\(311\) 15.3485 26.5843i 0.870332 1.50746i 0.00867810 0.999962i \(-0.497238\pi\)
0.861654 0.507497i \(-0.169429\pi\)
\(312\) 0 0
\(313\) 2.34847 + 4.06767i 0.132743 + 0.229918i 0.924733 0.380616i \(-0.124288\pi\)
−0.791990 + 0.610534i \(0.790955\pi\)
\(314\) 8.34847 0.471131
\(315\) 0 0
\(316\) −1.89898 −0.106826
\(317\) 10.3485 + 17.9241i 0.581228 + 1.00672i 0.995334 + 0.0964878i \(0.0307609\pi\)
−0.414106 + 0.910229i \(0.635906\pi\)
\(318\) 0 0
\(319\) 6.89898 11.9494i 0.386269 0.669037i
\(320\) 1.44949 0.0810289
\(321\) 0 0
\(322\) 0 0
\(323\) −5.10102 −0.283828
\(324\) 0 0
\(325\) 7.10102 + 12.2993i 0.393894 + 0.682244i
\(326\) 19.7980 1.09651
\(327\) 0 0
\(328\) −4.89898 8.48528i −0.270501 0.468521i
\(329\) 0 0
\(330\) 0 0
\(331\) −2.34847 4.06767i −0.129084 0.223579i 0.794238 0.607606i \(-0.207870\pi\)
−0.923322 + 0.384027i \(0.874537\pi\)
\(332\) 1.00000 + 1.73205i 0.0548821 + 0.0950586i
\(333\) 0 0
\(334\) 5.34847 9.26382i 0.292655 0.506894i
\(335\) 9.34847 16.1920i 0.510761 0.884665i
\(336\) 0 0
\(337\) 11.6969 + 20.2597i 0.637173 + 1.10362i 0.986050 + 0.166447i \(0.0532296\pi\)
−0.348877 + 0.937168i \(0.613437\pi\)
\(338\) −11.0000 −0.598321
\(339\) 0 0
\(340\) −2.89898 −0.157219
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 0 0
\(343\) 0 0
\(344\) 3.44949 5.97469i 0.185984 0.322134i
\(345\) 0 0
\(346\) 1.55051 2.68556i 0.0833559 0.144377i
\(347\) 9.79796 16.9706i 0.525982 0.911028i −0.473560 0.880762i \(-0.657031\pi\)
0.999542 0.0302659i \(-0.00963541\pi\)
\(348\) 0 0
\(349\) −5.55051 + 9.61377i −0.297112 + 0.514613i −0.975474 0.220115i \(-0.929357\pi\)
0.678362 + 0.734728i \(0.262690\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 + 1.73205i −0.0533002 + 0.0923186i
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) −0.146428 −0.00777160
\(356\) −8.44949 14.6349i −0.447822 0.775651i
\(357\) 0 0
\(358\) −10.3485 + 17.9241i −0.546934 + 0.947317i
\(359\) −4.39898 + 7.61926i −0.232169 + 0.402129i −0.958446 0.285273i \(-0.907916\pi\)
0.726277 + 0.687402i \(0.241249\pi\)
\(360\) 0 0
\(361\) 6.24745 + 10.8209i 0.328813 + 0.569521i
\(362\) −5.17423 8.96204i −0.271952 0.471034i
\(363\) 0 0
\(364\) 0 0
\(365\) 5.00000 + 8.66025i 0.261712 + 0.453298i
\(366\) 0 0
\(367\) −13.7980 −0.720248 −0.360124 0.932905i \(-0.617266\pi\)
−0.360124 + 0.932905i \(0.617266\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) 0 0
\(370\) −17.1010 −0.889040
\(371\) 0 0
\(372\) 0 0
\(373\) −6.89898 −0.357216 −0.178608 0.983920i \(-0.557159\pi\)
−0.178608 + 0.983920i \(0.557159\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) 0 0
\(376\) −4.89898 8.48528i −0.252646 0.437595i
\(377\) 33.7980 1.74068
\(378\) 0 0
\(379\) 22.4949 1.15549 0.577743 0.816219i \(-0.303934\pi\)
0.577743 + 0.816219i \(0.303934\pi\)
\(380\) −1.84847 3.20164i −0.0948245 0.164241i
\(381\) 0 0
\(382\) −2.05051 + 3.55159i −0.104913 + 0.181715i
\(383\) 2.89898 0.148131 0.0740655 0.997253i \(-0.476403\pi\)
0.0740655 + 0.997253i \(0.476403\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.8990 0.911034
\(387\) 0 0
\(388\) −1.44949 2.51059i −0.0735867 0.127456i
\(389\) 24.8990 1.26243 0.631214 0.775609i \(-0.282557\pi\)
0.631214 + 0.775609i \(0.282557\pi\)
\(390\) 0 0
\(391\) 1.00000 + 1.73205i 0.0505722 + 0.0875936i
\(392\) 0 0
\(393\) 0 0
\(394\) −8.34847 14.4600i −0.420590 0.728483i
\(395\) 1.37628 + 2.38378i 0.0692479 + 0.119941i
\(396\) 0 0
\(397\) −19.3485 + 33.5125i −0.971072 + 1.68195i −0.278740 + 0.960367i \(0.589917\pi\)
−0.692332 + 0.721579i \(0.743417\pi\)
\(398\) −1.44949 + 2.51059i −0.0726564 + 0.125844i
\(399\) 0 0
\(400\) 1.44949 + 2.51059i 0.0724745 + 0.125529i
\(401\) 19.8990 0.993708 0.496854 0.867834i \(-0.334489\pi\)
0.496854 + 0.867834i \(0.334489\pi\)
\(402\) 0 0
\(403\) 29.3939 1.46421
\(404\) −8.62372 + 14.9367i −0.429046 + 0.743130i
\(405\) 0 0
\(406\) 0 0
\(407\) 11.7980 20.4347i 0.584803 1.01291i
\(408\) 0 0
\(409\) 6.89898 11.9494i 0.341133 0.590859i −0.643511 0.765437i \(-0.722523\pi\)
0.984643 + 0.174578i \(0.0558562\pi\)
\(410\) −7.10102 + 12.2993i −0.350694 + 0.607421i
\(411\) 0 0
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 0 0
\(414\) 0 0
\(415\) 1.44949 2.51059i 0.0711527 0.123240i
\(416\) −4.89898 −0.240192
\(417\) 0 0
\(418\) 5.10102 0.249499
\(419\) 14.7247 + 25.5040i 0.719351 + 1.24595i 0.961257 + 0.275653i \(0.0888940\pi\)
−0.241906 + 0.970300i \(0.577773\pi\)
\(420\) 0 0
\(421\) −11.4495 + 19.8311i −0.558014 + 0.966509i 0.439648 + 0.898170i \(0.355103\pi\)
−0.997662 + 0.0683385i \(0.978230\pi\)
\(422\) 6.44949 11.1708i 0.313956 0.543788i
\(423\) 0 0
\(424\) 5.44949 + 9.43879i 0.264651 + 0.458388i
\(425\) −2.89898 5.02118i −0.140621 0.243563i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.00000 10.3923i −0.290021 0.502331i
\(429\) 0 0
\(430\) −10.0000 −0.482243
\(431\) 15.7980 + 27.3629i 0.760961 + 1.31802i 0.942356 + 0.334613i \(0.108605\pi\)
−0.181395 + 0.983410i \(0.558061\pi\)
\(432\) 0 0
\(433\) −7.79796 −0.374746 −0.187373 0.982289i \(-0.559997\pi\)
−0.187373 + 0.982289i \(0.559997\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 12.6969 0.608073
\(437\) −1.27526 + 2.20881i −0.0610037 + 0.105662i
\(438\) 0 0
\(439\) −1.10102 1.90702i −0.0525488 0.0910173i 0.838554 0.544818i \(-0.183401\pi\)
−0.891103 + 0.453801i \(0.850068\pi\)
\(440\) 2.89898 0.138203
\(441\) 0 0
\(442\) 9.79796 0.466041
\(443\) −7.44949 12.9029i −0.353936 0.613035i 0.632999 0.774152i \(-0.281824\pi\)
−0.986935 + 0.161117i \(0.948490\pi\)
\(444\) 0 0
\(445\) −12.2474 + 21.2132i −0.580585 + 1.00560i
\(446\) 11.1010 0.525649
\(447\) 0 0
\(448\) 0 0
\(449\) −20.5959 −0.971981 −0.485991 0.873964i \(-0.661541\pi\)
−0.485991 + 0.873964i \(0.661541\pi\)
\(450\) 0 0
\(451\) −9.79796 16.9706i −0.461368 0.799113i
\(452\) 6.10102 0.286968
\(453\) 0 0
\(454\) 2.72474 + 4.71940i 0.127879 + 0.221492i
\(455\) 0 0
\(456\) 0 0
\(457\) 8.74745 + 15.1510i 0.409188 + 0.708735i 0.994799 0.101857i \(-0.0324785\pi\)
−0.585611 + 0.810593i \(0.699145\pi\)
\(458\) 0.623724 + 1.08032i 0.0291447 + 0.0504801i
\(459\) 0 0
\(460\) −0.724745 + 1.25529i −0.0337914 + 0.0585284i
\(461\) 2.82577 4.89437i 0.131609 0.227954i −0.792688 0.609628i \(-0.791319\pi\)
0.924297 + 0.381674i \(0.124652\pi\)
\(462\) 0 0
\(463\) −1.84847 3.20164i −0.0859057 0.148793i 0.819871 0.572548i \(-0.194045\pi\)
−0.905777 + 0.423755i \(0.860712\pi\)
\(464\) 6.89898 0.320277
\(465\) 0 0
\(466\) −7.00000 −0.324269
\(467\) 5.00000 8.66025i 0.231372 0.400749i −0.726840 0.686807i \(-0.759012\pi\)
0.958212 + 0.286058i \(0.0923451\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −7.10102 + 12.2993i −0.327546 + 0.567326i
\(471\) 0 0
\(472\) 1.00000 1.73205i 0.0460287 0.0797241i
\(473\) 6.89898 11.9494i 0.317215 0.549433i
\(474\) 0 0
\(475\) 3.69694 6.40329i 0.169627 0.293803i
\(476\) 0 0
\(477\) 0 0
\(478\) −3.39898 + 5.88721i −0.155466 + 0.269274i
\(479\) −9.59592 −0.438449 −0.219224 0.975674i \(-0.570353\pi\)
−0.219224 + 0.975674i \(0.570353\pi\)
\(480\) 0 0
\(481\) 57.7980 2.63536
\(482\) 0.449490 + 0.778539i 0.0204737 + 0.0354615i
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) −2.10102 + 3.63907i −0.0954024 + 0.165242i
\(486\) 0 0
\(487\) 18.1969 + 31.5180i 0.824582 + 1.42822i 0.902238 + 0.431238i \(0.141923\pi\)
−0.0776564 + 0.996980i \(0.524744\pi\)
\(488\) 3.27526 + 5.67291i 0.148264 + 0.256800i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.89898 + 13.6814i 0.356476 + 0.617434i 0.987369 0.158435i \(-0.0506448\pi\)
−0.630893 + 0.775869i \(0.717312\pi\)
\(492\) 0 0
\(493\) −13.7980 −0.621429
\(494\) 6.24745 + 10.8209i 0.281086 + 0.486855i
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 0 0
\(498\) 0 0
\(499\) −25.3939 −1.13679 −0.568393 0.822757i \(-0.692435\pi\)
−0.568393 + 0.822757i \(0.692435\pi\)
\(500\) 5.72474 9.91555i 0.256018 0.443437i
\(501\) 0 0
\(502\) −8.72474 15.1117i −0.389404 0.674468i
\(503\) 24.4949 1.09217 0.546087 0.837729i \(-0.316117\pi\)
0.546087 + 0.837729i \(0.316117\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) −1.00000 1.73205i −0.0444554 0.0769991i
\(507\) 0 0
\(508\) 1.50000 2.59808i 0.0665517 0.115271i
\(509\) 7.10102 0.314747 0.157374 0.987539i \(-0.449697\pi\)
0.157374 + 0.987539i \(0.449697\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −4.10102 7.10318i −0.180888 0.313308i
\(515\) 20.2929 0.894210
\(516\) 0 0
\(517\) −9.79796 16.9706i −0.430914 0.746364i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.55051 + 6.14966i 0.155700 + 0.269681i
\(521\) −4.65153 8.05669i −0.203787 0.352970i 0.745958 0.665993i \(-0.231992\pi\)
−0.949746 + 0.313023i \(0.898658\pi\)
\(522\) 0 0
\(523\) 7.17423 12.4261i 0.313707 0.543357i −0.665455 0.746438i \(-0.731762\pi\)
0.979162 + 0.203081i \(0.0650956\pi\)
\(524\) −4.27526 + 7.40496i −0.186765 + 0.323487i
\(525\) 0 0
\(526\) −12.9495 22.4292i −0.564625 0.977958i
\(527\) −12.0000 −0.522728
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) 7.89898 13.6814i 0.343110 0.594284i
\(531\) 0 0
\(532\) 0 0
\(533\) 24.0000 41.5692i 1.03956 1.80056i
\(534\) 0 0
\(535\) −8.69694 + 15.0635i −0.376001 + 0.651254i
\(536\) −6.44949 + 11.1708i −0.278576 + 0.482507i
\(537\) 0 0
\(538\) 9.17423 15.8902i 0.395529 0.685077i
\(539\) 0 0
\(540\) 0 0
\(541\) 9.24745 16.0171i 0.397579 0.688627i −0.595848 0.803097i \(-0.703184\pi\)
0.993427 + 0.114471i \(0.0365172\pi\)
\(542\) −7.10102 −0.305015
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) −9.20204 15.9384i −0.394172 0.682726i
\(546\) 0 0
\(547\) 3.79796 6.57826i 0.162389 0.281266i −0.773336 0.633996i \(-0.781413\pi\)
0.935725 + 0.352730i \(0.114747\pi\)
\(548\) 3.89898 6.75323i 0.166556 0.288484i
\(549\) 0 0
\(550\) 2.89898 + 5.02118i 0.123613 + 0.214104i
\(551\) −8.79796 15.2385i −0.374806 0.649182i
\(552\) 0 0
\(553\) 0 0
\(554\) −9.34847 16.1920i −0.397178 0.687933i
\(555\) 0 0
\(556\) 4.55051 0.192985
\(557\) −6.44949 11.1708i −0.273274 0.473324i 0.696424 0.717630i \(-0.254773\pi\)
−0.969698 + 0.244306i \(0.921440\pi\)
\(558\) 0 0
\(559\) 33.7980 1.42950
\(560\) 0 0
\(561\) 0 0
\(562\) −19.0000 −0.801467
\(563\) −19.9722 + 34.5929i −0.841728 + 1.45791i 0.0467054 + 0.998909i \(0.485128\pi\)
−0.888433 + 0.459006i \(0.848206\pi\)
\(564\) 0 0
\(565\) −4.42168 7.65858i −0.186022 0.322199i
\(566\) 25.4495 1.06972
\(567\) 0 0
\(568\) 0.101021 0.00423873
\(569\) −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i \(-0.950200\pi\)
0.358954 0.933355i \(-0.383134\pi\)
\(570\) 0 0
\(571\) −16.8990 + 29.2699i −0.707200 + 1.22491i 0.258691 + 0.965960i \(0.416709\pi\)
−0.965892 + 0.258947i \(0.916625\pi\)
\(572\) −9.79796 −0.409673
\(573\) 0 0
\(574\) 0 0
\(575\) −2.89898 −0.120896
\(576\) 0 0
\(577\) 7.79796 + 13.5065i 0.324633 + 0.562281i 0.981438 0.191779i \(-0.0614258\pi\)
−0.656805 + 0.754061i \(0.728092\pi\)
\(578\) 13.0000 0.540729
\(579\) 0 0
\(580\) −5.00000 8.66025i −0.207614 0.359597i
\(581\) 0 0
\(582\) 0 0
\(583\) 10.8990 + 18.8776i 0.451390 + 0.781830i
\(584\) −3.44949 5.97469i −0.142741 0.247234i
\(585\) 0 0
\(586\) −1.37628 + 2.38378i −0.0568534 + 0.0984730i
\(587\) 8.07321 13.9832i 0.333217 0.577149i −0.649924 0.760000i \(-0.725199\pi\)
0.983141 + 0.182850i \(0.0585324\pi\)
\(588\) 0 0
\(589\) −7.65153 13.2528i −0.315276 0.546074i
\(590\) −2.89898 −0.119349
\(591\) 0 0
\(592\) 11.7980 0.484893
\(593\) 7.34847 12.7279i 0.301765 0.522673i −0.674770 0.738028i \(-0.735757\pi\)
0.976536 + 0.215355i \(0.0690907\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 + 5.19615i −0.122885 + 0.212843i
\(597\) 0 0
\(598\) 2.44949 4.24264i 0.100167 0.173494i
\(599\) −16.8990 + 29.2699i −0.690474 + 1.19594i 0.281209 + 0.959646i \(0.409264\pi\)
−0.971683 + 0.236289i \(0.924069\pi\)
\(600\) 0 0
\(601\) −8.34847 + 14.4600i −0.340541 + 0.589835i −0.984533 0.175198i \(-0.943944\pi\)
0.643992 + 0.765032i \(0.277277\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2.50000 4.33013i 0.101724 0.176190i
\(605\) −10.1464 −0.412511
\(606\) 0 0
\(607\) 20.6969 0.840063 0.420031 0.907510i \(-0.362019\pi\)
0.420031 + 0.907510i \(0.362019\pi\)
\(608\) 1.27526 + 2.20881i 0.0517184 + 0.0895789i
\(609\) 0 0
\(610\) 4.74745 8.22282i 0.192219 0.332932i
\(611\) 24.0000 41.5692i 0.970936 1.68171i
\(612\) 0 0
\(613\) 7.34847 + 12.7279i 0.296802 + 0.514076i 0.975402 0.220432i \(-0.0707466\pi\)
−0.678601 + 0.734508i \(0.737413\pi\)
\(614\) 12.6237 + 21.8649i 0.509452 + 0.882397i
\(615\) 0 0
\(616\) 0 0
\(617\) −7.69694 13.3315i −0.309867 0.536706i 0.668466 0.743743i \(-0.266951\pi\)
−0.978333 + 0.207037i \(0.933618\pi\)
\(618\) 0 0
\(619\) 30.1464 1.21169 0.605844 0.795584i \(-0.292836\pi\)
0.605844 + 0.795584i \(0.292836\pi\)
\(620\) −4.34847 7.53177i −0.174639 0.302483i
\(621\) 0 0
\(622\) 30.6969 1.23084
\(623\) 0 0
\(624\) 0 0
\(625\) −2.10102 −0.0840408
\(626\) −2.34847 + 4.06767i −0.0938637 + 0.162577i
\(627\) 0 0
\(628\) 4.17423 + 7.22999i 0.166570 + 0.288508i
\(629\) −23.5959 −0.940831
\(630\) 0 0
\(631\) 27.8990 1.11064 0.555320 0.831636i \(-0.312596\pi\)
0.555320 + 0.831636i \(0.312596\pi\)
\(632\) −0.949490 1.64456i −0.0377687 0.0654173i
\(633\) 0 0
\(634\) −10.3485 + 17.9241i −0.410990 + 0.711856i
\(635\) −4.34847 −0.172564
\(636\) 0 0
\(637\) 0 0
\(638\) 13.7980 0.546266
\(639\) 0 0
\(640\) 0.724745 + 1.25529i 0.0286481 + 0.0496199i
\(641\) 7.49490 0.296031 0.148015 0.988985i \(-0.452712\pi\)
0.148015 + 0.988985i \(0.452712\pi\)
\(642\) 0 0
\(643\) 19.6969 + 34.1161i 0.776771 + 1.34541i 0.933793 + 0.357812i \(0.116477\pi\)
−0.157022 + 0.987595i \(0.550189\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.55051 4.41761i −0.100348 0.173809i
\(647\) −25.3485 43.9048i −0.996551 1.72608i −0.570139 0.821548i \(-0.693111\pi\)
−0.426412 0.904529i \(-0.640223\pi\)
\(648\) 0 0
\(649\) 2.00000 3.46410i 0.0785069 0.135978i
\(650\) −7.10102 + 12.2993i −0.278525 + 0.482419i
\(651\) 0 0
\(652\) 9.89898 + 17.1455i 0.387674 + 0.671471i
\(653\) −9.79796 −0.383424 −0.191712 0.981451i \(-0.561404\pi\)
−0.191712 + 0.981451i \(0.561404\pi\)
\(654\) 0 0
\(655\) 12.3939 0.484269
\(656\) 4.89898 8.48528i 0.191273 0.331295i
\(657\) 0 0
\(658\) 0 0
\(659\) −12.3485 + 21.3882i −0.481028 + 0.833165i −0.999763 0.0217701i \(-0.993070\pi\)
0.518735 + 0.854935i \(0.326403\pi\)
\(660\) 0 0
\(661\) −2.27526 + 3.94086i −0.0884972 + 0.153282i −0.906876 0.421397i \(-0.861540\pi\)
0.818379 + 0.574679i \(0.194873\pi\)
\(662\) 2.34847 4.06767i 0.0912758 0.158094i
\(663\) 0 0
\(664\) −1.00000 + 1.73205i −0.0388075 + 0.0672166i
\(665\) 0 0
\(666\) 0 0
\(667\) −3.44949 + 5.97469i −0.133565 + 0.231341i
\(668\) 10.6969 0.413877
\(669\) 0 0
\(670\) 18.6969 0.722326
\(671\) 6.55051 + 11.3458i 0.252880 + 0.438000i
\(672\) 0 0
\(673\) 4.29796 7.44428i 0.165674 0.286956i −0.771220 0.636568i \(-0.780353\pi\)
0.936894 + 0.349612i \(0.113687\pi\)
\(674\) −11.6969 + 20.2597i −0.450549 + 0.780374i
\(675\) 0 0
\(676\) −5.50000 9.52628i −0.211538 0.366395i
\(677\) 7.34847 + 12.7279i 0.282425 + 0.489174i 0.971981 0.235058i \(-0.0755280\pi\)
−0.689557 + 0.724232i \(0.742195\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.44949 2.51059i −0.0555854 0.0962767i
\(681\) 0 0
\(682\) 12.0000 0.459504
\(683\) 25.8990 + 44.8583i 0.990997 + 1.71646i 0.611446 + 0.791286i \(0.290588\pi\)
0.379551 + 0.925171i \(0.376079\pi\)
\(684\) 0 0
\(685\) −11.3031 −0.431868
\(686\) 0 0
\(687\) 0 0
\(688\) 6.89898 0.263021
\(689\) −26.6969 + 46.2405i −1.01707 + 1.76162i
\(690\) 0 0
\(691\) −25.5227 44.2066i −0.970929 1.68170i −0.692762 0.721167i \(-0.743606\pi\)
−0.278168 0.960533i \(-0.589727\pi\)
\(692\) 3.10102 0.117883
\(693\) 0 0
\(694\) 19.5959 0.743851
\(695\) −3.29796 5.71223i −0.125099 0.216677i
\(696\) 0 0
\(697\) −9.79796 + 16.9706i −0.371124 + 0.642806i
\(698\) −11.1010 −0.420180
\(699\) 0 0
\(700\) 0 0
\(701\) 7.39388 0.279263 0.139631 0.990204i \(-0.455408\pi\)
0.139631 + 0.990204i \(0.455408\pi\)
\(702\) 0 0
\(703\) −15.0454 26.0594i −0.567448 0.982849i
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) 3.00000 + 5.19615i 0.112906 + 0.195560i
\(707\) 0 0
\(708\) 0 0
\(709\) −13.7980 23.8988i −0.518193 0.897537i −0.999777 0.0211367i \(-0.993271\pi\)
0.481583 0.876400i \(-0.340062\pi\)
\(710\) −0.0732141 0.126811i −0.00274768 0.00475911i
\(711\) 0 0
\(712\) 8.44949 14.6349i 0.316658 0.548468i
\(713\) −3.00000 + 5.19615i −0.112351 + 0.194597i
\(714\) 0 0
\(715\) 7.10102 + 12.2993i 0.265563 + 0.459969i
\(716\) −20.6969 −0.773481
\(717\) 0 0
\(718\) −8.79796 −0.328337
\(719\) 4.89898 8.48528i 0.182701 0.316448i −0.760098 0.649808i \(-0.774849\pi\)
0.942799 + 0.333360i \(0.108183\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −6.24745 + 10.8209i −0.232506 + 0.402712i
\(723\) 0 0
\(724\) 5.17423 8.96204i 0.192299 0.333071i
\(725\) 10.0000 17.3205i 0.371391 0.643268i
\(726\) 0 0
\(727\) 4.24745 7.35680i 0.157529 0.272848i −0.776448 0.630181i \(-0.782981\pi\)
0.933977 + 0.357333i \(0.116314\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −5.00000 + 8.66025i −0.185058 + 0.320530i
\(731\) −13.7980 −0.510336
\(732\) 0 0
\(733\) −17.4495 −0.644512 −0.322256 0.946653i \(-0.604441\pi\)
−0.322256 + 0.946653i \(0.604441\pi\)
\(734\) −6.89898 11.9494i −0.254646 0.441060i
\(735\) 0 0
\(736\) 0.500000 0.866025i 0.0184302 0.0319221i
\(737\) −12.8990 + 22.3417i −0.475140 + 0.822967i
\(738\) 0 0
\(739\) −6.79796 11.7744i −0.250067 0.433129i 0.713477 0.700679i \(-0.247119\pi\)
−0.963544 + 0.267550i \(0.913786\pi\)
\(740\) −8.55051 14.8099i −0.314323 0.544423i
\(741\) 0 0
\(742\) 0 0
\(743\) 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i \(0.0629279\pi\)
−0.320166 + 0.947361i \(0.603739\pi\)
\(744\) 0 0
\(745\) 8.69694 0.318631
\(746\) −3.44949 5.97469i −0.126295 0.218749i
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) 0 0
\(750\) 0 0
\(751\) 1.40408 0.0512357 0.0256178 0.999672i \(-0.491845\pi\)
0.0256178 + 0.999672i \(0.491845\pi\)
\(752\) 4.89898 8.48528i 0.178647 0.309426i
\(753\) 0 0
\(754\) 16.8990 + 29.2699i 0.615425 + 1.06595i
\(755\) −7.24745 −0.263762
\(756\) 0 0
\(757\) −35.3939 −1.28641 −0.643206 0.765693i \(-0.722396\pi\)
−0.643206 + 0.765693i \(0.722396\pi\)
\(758\) 11.2474 + 19.4812i 0.408526 + 0.707587i
\(759\) 0 0
\(760\) 1.84847 3.20164i 0.0670510 0.116136i
\(761\) −2.00000 −0.0724999 −0.0362500 0.999343i \(-0.511541\pi\)
−0.0362500 + 0.999343i \(0.511541\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4.10102 −0.148370
\(765\) 0 0
\(766\) 1.44949 + 2.51059i 0.0523722 + 0.0907113i
\(767\) 9.79796 0.353784
\(768\) 0 0
\(769\) 17.0454 + 29.5235i 0.614673 + 1.06465i 0.990442 + 0.137932i \(0.0440454\pi\)
−0.375769 + 0.926714i \(0.622621\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.94949 + 15.5010i 0.322099 + 0.557892i
\(773\) 16.9722 + 29.3967i 0.610447 + 1.05733i 0.991165 + 0.132635i \(0.0423437\pi\)
−0.380718 + 0.924691i \(0.624323\pi\)
\(774\) 0 0
\(775\) 8.69694 15.0635i 0.312403 0.541098i
\(776\) 1.44949 2.51059i 0.0520336 0.0901249i
\(777\) 0 0
\(778\) 12.4495 + 21.5631i 0.446336 + 0.773076i
\(779\) −24.9898 −0.895352
\(780\) 0 0
\(781\) 0.202041 0.00722960
\(782\) −1.00000 + 1.73205i −0.0357599 + 0.0619380i
\(783\) 0 0
\(784\) 0 0
\(785\) 6.05051 10.4798i 0.215952 0.374040i
\(786\) 0 0
\(787\) 5.69694 9.86739i 0.203074 0.351734i −0.746443 0.665449i \(-0.768240\pi\)
0.949517 + 0.313715i \(0.101573\pi\)
\(788\) 8.34847 14.4600i 0.297402 0.515115i
\(789\) 0 0
\(790\) −1.37628 + 2.38378i −0.0489657 + 0.0848111i
\(791\) 0 0
\(792\) 0 0
\(793\) −16.0454 + 27.7915i −0.569789 + 0.986904i
\(794\) −38.6969