Properties

Label 2646.2.m.b.1763.2
Level $2646$
Weight $2$
Character 2646.1763
Analytic conductor $21.128$
Analytic rank $0$
Dimension $16$
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.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + 2785 x^{8} - 2640 x^{7} - 2601 x^{6} + 10260 x^{5} - 10611 x^{4} - 1944 x^{3} + 16767 x^{2} - 17496 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1763.2
Root \(-1.70672 + 0.295146i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1763
Dual form 2646.2.m.b.881.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.483662 - 0.837727i) q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.483662 - 0.837727i) q^{5} -1.00000i q^{8} +0.967324i q^{10} +(4.82689 + 2.78681i) q^{11} +(-3.76893 + 2.17600i) q^{13} +(-0.500000 + 0.866025i) q^{16} +3.94535 q^{17} +4.46634i q^{19} +(0.483662 - 0.837727i) q^{20} +(-2.78681 - 4.82689i) q^{22} +(2.29786 - 1.32667i) q^{23} +(2.03214 - 3.51977i) q^{25} +4.35199 q^{26} +(-4.61157 - 2.66249i) q^{29} +(-5.34038 + 3.08327i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.41677 - 1.97267i) q^{34} -0.487217 q^{37} +(2.23317 - 3.86796i) q^{38} +(-0.837727 + 0.483662i) q^{40} +(-0.0818856 - 0.141830i) q^{41} +(-4.35045 + 7.53520i) q^{43} +5.57361i q^{44} -2.65334 q^{46} +(-4.74500 + 8.21859i) q^{47} +(-3.51977 + 2.03214i) q^{50} +(-3.76893 - 2.17600i) q^{52} -2.01518i q^{53} -5.39149i q^{55} +(2.66249 + 4.61157i) q^{58} +(0.836931 + 1.44961i) q^{59} +(-4.47927 - 2.58611i) q^{61} +6.16655 q^{62} -1.00000 q^{64} +(3.64578 + 2.10489i) q^{65} +(2.72126 + 4.71336i) q^{67} +(1.97267 + 3.41677i) q^{68} +3.64006i q^{71} +2.48801i q^{73} +(0.421942 + 0.243608i) q^{74} +(-3.86796 + 2.23317i) q^{76} +(-2.30121 + 3.98581i) q^{79} +0.967324 q^{80} +0.163771i q^{82} +(4.20979 - 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +(7.53520 - 4.35045i) q^{86} +(2.78681 - 4.82689i) q^{88} -4.11622 q^{89} +(2.29786 + 1.32667i) q^{92} +(8.21859 - 4.74500i) q^{94} +(3.74157 - 2.16020i) q^{95} +(10.2669 + 5.92762i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + O(q^{10}) \) \( 16 q + 8 q^{4} + 12 q^{11} + 6 q^{13} - 8 q^{16} - 36 q^{17} - 6 q^{23} - 8 q^{25} + 24 q^{26} - 6 q^{29} + 6 q^{31} + 4 q^{37} + 6 q^{41} - 2 q^{43} - 12 q^{46} - 18 q^{47} + 12 q^{50} + 6 q^{52} + 6 q^{58} + 30 q^{59} - 60 q^{61} - 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} - 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{89} - 6 q^{92} - 66 q^{95} + 6 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.483662 0.837727i −0.216300 0.374643i 0.737374 0.675485i \(-0.236066\pi\)
−0.953674 + 0.300842i \(0.902732\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.967324i 0.305895i
\(11\) 4.82689 + 2.78681i 1.45536 + 0.840254i 0.998778 0.0494264i \(-0.0157393\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(12\) 0 0
\(13\) −3.76893 + 2.17600i −1.04531 + 0.603512i −0.921334 0.388772i \(-0.872899\pi\)
−0.123980 + 0.992285i \(0.539566\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.94535 0.956887 0.478443 0.878118i \(-0.341201\pi\)
0.478443 + 0.878118i \(0.341201\pi\)
\(18\) 0 0
\(19\) 4.46634i 1.02465i 0.858792 + 0.512324i \(0.171215\pi\)
−0.858792 + 0.512324i \(0.828785\pi\)
\(20\) 0.483662 0.837727i 0.108150 0.187322i
\(21\) 0 0
\(22\) −2.78681 4.82689i −0.594149 1.02910i
\(23\) 2.29786 1.32667i 0.479137 0.276630i −0.240920 0.970545i \(-0.577449\pi\)
0.720057 + 0.693915i \(0.244116\pi\)
\(24\) 0 0
\(25\) 2.03214 3.51977i 0.406428 0.703955i
\(26\) 4.35199 0.853496
\(27\) 0 0
\(28\) 0 0
\(29\) −4.61157 2.66249i −0.856347 0.494412i 0.00644015 0.999979i \(-0.497950\pi\)
−0.862787 + 0.505567i \(0.831283\pi\)
\(30\) 0 0
\(31\) −5.34038 + 3.08327i −0.959161 + 0.553772i −0.895915 0.444226i \(-0.853479\pi\)
−0.0632466 + 0.997998i \(0.520145\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −3.41677 1.97267i −0.585971 0.338311i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.487217 −0.0800980 −0.0400490 0.999198i \(-0.512751\pi\)
−0.0400490 + 0.999198i \(0.512751\pi\)
\(38\) 2.23317 3.86796i 0.362268 0.627466i
\(39\) 0 0
\(40\) −0.837727 + 0.483662i −0.132456 + 0.0764737i
\(41\) −0.0818856 0.141830i −0.0127884 0.0221501i 0.859560 0.511034i \(-0.170737\pi\)
−0.872349 + 0.488884i \(0.837404\pi\)
\(42\) 0 0
\(43\) −4.35045 + 7.53520i −0.663437 + 1.14911i 0.316270 + 0.948669i \(0.397570\pi\)
−0.979707 + 0.200437i \(0.935764\pi\)
\(44\) 5.57361i 0.840254i
\(45\) 0 0
\(46\) −2.65334 −0.391214
\(47\) −4.74500 + 8.21859i −0.692130 + 1.19880i 0.279009 + 0.960289i \(0.409994\pi\)
−0.971139 + 0.238516i \(0.923339\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −3.51977 + 2.03214i −0.497771 + 0.287388i
\(51\) 0 0
\(52\) −3.76893 2.17600i −0.522657 0.301756i
\(53\) 2.01518i 0.276807i −0.990376 0.138403i \(-0.955803\pi\)
0.990376 0.138403i \(-0.0441970\pi\)
\(54\) 0 0
\(55\) 5.39149i 0.726988i
\(56\) 0 0
\(57\) 0 0
\(58\) 2.66249 + 4.61157i 0.349602 + 0.605529i
\(59\) 0.836931 + 1.44961i 0.108959 + 0.188723i 0.915349 0.402662i \(-0.131915\pi\)
−0.806390 + 0.591384i \(0.798582\pi\)
\(60\) 0 0
\(61\) −4.47927 2.58611i −0.573512 0.331117i 0.185039 0.982731i \(-0.440759\pi\)
−0.758551 + 0.651614i \(0.774092\pi\)
\(62\) 6.16655 0.783152
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.64578 + 2.10489i 0.452203 + 0.261080i
\(66\) 0 0
\(67\) 2.72126 + 4.71336i 0.332455 + 0.575828i 0.982993 0.183645i \(-0.0587898\pi\)
−0.650538 + 0.759474i \(0.725456\pi\)
\(68\) 1.97267 + 3.41677i 0.239222 + 0.414344i
\(69\) 0 0
\(70\) 0 0
\(71\) 3.64006i 0.431996i 0.976394 + 0.215998i \(0.0693005\pi\)
−0.976394 + 0.215998i \(0.930700\pi\)
\(72\) 0 0
\(73\) 2.48801i 0.291200i 0.989344 + 0.145600i \(0.0465112\pi\)
−0.989344 + 0.145600i \(0.953489\pi\)
\(74\) 0.421942 + 0.243608i 0.0490498 + 0.0283189i
\(75\) 0 0
\(76\) −3.86796 + 2.23317i −0.443686 + 0.256162i
\(77\) 0 0
\(78\) 0 0
\(79\) −2.30121 + 3.98581i −0.258906 + 0.448438i −0.965949 0.258732i \(-0.916695\pi\)
0.707043 + 0.707170i \(0.250029\pi\)
\(80\) 0.967324 0.108150
\(81\) 0 0
\(82\) 0.163771i 0.0180855i
\(83\) 4.20979 7.29158i 0.462085 0.800355i −0.536980 0.843595i \(-0.680435\pi\)
0.999065 + 0.0432405i \(0.0137682\pi\)
\(84\) 0 0
\(85\) −1.90821 3.30512i −0.206975 0.358491i
\(86\) 7.53520 4.35045i 0.812541 0.469121i
\(87\) 0 0
\(88\) 2.78681 4.82689i 0.297075 0.514548i
\(89\) −4.11622 −0.436318 −0.218159 0.975913i \(-0.570005\pi\)
−0.218159 + 0.975913i \(0.570005\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.29786 + 1.32667i 0.239569 + 0.138315i
\(93\) 0 0
\(94\) 8.21859 4.74500i 0.847683 0.489410i
\(95\) 3.74157 2.16020i 0.383877 0.221632i
\(96\) 0 0
\(97\) 10.2669 + 5.92762i 1.04245 + 0.601859i 0.920526 0.390681i \(-0.127760\pi\)
0.121924 + 0.992539i \(0.461094\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 4.06428 0.406428
\(101\) −2.65813 + 4.60402i −0.264494 + 0.458117i −0.967431 0.253135i \(-0.918538\pi\)
0.702937 + 0.711252i \(0.251872\pi\)
\(102\) 0 0
\(103\) −7.74616 + 4.47225i −0.763252 + 0.440664i −0.830462 0.557075i \(-0.811924\pi\)
0.0672102 + 0.997739i \(0.478590\pi\)
\(104\) 2.17600 + 3.76893i 0.213374 + 0.369574i
\(105\) 0 0
\(106\) −1.00759 + 1.74520i −0.0978659 + 0.169509i
\(107\) 19.1563i 1.85191i −0.377639 0.925953i \(-0.623264\pi\)
0.377639 0.925953i \(-0.376736\pi\)
\(108\) 0 0
\(109\) 19.2434 1.84318 0.921590 0.388164i \(-0.126891\pi\)
0.921590 + 0.388164i \(0.126891\pi\)
\(110\) −2.69574 + 4.66917i −0.257029 + 0.445188i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.31199 + 4.22158i −0.687854 + 0.397133i −0.802808 0.596238i \(-0.796661\pi\)
0.114953 + 0.993371i \(0.463328\pi\)
\(114\) 0 0
\(115\) −2.22278 1.28332i −0.207275 0.119670i
\(116\) 5.32498i 0.494412i
\(117\) 0 0
\(118\) 1.67386i 0.154091i
\(119\) 0 0
\(120\) 0 0
\(121\) 10.0326 + 17.3769i 0.912053 + 1.57972i
\(122\) 2.58611 + 4.47927i 0.234135 + 0.405534i
\(123\) 0 0
\(124\) −5.34038 3.08327i −0.479581 0.276886i
\(125\) −8.76810 −0.784243
\(126\) 0 0
\(127\) 3.31883 0.294498 0.147249 0.989099i \(-0.452958\pi\)
0.147249 + 0.989099i \(0.452958\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −2.10489 3.64578i −0.184611 0.319756i
\(131\) 9.37335 + 16.2351i 0.818954 + 1.41847i 0.906454 + 0.422305i \(0.138779\pi\)
−0.0875000 + 0.996165i \(0.527888\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 5.44252i 0.470162i
\(135\) 0 0
\(136\) 3.94535i 0.338311i
\(137\) 14.6656 + 8.46717i 1.25296 + 0.723399i 0.971697 0.236230i \(-0.0759120\pi\)
0.281267 + 0.959630i \(0.409245\pi\)
\(138\) 0 0
\(139\) −10.5033 + 6.06406i −0.890875 + 0.514347i −0.874229 0.485514i \(-0.838632\pi\)
−0.0166466 + 0.999861i \(0.505299\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.82003 3.15239i 0.152734 0.264543i
\(143\) −24.2563 −2.02841
\(144\) 0 0
\(145\) 5.15098i 0.427766i
\(146\) 1.24401 2.15468i 0.102955 0.178323i
\(147\) 0 0
\(148\) −0.243608 0.421942i −0.0200245 0.0346834i
\(149\) −7.56951 + 4.37026i −0.620118 + 0.358025i −0.776915 0.629606i \(-0.783217\pi\)
0.156797 + 0.987631i \(0.449883\pi\)
\(150\) 0 0
\(151\) −11.0471 + 19.1341i −0.898997 + 1.55711i −0.0702195 + 0.997532i \(0.522370\pi\)
−0.828778 + 0.559578i \(0.810963\pi\)
\(152\) 4.46634 0.362268
\(153\) 0 0
\(154\) 0 0
\(155\) 5.16588 + 2.98252i 0.414934 + 0.239562i
\(156\) 0 0
\(157\) 1.23372 0.712287i 0.0984614 0.0568467i −0.449961 0.893048i \(-0.648562\pi\)
0.548422 + 0.836202i \(0.315229\pi\)
\(158\) 3.98581 2.30121i 0.317094 0.183074i
\(159\) 0 0
\(160\) −0.837727 0.483662i −0.0662282 0.0382368i
\(161\) 0 0
\(162\) 0 0
\(163\) 7.44296 0.582977 0.291489 0.956574i \(-0.405849\pi\)
0.291489 + 0.956574i \(0.405849\pi\)
\(164\) 0.0818856 0.141830i 0.00639419 0.0110751i
\(165\) 0 0
\(166\) −7.29158 + 4.20979i −0.565936 + 0.326743i
\(167\) 3.24855 + 5.62665i 0.251380 + 0.435404i 0.963906 0.266242i \(-0.0857822\pi\)
−0.712526 + 0.701646i \(0.752449\pi\)
\(168\) 0 0
\(169\) 2.96991 5.14404i 0.228455 0.395695i
\(170\) 3.81643i 0.292707i
\(171\) 0 0
\(172\) −8.70089 −0.663437
\(173\) 5.90938 10.2354i 0.449282 0.778179i −0.549057 0.835785i \(-0.685013\pi\)
0.998339 + 0.0576053i \(0.0183465\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.82689 + 2.78681i −0.363841 + 0.210063i
\(177\) 0 0
\(178\) 3.56475 + 2.05811i 0.267189 + 0.154262i
\(179\) 2.43370i 0.181903i −0.995855 0.0909515i \(-0.971009\pi\)
0.995855 0.0909515i \(-0.0289908\pi\)
\(180\) 0 0
\(181\) 11.5342i 0.857327i −0.903464 0.428663i \(-0.858985\pi\)
0.903464 0.428663i \(-0.141015\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.32667 2.29786i −0.0978035 0.169401i
\(185\) 0.235648 + 0.408155i 0.0173252 + 0.0300081i
\(186\) 0 0
\(187\) 19.0438 + 10.9949i 1.39262 + 0.804028i
\(188\) −9.49001 −0.692130
\(189\) 0 0
\(190\) −4.32040 −0.313435
\(191\) 19.1122 + 11.0345i 1.38291 + 0.798425i 0.992503 0.122216i \(-0.0390002\pi\)
0.390409 + 0.920641i \(0.372334\pi\)
\(192\) 0 0
\(193\) 9.96979 + 17.2682i 0.717641 + 1.24299i 0.961932 + 0.273289i \(0.0881116\pi\)
−0.244291 + 0.969702i \(0.578555\pi\)
\(194\) −5.92762 10.2669i −0.425578 0.737123i
\(195\) 0 0
\(196\) 0 0
\(197\) 4.62560i 0.329560i −0.986330 0.164780i \(-0.947309\pi\)
0.986330 0.164780i \(-0.0526914\pi\)
\(198\) 0 0
\(199\) 20.9028i 1.48176i 0.671635 + 0.740882i \(0.265592\pi\)
−0.671635 + 0.740882i \(0.734408\pi\)
\(200\) −3.51977 2.03214i −0.248886 0.143694i
\(201\) 0 0
\(202\) 4.60402 2.65813i 0.323938 0.187025i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.0792099 + 0.137196i −0.00553226 + 0.00958215i
\(206\) 8.94450 0.623193
\(207\) 0 0
\(208\) 4.35199i 0.301756i
\(209\) −12.4468 + 21.5585i −0.860965 + 1.49123i
\(210\) 0 0
\(211\) −3.34310 5.79042i −0.230148 0.398629i 0.727703 0.685892i \(-0.240588\pi\)
−0.957852 + 0.287263i \(0.907254\pi\)
\(212\) 1.74520 1.00759i 0.119861 0.0692017i
\(213\) 0 0
\(214\) −9.57813 + 16.5898i −0.654747 + 1.13406i
\(215\) 8.41658 0.574006
\(216\) 0 0
\(217\) 0 0
\(218\) −16.6652 9.62168i −1.12871 0.651663i
\(219\) 0 0
\(220\) 4.66917 2.69574i 0.314795 0.181747i
\(221\) −14.8697 + 8.58505i −1.00025 + 0.577493i
\(222\) 0 0
\(223\) 7.08622 + 4.09123i 0.474528 + 0.273969i 0.718133 0.695905i \(-0.244997\pi\)
−0.243605 + 0.969875i \(0.578330\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 8.44316 0.561631
\(227\) 5.34688 9.26106i 0.354885 0.614678i −0.632214 0.774794i \(-0.717853\pi\)
0.987098 + 0.160116i \(0.0511868\pi\)
\(228\) 0 0
\(229\) −25.2942 + 14.6036i −1.67149 + 0.965034i −0.704682 + 0.709524i \(0.748910\pi\)
−0.966806 + 0.255510i \(0.917757\pi\)
\(230\) 1.28332 + 2.22278i 0.0846197 + 0.146566i
\(231\) 0 0
\(232\) −2.66249 + 4.61157i −0.174801 + 0.302764i
\(233\) 6.43935i 0.421856i −0.977502 0.210928i \(-0.932352\pi\)
0.977502 0.210928i \(-0.0676485\pi\)
\(234\) 0 0
\(235\) 9.17991 0.598832
\(236\) −0.836931 + 1.44961i −0.0544796 + 0.0943614i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.01452 2.31778i 0.259678 0.149925i −0.364510 0.931200i \(-0.618763\pi\)
0.624187 + 0.781275i \(0.285430\pi\)
\(240\) 0 0
\(241\) −9.08846 5.24722i −0.585439 0.338003i 0.177853 0.984057i \(-0.443085\pi\)
−0.763292 + 0.646054i \(0.776418\pi\)
\(242\) 20.0652i 1.28984i
\(243\) 0 0
\(244\) 5.17221i 0.331117i
\(245\) 0 0
\(246\) 0 0
\(247\) −9.71873 16.8333i −0.618388 1.07108i
\(248\) 3.08327 + 5.34038i 0.195788 + 0.339115i
\(249\) 0 0
\(250\) 7.59340 + 4.38405i 0.480249 + 0.277272i
\(251\) −7.85271 −0.495659 −0.247829 0.968804i \(-0.579717\pi\)
−0.247829 + 0.968804i \(0.579717\pi\)
\(252\) 0 0
\(253\) 14.7887 0.929758
\(254\) −2.87419 1.65941i −0.180343 0.104121i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.71568 + 2.97164i 0.107021 + 0.185366i 0.914562 0.404445i \(-0.132535\pi\)
−0.807541 + 0.589811i \(0.799202\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.20979i 0.261080i
\(261\) 0 0
\(262\) 18.7467i 1.15818i
\(263\) −3.17080 1.83066i −0.195520 0.112883i 0.399044 0.916932i \(-0.369342\pi\)
−0.594564 + 0.804048i \(0.702675\pi\)
\(264\) 0 0
\(265\) −1.68817 + 0.974668i −0.103704 + 0.0598734i
\(266\) 0 0
\(267\) 0 0
\(268\) −2.72126 + 4.71336i −0.166227 + 0.287914i
\(269\) −12.6861 −0.773483 −0.386741 0.922188i \(-0.626399\pi\)
−0.386741 + 0.922188i \(0.626399\pi\)
\(270\) 0 0
\(271\) 19.8766i 1.20742i −0.797206 0.603708i \(-0.793689\pi\)
0.797206 0.603708i \(-0.206311\pi\)
\(272\) −1.97267 + 3.41677i −0.119611 + 0.207172i
\(273\) 0 0
\(274\) −8.46717 14.6656i −0.511520 0.885979i
\(275\) 19.6179 11.3264i 1.18300 0.683006i
\(276\) 0 0
\(277\) 3.73302 6.46579i 0.224296 0.388491i −0.731812 0.681506i \(-0.761325\pi\)
0.956108 + 0.293015i \(0.0946585\pi\)
\(278\) 12.1281 0.727397
\(279\) 0 0
\(280\) 0 0
\(281\) 19.2746 + 11.1282i 1.14983 + 0.663854i 0.948845 0.315741i \(-0.102253\pi\)
0.200983 + 0.979595i \(0.435586\pi\)
\(282\) 0 0
\(283\) 14.0125 8.09012i 0.832957 0.480908i −0.0219073 0.999760i \(-0.506974\pi\)
0.854864 + 0.518852i \(0.173641\pi\)
\(284\) −3.15239 + 1.82003i −0.187060 + 0.107999i
\(285\) 0 0
\(286\) 21.0066 + 12.1282i 1.24215 + 0.717153i
\(287\) 0 0
\(288\) 0 0
\(289\) −1.43425 −0.0843675
\(290\) 2.57549 4.46088i 0.151238 0.261952i
\(291\) 0 0
\(292\) −2.15468 + 1.24401i −0.126093 + 0.0727999i
\(293\) 4.43406 + 7.68002i 0.259041 + 0.448672i 0.965985 0.258597i \(-0.0832603\pi\)
−0.706944 + 0.707269i \(0.749927\pi\)
\(294\) 0 0
\(295\) 0.809584 1.40224i 0.0471358 0.0816416i
\(296\) 0.487217i 0.0283189i
\(297\) 0 0
\(298\) 8.74051 0.506324
\(299\) −5.77366 + 10.0003i −0.333899 + 0.578331i
\(300\) 0 0
\(301\) 0 0
\(302\) 19.1341 11.0471i 1.10104 0.635687i
\(303\) 0 0
\(304\) −3.86796 2.23317i −0.221843 0.128081i
\(305\) 5.00321i 0.286483i
\(306\) 0 0
\(307\) 27.1427i 1.54912i 0.632501 + 0.774559i \(0.282028\pi\)
−0.632501 + 0.774559i \(0.717972\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.98252 5.16588i −0.169396 0.293402i
\(311\) 8.44774 + 14.6319i 0.479028 + 0.829700i 0.999711 0.0240499i \(-0.00765605\pi\)
−0.520683 + 0.853750i \(0.674323\pi\)
\(312\) 0 0
\(313\) 3.70433 + 2.13870i 0.209381 + 0.120886i 0.601024 0.799231i \(-0.294760\pi\)
−0.391643 + 0.920117i \(0.628093\pi\)
\(314\) −1.42457 −0.0803934
\(315\) 0 0
\(316\) −4.60242 −0.258906
\(317\) −5.74123 3.31470i −0.322460 0.186172i 0.330029 0.943971i \(-0.392942\pi\)
−0.652488 + 0.757799i \(0.726275\pi\)
\(318\) 0 0
\(319\) −14.8397 25.7031i −0.830864 1.43910i
\(320\) 0.483662 + 0.837727i 0.0270375 + 0.0468304i
\(321\) 0 0
\(322\) 0 0
\(323\) 17.6212i 0.980472i
\(324\) 0 0
\(325\) 17.6877i 0.981138i
\(326\) −6.44579 3.72148i −0.356999 0.206114i
\(327\) 0 0
\(328\) −0.141830 + 0.0818856i −0.00783125 + 0.00452137i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.378896 0.656267i 0.0208260 0.0360717i −0.855425 0.517927i \(-0.826704\pi\)
0.876251 + 0.481856i \(0.160037\pi\)
\(332\) 8.41959 0.462085
\(333\) 0 0
\(334\) 6.49710i 0.355506i
\(335\) 2.63234 4.55935i 0.143820 0.249104i
\(336\) 0 0
\(337\) 1.01088 + 1.75089i 0.0550660 + 0.0953772i 0.892244 0.451553i \(-0.149130\pi\)
−0.837178 + 0.546930i \(0.815796\pi\)
\(338\) −5.14404 + 2.96991i −0.279799 + 0.161542i
\(339\) 0 0
\(340\) 1.90821 3.30512i 0.103487 0.179245i
\(341\) −34.3699 −1.86124
\(342\) 0 0
\(343\) 0 0
\(344\) 7.53520 + 4.35045i 0.406271 + 0.234560i
\(345\) 0 0
\(346\) −10.2354 + 5.90938i −0.550256 + 0.317690i
\(347\) 18.1572 10.4831i 0.974730 0.562761i 0.0740550 0.997254i \(-0.476406\pi\)
0.900675 + 0.434494i \(0.143073\pi\)
\(348\) 0 0
\(349\) −5.36406 3.09694i −0.287132 0.165776i 0.349516 0.936930i \(-0.386346\pi\)
−0.636648 + 0.771155i \(0.719679\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 5.57361 0.297075
\(353\) −9.41889 + 16.3140i −0.501317 + 0.868306i 0.498682 + 0.866785i \(0.333818\pi\)
−0.999999 + 0.00152110i \(0.999516\pi\)
\(354\) 0 0
\(355\) 3.04938 1.76056i 0.161844 0.0934409i
\(356\) −2.05811 3.56475i −0.109080 0.188931i
\(357\) 0 0
\(358\) −1.21685 + 2.10764i −0.0643124 + 0.111392i
\(359\) 27.7977i 1.46711i 0.679633 + 0.733553i \(0.262139\pi\)
−0.679633 + 0.733553i \(0.737861\pi\)
\(360\) 0 0
\(361\) −0.948177 −0.0499041
\(362\) −5.76708 + 9.98887i −0.303111 + 0.525003i
\(363\) 0 0
\(364\) 0 0
\(365\) 2.08428 1.20336i 0.109096 0.0629866i
\(366\) 0 0
\(367\) 18.8390 + 10.8767i 0.983388 + 0.567759i 0.903291 0.429028i \(-0.141144\pi\)
0.0800968 + 0.996787i \(0.474477\pi\)
\(368\) 2.65334i 0.138315i
\(369\) 0 0
\(370\) 0.471297i 0.0245016i
\(371\) 0 0
\(372\) 0 0
\(373\) −5.86560 10.1595i −0.303709 0.526040i 0.673264 0.739402i \(-0.264892\pi\)
−0.976973 + 0.213362i \(0.931558\pi\)
\(374\) −10.9949 19.0438i −0.568533 0.984729i
\(375\) 0 0
\(376\) 8.21859 + 4.74500i 0.423841 + 0.244705i
\(377\) 23.1743 1.19354
\(378\) 0 0
\(379\) 34.8881 1.79208 0.896041 0.443971i \(-0.146431\pi\)
0.896041 + 0.443971i \(0.146431\pi\)
\(380\) 3.74157 + 2.16020i 0.191939 + 0.110816i
\(381\) 0 0
\(382\) −11.0345 19.1122i −0.564572 0.977867i
\(383\) −5.92412 10.2609i −0.302708 0.524306i 0.674040 0.738695i \(-0.264557\pi\)
−0.976748 + 0.214389i \(0.931224\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 19.9396i 1.01490i
\(387\) 0 0
\(388\) 11.8552i 0.601859i
\(389\) −5.50224 3.17672i −0.278975 0.161066i 0.353984 0.935251i \(-0.384827\pi\)
−0.632959 + 0.774185i \(0.718160\pi\)
\(390\) 0 0
\(391\) 9.06586 5.23418i 0.458480 0.264704i
\(392\) 0 0
\(393\) 0 0
\(394\) −2.31280 + 4.00588i −0.116517 + 0.201814i
\(395\) 4.45203 0.224006
\(396\) 0 0
\(397\) 8.57535i 0.430385i −0.976572 0.215192i \(-0.930962\pi\)
0.976572 0.215192i \(-0.0690378\pi\)
\(398\) 10.4514 18.1024i 0.523883 0.907391i
\(399\) 0 0
\(400\) 2.03214 + 3.51977i 0.101607 + 0.175989i
\(401\) −20.0216 + 11.5595i −0.999833 + 0.577254i −0.908199 0.418539i \(-0.862542\pi\)
−0.0916343 + 0.995793i \(0.529209\pi\)
\(402\) 0 0
\(403\) 13.4184 23.2413i 0.668417 1.15773i
\(404\) −5.31626 −0.264494
\(405\) 0 0
\(406\) 0 0
\(407\) −2.35174 1.35778i −0.116572 0.0673026i
\(408\) 0 0
\(409\) −1.35091 + 0.779947i −0.0667981 + 0.0385659i −0.533027 0.846098i \(-0.678946\pi\)
0.466229 + 0.884664i \(0.345612\pi\)
\(410\) 0.137196 0.0792099i 0.00677561 0.00391190i
\(411\) 0 0
\(412\) −7.74616 4.47225i −0.381626 0.220332i
\(413\) 0 0
\(414\) 0 0
\(415\) −8.14447 −0.399796
\(416\) −2.17600 + 3.76893i −0.106687 + 0.184787i
\(417\) 0 0
\(418\) 21.5585 12.4468i 1.05446 0.608794i
\(419\) −3.40822 5.90321i −0.166502 0.288391i 0.770685 0.637216i \(-0.219914\pi\)
−0.937188 + 0.348825i \(0.886581\pi\)
\(420\) 0 0
\(421\) −6.75727 + 11.7039i −0.329329 + 0.570415i −0.982379 0.186900i \(-0.940156\pi\)
0.653050 + 0.757315i \(0.273489\pi\)
\(422\) 6.68620i 0.325479i
\(423\) 0 0
\(424\) −2.01518 −0.0978659
\(425\) 8.01750 13.8867i 0.388906 0.673605i
\(426\) 0 0
\(427\) 0 0
\(428\) 16.5898 9.57813i 0.801899 0.462976i
\(429\) 0 0
\(430\) −7.28898 4.20829i −0.351506 0.202942i
\(431\) 14.1598i 0.682054i 0.940053 + 0.341027i \(0.110775\pi\)
−0.940053 + 0.341027i \(0.889225\pi\)
\(432\) 0 0
\(433\) 23.4830i 1.12852i −0.825597 0.564260i \(-0.809161\pi\)
0.825597 0.564260i \(-0.190839\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9.62168 + 16.6652i 0.460795 + 0.798121i
\(437\) 5.92536 + 10.2630i 0.283449 + 0.490947i
\(438\) 0 0
\(439\) 3.66398 + 2.11540i 0.174872 + 0.100963i 0.584881 0.811119i \(-0.301141\pi\)
−0.410009 + 0.912081i \(0.634474\pi\)
\(440\) −5.39149 −0.257029
\(441\) 0 0
\(442\) 17.1701 0.816699
\(443\) −25.8161 14.9049i −1.22656 0.708154i −0.260250 0.965541i \(-0.583805\pi\)
−0.966308 + 0.257388i \(0.917138\pi\)
\(444\) 0 0
\(445\) 1.99086 + 3.44827i 0.0943757 + 0.163464i
\(446\) −4.09123 7.08622i −0.193725 0.335542i
\(447\) 0 0
\(448\) 0 0
\(449\) 8.41716i 0.397230i 0.980078 + 0.198615i \(0.0636444\pi\)
−0.980078 + 0.198615i \(0.936356\pi\)
\(450\) 0 0
\(451\) 0.912797i 0.0429819i
\(452\) −7.31199 4.22158i −0.343927 0.198566i
\(453\) 0 0
\(454\) −9.26106 + 5.34688i −0.434643 + 0.250941i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.94109 3.36207i 0.0908006 0.157271i −0.817048 0.576570i \(-0.804391\pi\)
0.907848 + 0.419299i \(0.137724\pi\)
\(458\) 29.2072 1.36476
\(459\) 0 0
\(460\) 2.56664i 0.119670i
\(461\) 17.0423 29.5181i 0.793739 1.37480i −0.129898 0.991527i \(-0.541465\pi\)
0.923637 0.383269i \(-0.125202\pi\)
\(462\) 0 0
\(463\) −6.10962 10.5822i −0.283938 0.491796i 0.688413 0.725319i \(-0.258308\pi\)
−0.972351 + 0.233523i \(0.924974\pi\)
\(464\) 4.61157 2.66249i 0.214087 0.123603i
\(465\) 0 0
\(466\) −3.21967 + 5.57664i −0.149148 + 0.258333i
\(467\) 30.8115 1.42579 0.712893 0.701273i \(-0.247385\pi\)
0.712893 + 0.701273i \(0.247385\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −7.95004 4.58996i −0.366708 0.211719i
\(471\) 0 0
\(472\) 1.44961 0.836931i 0.0667236 0.0385229i
\(473\) −41.9983 + 24.2477i −1.93108 + 1.11491i
\(474\) 0 0
\(475\) 15.7205 + 9.07623i 0.721306 + 0.416446i
\(476\) 0 0
\(477\) 0 0
\(478\) −4.63557 −0.212026
\(479\) 20.8747 36.1560i 0.953788 1.65201i 0.216670 0.976245i \(-0.430481\pi\)
0.737118 0.675764i \(-0.236186\pi\)
\(480\) 0 0
\(481\) 1.83629 1.06018i 0.0837276 0.0483401i
\(482\) 5.24722 + 9.08846i 0.239004 + 0.413968i
\(483\) 0 0
\(484\) −10.0326 + 17.3769i −0.456026 + 0.789861i
\(485\) 11.4679i 0.520729i
\(486\) 0 0
\(487\) −21.1663 −0.959137 −0.479568 0.877504i \(-0.659207\pi\)
−0.479568 + 0.877504i \(0.659207\pi\)
\(488\) −2.58611 + 4.47927i −0.117068 + 0.202767i
\(489\) 0 0
\(490\) 0 0
\(491\) −32.3428 + 18.6731i −1.45961 + 0.842707i −0.998992 0.0448915i \(-0.985706\pi\)
−0.460619 + 0.887598i \(0.652372\pi\)
\(492\) 0 0
\(493\) −18.1942 10.5044i −0.819427 0.473097i
\(494\) 19.4375i 0.874533i
\(495\) 0 0
\(496\) 6.16655i 0.276886i
\(497\) 0 0
\(498\) 0 0
\(499\) −13.7099 23.7462i −0.613738 1.06303i −0.990605 0.136758i \(-0.956332\pi\)
0.376867 0.926267i \(-0.377001\pi\)
\(500\) −4.38405 7.59340i −0.196061 0.339587i
\(501\) 0 0
\(502\) 6.80065 + 3.92635i 0.303528 + 0.175242i
\(503\) 11.2791 0.502909 0.251454 0.967869i \(-0.419091\pi\)
0.251454 + 0.967869i \(0.419091\pi\)
\(504\) 0 0
\(505\) 5.14255 0.228840
\(506\) −12.8074 7.39435i −0.569358 0.328719i
\(507\) 0 0
\(508\) 1.65941 + 2.87419i 0.0736246 + 0.127522i
\(509\) −9.31667 16.1370i −0.412954 0.715258i 0.582257 0.813005i \(-0.302170\pi\)
−0.995211 + 0.0977470i \(0.968836\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.43136i 0.151351i
\(515\) 7.49305 + 4.32611i 0.330183 + 0.190631i
\(516\) 0 0
\(517\) −45.8072 + 26.4468i −2.01460 + 1.16313i
\(518\) 0 0
\(519\) 0 0
\(520\) 2.10489 3.64578i 0.0923056 0.159878i
\(521\) −15.2851 −0.669652 −0.334826 0.942280i \(-0.608678\pi\)
−0.334826 + 0.942280i \(0.608678\pi\)
\(522\) 0 0
\(523\) 36.4875i 1.59549i −0.602997 0.797743i \(-0.706027\pi\)
0.602997 0.797743i \(-0.293973\pi\)
\(524\) −9.37335 + 16.2351i −0.409477 + 0.709235i
\(525\) 0 0
\(526\) 1.83066 + 3.17080i 0.0798207 + 0.138253i
\(527\) −21.0697 + 12.1646i −0.917809 + 0.529897i
\(528\) 0 0
\(529\) −7.97989 + 13.8216i −0.346952 + 0.600938i
\(530\) 1.94934 0.0846737
\(531\) 0 0
\(532\) 0 0
\(533\) 0.617243 + 0.356365i 0.0267358 + 0.0154359i
\(534\) 0 0
\(535\) −16.0477 + 9.26516i −0.693803 + 0.400568i
\(536\) 4.71336 2.72126i 0.203586 0.117540i
\(537\) 0 0
\(538\) 10.9865 + 6.34303i 0.473660 + 0.273467i
\(539\) 0 0
\(540\) 0 0
\(541\) −5.27293 −0.226701 −0.113351 0.993555i \(-0.536158\pi\)
−0.113351 + 0.993555i \(0.536158\pi\)
\(542\) −9.93828 + 17.2136i −0.426886 + 0.739388i
\(543\) 0 0
\(544\) 3.41677 1.97267i 0.146493 0.0845776i
\(545\) −9.30729 16.1207i −0.398680 0.690535i
\(546\) 0 0
\(547\) −9.29831 + 16.1051i −0.397567 + 0.688606i −0.993425 0.114484i \(-0.963479\pi\)
0.595858 + 0.803090i \(0.296812\pi\)
\(548\) 16.9343i 0.723399i
\(549\) 0 0
\(550\) −22.6527 −0.965916
\(551\) 11.8916 20.5968i 0.506599 0.877455i
\(552\) 0 0
\(553\) 0 0
\(554\) −6.46579 + 3.73302i −0.274705 + 0.158601i
\(555\) 0 0
\(556\) −10.5033 6.06406i −0.445438 0.257174i
\(557\) 27.5620i 1.16784i 0.811811 + 0.583920i \(0.198482\pi\)
−0.811811 + 0.583920i \(0.801518\pi\)
\(558\) 0 0
\(559\) 37.8662i 1.60157i
\(560\) 0 0
\(561\) 0 0
\(562\) −11.1282 19.2746i −0.469416 0.813052i
\(563\) −9.42577 16.3259i −0.397249 0.688055i 0.596137 0.802883i \(-0.296702\pi\)
−0.993385 + 0.114828i \(0.963368\pi\)
\(564\) 0 0
\(565\) 7.07306 + 4.08364i 0.297566 + 0.171800i
\(566\) −16.1802 −0.680106
\(567\) 0 0
\(568\) 3.64006 0.152734
\(569\) 3.87103 + 2.23494i 0.162282 + 0.0936936i 0.578942 0.815369i \(-0.303466\pi\)
−0.416659 + 0.909063i \(0.636799\pi\)
\(570\) 0 0
\(571\) −9.31245 16.1296i −0.389714 0.675004i 0.602697 0.797970i \(-0.294093\pi\)
−0.992411 + 0.122966i \(0.960759\pi\)
\(572\) −12.1282 21.0066i −0.507104 0.878329i
\(573\) 0 0
\(574\) 0 0
\(575\) 10.7839i 0.449721i
\(576\) 0 0
\(577\) 36.8833i 1.53547i −0.640767 0.767735i \(-0.721384\pi\)
0.640767 0.767735i \(-0.278616\pi\)
\(578\) 1.24210 + 0.717124i 0.0516644 + 0.0298284i
\(579\) 0 0
\(580\) −4.46088 + 2.57549i −0.185228 + 0.106941i
\(581\) 0 0
\(582\) 0 0
\(583\) 5.61593 9.72707i 0.232588 0.402854i
\(584\) 2.48801 0.102955
\(585\) 0 0
\(586\) 8.86813i 0.366339i
\(587\) −13.2295 + 22.9141i −0.546039 + 0.945766i 0.452502 + 0.891763i \(0.350531\pi\)
−0.998541 + 0.0540032i \(0.982802\pi\)
\(588\) 0 0
\(589\) −13.7709 23.8520i −0.567422 0.982803i
\(590\) −1.40224 + 0.809584i −0.0577293 + 0.0333300i
\(591\) 0 0
\(592\) 0.243608 0.421942i 0.0100122 0.0173417i
\(593\) −34.6703 −1.42374 −0.711869 0.702312i \(-0.752151\pi\)
−0.711869 + 0.702312i \(0.752151\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −7.56951 4.37026i −0.310059 0.179013i
\(597\) 0 0
\(598\) 10.0003 5.77366i 0.408942 0.236103i
\(599\) 21.2079 12.2444i 0.866530 0.500291i 0.000336253 1.00000i \(-0.499893\pi\)
0.866193 + 0.499709i \(0.166560\pi\)
\(600\) 0 0
\(601\) −19.3812 11.1898i −0.790577 0.456440i 0.0495885 0.998770i \(-0.484209\pi\)
−0.840166 + 0.542330i \(0.817542\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −22.0941 −0.898997
\(605\) 9.70476 16.8091i 0.394554 0.683388i
\(606\) 0 0
\(607\) 28.2180 16.2917i 1.14533 0.661259i 0.197589 0.980285i \(-0.436689\pi\)
0.947746 + 0.319026i \(0.103356\pi\)
\(608\) 2.23317 + 3.86796i 0.0905670 + 0.156867i
\(609\) 0 0
\(610\) 2.50160 4.33290i 0.101287 0.175434i
\(611\) 41.3004i 1.67084i
\(612\) 0 0
\(613\) −11.7386 −0.474118 −0.237059 0.971495i \(-0.576183\pi\)
−0.237059 + 0.971495i \(0.576183\pi\)
\(614\) 13.5714 23.5063i 0.547696 0.948637i
\(615\) 0 0
\(616\) 0 0
\(617\) 38.1947 22.0517i 1.53766 0.887770i 0.538687 0.842506i \(-0.318920\pi\)
0.998975 0.0452639i \(-0.0144129\pi\)
\(618\) 0 0
\(619\) 4.28374 + 2.47322i 0.172178 + 0.0994070i 0.583612 0.812032i \(-0.301639\pi\)
−0.411434 + 0.911439i \(0.634972\pi\)
\(620\) 5.96505i 0.239562i
\(621\) 0 0
\(622\) 16.8955i 0.677447i
\(623\) 0 0
\(624\) 0 0
\(625\) −5.91991 10.2536i −0.236797 0.410144i
\(626\) −2.13870 3.70433i −0.0854795 0.148055i
\(627\) 0 0
\(628\) 1.23372 + 0.712287i 0.0492307 + 0.0284233i
\(629\) −1.92224 −0.0766447
\(630\) 0 0
\(631\) −9.08478 −0.361659 −0.180830 0.983514i \(-0.557878\pi\)
−0.180830 + 0.983514i \(0.557878\pi\)
\(632\) 3.98581 + 2.30121i 0.158547 + 0.0915371i
\(633\) 0 0
\(634\) 3.31470 + 5.74123i 0.131644 + 0.228013i
\(635\) −1.60519 2.78027i −0.0637001 0.110332i
\(636\) 0 0
\(637\) 0 0
\(638\) 29.6794i 1.17502i
\(639\) 0 0
\(640\) 0.967324i 0.0382368i
\(641\) −12.1954 7.04105i −0.481691 0.278105i 0.239430 0.970914i \(-0.423040\pi\)
−0.721121 + 0.692809i \(0.756373\pi\)
\(642\) 0 0
\(643\) 7.33157 4.23288i 0.289129 0.166929i −0.348420 0.937339i \(-0.613282\pi\)
0.637549 + 0.770410i \(0.279948\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8.81062 15.2604i 0.346649 0.600414i
\(647\) −24.3324 −0.956607 −0.478304 0.878195i \(-0.658748\pi\)
−0.478304 + 0.878195i \(0.658748\pi\)
\(648\) 0 0
\(649\) 9.32946i 0.366213i
\(650\) 8.84386 15.3180i 0.346885 0.600822i
\(651\) 0 0
\(652\) 3.72148 + 6.44579i 0.145744 + 0.252437i
\(653\) −36.0653 + 20.8223i −1.41134 + 0.814840i −0.995515 0.0946029i \(-0.969842\pi\)
−0.415829 + 0.909443i \(0.636509\pi\)
\(654\) 0 0
\(655\) 9.06707 15.7046i 0.354280 0.613631i
\(656\) 0.163771 0.00639419
\(657\) 0 0
\(658\) 0 0
\(659\) 9.09866 + 5.25312i 0.354434 + 0.204632i 0.666636 0.745383i \(-0.267733\pi\)
−0.312203 + 0.950016i \(0.601067\pi\)
\(660\) 0 0
\(661\) −16.8988 + 9.75655i −0.657289 + 0.379486i −0.791243 0.611502i \(-0.790566\pi\)
0.133954 + 0.990987i \(0.457232\pi\)
\(662\) −0.656267 + 0.378896i −0.0255065 + 0.0147262i
\(663\) 0 0
\(664\) −7.29158 4.20979i −0.282968 0.163372i
\(665\) 0 0
\(666\) 0 0
\(667\) −14.1290 −0.547077
\(668\) −3.24855 + 5.62665i −0.125690 + 0.217702i
\(669\) 0 0
\(670\) −4.55935 + 2.63234i −0.176143 + 0.101696i
\(671\) −14.4140 24.9657i −0.556445 0.963790i
\(672\) 0 0
\(673\) −3.10277 + 5.37415i −0.119603 + 0.207158i −0.919610 0.392832i \(-0.871495\pi\)
0.800007 + 0.599990i \(0.204829\pi\)
\(674\) 2.02176i 0.0778751i
\(675\) 0 0
\(676\) 5.93982 0.228455
\(677\) 12.3765 21.4368i 0.475669 0.823883i −0.523942 0.851754i \(-0.675539\pi\)
0.999612 + 0.0278703i \(0.00887255\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.30512 + 1.90821i −0.126746 + 0.0731767i
\(681\) 0 0
\(682\) 29.7652 + 17.1850i 1.13977 + 0.658046i
\(683\) 21.1448i 0.809083i −0.914520 0.404542i \(-0.867431\pi\)
0.914520 0.404542i \(-0.132569\pi\)
\(684\) 0 0
\(685\) 16.3810i 0.625886i
\(686\) 0 0
\(687\) 0 0
\(688\) −4.35045 7.53520i −0.165859 0.287277i
\(689\) 4.38503 + 7.59509i 0.167056 + 0.289350i
\(690\) 0 0
\(691\) 5.58127 + 3.22235i 0.212322 + 0.122584i 0.602390 0.798202i \(-0.294215\pi\)
−0.390068 + 0.920786i \(0.627549\pi\)
\(692\) 11.8188 0.449282
\(693\) 0 0
\(694\) −20.9661 −0.795864
\(695\) 10.1601 + 5.86591i 0.385393 + 0.222507i
\(696\) 0 0
\(697\) −0.323067 0.559568i −0.0122370 0.0211952i
\(698\) 3.09694 + 5.36406i 0.117221 + 0.203033i
\(699\) 0 0
\(700\) 0 0
\(701\) 24.5717i 0.928061i −0.885819 0.464031i \(-0.846403\pi\)
0.885819 0.464031i \(-0.153597\pi\)
\(702\) 0 0
\(703\) 2.17608i 0.0820723i
\(704\) −4.82689 2.78681i −0.181920 0.105032i
\(705\) 0 0
\(706\) 16.3140 9.41889i 0.613985 0.354484i
\(707\) 0 0
\(708\) 0 0
\(709\) −22.1370 + 38.3424i −0.831373 + 1.43998i 0.0655765 + 0.997848i \(0.479111\pi\)
−0.896950 + 0.442133i \(0.854222\pi\)
\(710\) −3.52112 −0.132145
\(711\) 0 0
\(712\) 4.11622i 0.154262i
\(713\) −8.18098 + 14.1699i −0.306380 + 0.530666i
\(714\) 0 0
\(715\) 11.7319 + 20.3202i 0.438747 + 0.759931i
\(716\) 2.10764 1.21685i 0.0787663 0.0454757i
\(717\) 0 0
\(718\) 13.8988 24.0735i 0.518700 0.898415i
\(719\) 4.44867 0.165907 0.0829537 0.996553i \(-0.473565\pi\)
0.0829537 + 0.996553i \(0.473565\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.821146 + 0.474089i 0.0305599 + 0.0176438i
\(723\) 0 0
\(724\) 9.98887 5.76708i 0.371233 0.214332i
\(725\) −18.7427 + 10.8211i −0.696088 + 0.401886i
\(726\) 0 0
\(727\) 30.4270 + 17.5670i 1.12848 + 0.651525i 0.943551 0.331227i \(-0.107463\pi\)
0.184924 + 0.982753i \(0.440796\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2.40671 −0.0890765
\(731\) −17.1640 + 29.7289i −0.634834 + 1.09956i
\(732\) 0 0
\(733\) 5.03789 2.90863i 0.186079 0.107433i −0.404067 0.914729i \(-0.632404\pi\)
0.590145 + 0.807297i \(0.299070\pi\)
\(734\) −10.8767 18.8390i −0.401467 0.695360i
\(735\) 0 0
\(736\) 1.32667 2.29786i 0.0489018 0.0847003i
\(737\) 30.3345i 1.11739i
\(738\) 0 0
\(739\) 11.0335 0.405874 0.202937 0.979192i \(-0.434951\pi\)
0.202937 + 0.979192i \(0.434951\pi\)
\(740\) −0.235648 + 0.408155i −0.00866261 + 0.0150041i
\(741\) 0 0
\(742\) 0 0
\(743\) 0.543196 0.313615i 0.0199279 0.0115054i −0.490003 0.871721i \(-0.663004\pi\)
0.509931 + 0.860215i \(0.329671\pi\)
\(744\) 0 0
\(745\) 7.32216 + 4.22745i 0.268263 + 0.154882i
\(746\) 11.7312i 0.429510i
\(747\) 0 0
\(748\) 21.9898i 0.804028i
\(749\) 0 0
\(750\) 0 0
\(751\) −2.23529 3.87163i −0.0815668 0.141278i 0.822356 0.568973i \(-0.192659\pi\)
−0.903923 + 0.427695i \(0.859326\pi\)
\(752\) −4.74500 8.21859i −0.173033 0.299701i
\(753\) 0 0
\(754\) −20.0695 11.5871i −0.730889 0.421979i
\(755\) 21.3722 0.777813
\(756\) 0 0
\(757\) 5.75624 0.209214 0.104607 0.994514i \(-0.466642\pi\)
0.104607 + 0.994514i \(0.466642\pi\)
\(758\) −30.2140 17.4441i −1.09742 0.633597i
\(759\) 0 0
\(760\) −2.16020 3.74157i −0.0783586 0.135721i
\(761\) 10.4970 + 18.1813i 0.380516 + 0.659073i 0.991136 0.132851i \(-0.0424131\pi\)
−0.610620 + 0.791924i \(0.709080\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 22.0689i 0.798425i
\(765\) 0 0
\(766\) 11.8482i 0.428094i
\(767\) −6.30868 3.64232i −0.227793 0.131516i
\(768\) 0 0
\(769\) 34.1729 19.7298i 1.23231 0.711473i 0.264797 0.964304i \(-0.414695\pi\)
0.967511 + 0.252831i \(0.0813616\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −9.96979 + 17.2682i −0.358821 + 0.621496i
\(773\) 34.6328 1.24566 0.622829 0.782358i \(-0.285983\pi\)
0.622829 + 0.782358i \(0.285983\pi\)
\(774\) 0 0
\(775\) 25.0626i 0.900275i
\(776\) 5.92762 10.2669i 0.212789 0.368562i
\(777\) 0 0
\(778\) 3.17672 + 5.50224i 0.113891 + 0.197265i
\(779\) 0.633461 0.365729i 0.0226961 0.0131036i
\(780\) 0 0
\(781\) −10.1442 + 17.5702i −0.362986 + 0.628711i
\(782\) −10.4684 −0.374348
\(783\) 0 0
\(784\) 0 0
\(785\) −1.19340 0.689012i −0.0425944 0.0245919i
\(786\) 0 0
\(787\) 30.5793 17.6550i 1.09003 0.629332i 0.156449 0.987686i \(-0.449995\pi\)
0.933586 + 0.358355i \(0.116662\pi\)
\(788\) 4.00588 2.31280i 0.142704 0.0823900i
\(789\) 0 0
\(790\) −3.85557 2.22601i −0.137175 0.0791980i
\(791\) 0 0
\(792\) 0 0
\(793\) 22.5094 0.799333