Properties

Label 252.2.x.a.41.2
Level $252$
Weight $2$
Character 252.41
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 3 x^{14} - 9 x^{12} - 9 x^{10} + 225 x^{8} - 81 x^{6} - 729 x^{4} - 2187 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.2
Root \(1.69483 - 0.357142i\) of defining polynomial
Character \(\chi\) \(=\) 252.41
Dual form 252.2.x.a.209.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.15671 - 1.28920i) q^{3} +(-1.21244 + 2.10001i) q^{5} +(1.57244 + 2.12778i) q^{7} +(-0.324049 + 2.98245i) q^{9} +O(q^{10})\) \(q+(-1.15671 - 1.28920i) q^{3} +(-1.21244 + 2.10001i) q^{5} +(1.57244 + 2.12778i) q^{7} +(-0.324049 + 2.98245i) q^{9} +(2.09680 - 1.21059i) q^{11} +(4.73574 + 2.73418i) q^{13} +(4.10976 - 0.866025i) q^{15} -2.58069 q^{17} -0.402708i q^{19} +(0.924268 - 4.48840i) q^{21} +(3.06895 + 1.77186i) q^{23} +(-0.440020 - 0.762137i) q^{25} +(4.21979 - 3.03206i) q^{27} +(-6.31784 + 3.64761i) q^{29} +(3.63732 + 2.10001i) q^{31} +(-3.98607 - 1.30289i) q^{33} +(-6.37484 + 0.722330i) q^{35} -3.19360 q^{37} +(-1.95298 - 9.26794i) q^{39} +(-4.03924 + 6.99618i) q^{41} +(-4.22573 - 7.31918i) q^{43} +(-5.87027 - 4.29654i) q^{45} +(2.25769 + 3.91043i) q^{47} +(-2.05488 + 6.69160i) q^{49} +(2.98510 + 3.32701i) q^{51} -14.0288i q^{53} +5.87106i q^{55} +(-0.519169 + 0.465816i) q^{57} +(0.0779043 - 0.134934i) q^{59} +(10.2288 - 5.90561i) q^{61} +(-6.85553 + 4.00021i) q^{63} +(-11.4836 + 6.63005i) q^{65} +(2.53682 - 4.39390i) q^{67} +(-1.26561 - 6.00600i) q^{69} -8.73987i q^{71} -8.80274i q^{73} +(-0.473569 + 1.44884i) q^{75} +(5.87296 + 2.55795i) q^{77} +(5.66575 + 9.81337i) q^{79} +(-8.78998 - 1.93292i) q^{81} +(-7.50937 - 13.0066i) q^{83} +(3.12893 - 5.41946i) q^{85} +(12.0104 + 3.92571i) q^{87} +15.6668 q^{89} +(1.62893 + 14.3759i) q^{91} +(-1.50000 - 7.11831i) q^{93} +(0.845690 + 0.488259i) q^{95} +(-4.97713 + 2.87355i) q^{97} +(2.93105 + 6.64589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + O(q^{10}) \) \( 16q - q^{7} + 6q^{11} - 12q^{15} + 9q^{21} + 6q^{23} - 8q^{25} - 12q^{29} + 4q^{37} + 18q^{39} + 4q^{43} - 5q^{49} - 18q^{51} - 42q^{57} - 27q^{63} - 24q^{65} + 14q^{67} - 21q^{77} + 20q^{79} - 36q^{81} + 6q^{85} - 18q^{91} - 24q^{93} - 60q^{95} + 90q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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 0
\(3\) −1.15671 1.28920i −0.667826 0.744317i
\(4\) 0 0
\(5\) −1.21244 + 2.10001i −0.542220 + 0.939152i 0.456557 + 0.889694i \(0.349083\pi\)
−0.998776 + 0.0494574i \(0.984251\pi\)
\(6\) 0 0
\(7\) 1.57244 + 2.12778i 0.594326 + 0.804224i
\(8\) 0 0
\(9\) −0.324049 + 2.98245i −0.108016 + 0.994149i
\(10\) 0 0
\(11\) 2.09680 1.21059i 0.632209 0.365006i −0.149398 0.988777i \(-0.547733\pi\)
0.781607 + 0.623771i \(0.214400\pi\)
\(12\) 0 0
\(13\) 4.73574 + 2.73418i 1.31346 + 0.758325i 0.982667 0.185380i \(-0.0593516\pi\)
0.330790 + 0.943704i \(0.392685\pi\)
\(14\) 0 0
\(15\) 4.10976 0.866025i 1.06114 0.223607i
\(16\) 0 0
\(17\) −2.58069 −0.625909 −0.312954 0.949768i \(-0.601319\pi\)
−0.312954 + 0.949768i \(0.601319\pi\)
\(18\) 0 0
\(19\) 0.402708i 0.0923876i −0.998932 0.0461938i \(-0.985291\pi\)
0.998932 0.0461938i \(-0.0147092\pi\)
\(20\) 0 0
\(21\) 0.924268 4.48840i 0.201692 0.979449i
\(22\) 0 0
\(23\) 3.06895 + 1.77186i 0.639920 + 0.369458i 0.784584 0.620023i \(-0.212877\pi\)
−0.144664 + 0.989481i \(0.546210\pi\)
\(24\) 0 0
\(25\) −0.440020 0.762137i −0.0880040 0.152427i
\(26\) 0 0
\(27\) 4.21979 3.03206i 0.812098 0.583520i
\(28\) 0 0
\(29\) −6.31784 + 3.64761i −1.17319 + 0.677343i −0.954430 0.298435i \(-0.903535\pi\)
−0.218763 + 0.975778i \(0.570202\pi\)
\(30\) 0 0
\(31\) 3.63732 + 2.10001i 0.653282 + 0.377172i 0.789712 0.613477i \(-0.210230\pi\)
−0.136431 + 0.990650i \(0.543563\pi\)
\(32\) 0 0
\(33\) −3.98607 1.30289i −0.693887 0.226804i
\(34\) 0 0
\(35\) −6.37484 + 0.722330i −1.07754 + 0.122096i
\(36\) 0 0
\(37\) −3.19360 −0.525025 −0.262513 0.964929i \(-0.584551\pi\)
−0.262513 + 0.964929i \(0.584551\pi\)
\(38\) 0 0
\(39\) −1.95298 9.26794i −0.312727 1.48406i
\(40\) 0 0
\(41\) −4.03924 + 6.99618i −0.630824 + 1.09262i 0.356560 + 0.934273i \(0.383950\pi\)
−0.987384 + 0.158346i \(0.949384\pi\)
\(42\) 0 0
\(43\) −4.22573 7.31918i −0.644418 1.11616i −0.984436 0.175745i \(-0.943766\pi\)
0.340018 0.940419i \(-0.389567\pi\)
\(44\) 0 0
\(45\) −5.87027 4.29654i −0.875088 0.640491i
\(46\) 0 0
\(47\) 2.25769 + 3.91043i 0.329317 + 0.570395i 0.982377 0.186912i \(-0.0598480\pi\)
−0.653059 + 0.757307i \(0.726515\pi\)
\(48\) 0 0
\(49\) −2.05488 + 6.69160i −0.293554 + 0.955943i
\(50\) 0 0
\(51\) 2.98510 + 3.32701i 0.417998 + 0.465875i
\(52\) 0 0
\(53\) 14.0288i 1.92701i −0.267690 0.963505i \(-0.586260\pi\)
0.267690 0.963505i \(-0.413740\pi\)
\(54\) 0 0
\(55\) 5.87106i 0.791654i
\(56\) 0 0
\(57\) −0.519169 + 0.465816i −0.0687657 + 0.0616989i
\(58\) 0 0
\(59\) 0.0779043 0.134934i 0.0101423 0.0175669i −0.860910 0.508758i \(-0.830105\pi\)
0.871052 + 0.491191i \(0.163438\pi\)
\(60\) 0 0
\(61\) 10.2288 5.90561i 1.30967 0.756136i 0.327626 0.944808i \(-0.393752\pi\)
0.982040 + 0.188672i \(0.0604182\pi\)
\(62\) 0 0
\(63\) −6.85553 + 4.00021i −0.863716 + 0.503979i
\(64\) 0 0
\(65\) −11.4836 + 6.63005i −1.42436 + 0.822357i
\(66\) 0 0
\(67\) 2.53682 4.39390i 0.309922 0.536801i −0.668423 0.743781i \(-0.733030\pi\)
0.978345 + 0.206981i \(0.0663637\pi\)
\(68\) 0 0
\(69\) −1.26561 6.00600i −0.152361 0.723037i
\(70\) 0 0
\(71\) 8.73987i 1.03723i −0.855007 0.518616i \(-0.826448\pi\)
0.855007 0.518616i \(-0.173552\pi\)
\(72\) 0 0
\(73\) 8.80274i 1.03028i −0.857105 0.515141i \(-0.827739\pi\)
0.857105 0.515141i \(-0.172261\pi\)
\(74\) 0 0
\(75\) −0.473569 + 1.44884i −0.0546830 + 0.167298i
\(76\) 0 0
\(77\) 5.87296 + 2.55795i 0.669285 + 0.291506i
\(78\) 0 0
\(79\) 5.66575 + 9.81337i 0.637447 + 1.10409i 0.985991 + 0.166798i \(0.0533427\pi\)
−0.348544 + 0.937292i \(0.613324\pi\)
\(80\) 0 0
\(81\) −8.78998 1.93292i −0.976665 0.214769i
\(82\) 0 0
\(83\) −7.50937 13.0066i −0.824260 1.42766i −0.902483 0.430725i \(-0.858258\pi\)
0.0782227 0.996936i \(-0.475075\pi\)
\(84\) 0 0
\(85\) 3.12893 5.41946i 0.339380 0.587823i
\(86\) 0 0
\(87\) 12.0104 + 3.92571i 1.28765 + 0.420880i
\(88\) 0 0
\(89\) 15.6668 1.66068 0.830338 0.557260i \(-0.188148\pi\)
0.830338 + 0.557260i \(0.188148\pi\)
\(90\) 0 0
\(91\) 1.62893 + 14.3759i 0.170758 + 1.50701i
\(92\) 0 0
\(93\) −1.50000 7.11831i −0.155543 0.738135i
\(94\) 0 0
\(95\) 0.845690 + 0.488259i 0.0867660 + 0.0500944i
\(96\) 0 0
\(97\) −4.97713 + 2.87355i −0.505351 + 0.291765i −0.730921 0.682462i \(-0.760909\pi\)
0.225569 + 0.974227i \(0.427576\pi\)
\(98\) 0 0
\(99\) 2.93105 + 6.64589i 0.294582 + 0.667937i
\(100\) 0 0
\(101\) 4.83838 + 8.38031i 0.481436 + 0.833872i 0.999773 0.0213045i \(-0.00678194\pi\)
−0.518337 + 0.855177i \(0.673449\pi\)
\(102\) 0 0
\(103\) −16.6863 9.63382i −1.64415 0.949249i −0.979337 0.202237i \(-0.935179\pi\)
−0.664811 0.747012i \(-0.731488\pi\)
\(104\) 0 0
\(105\) 8.30505 + 7.38288i 0.810490 + 0.720496i
\(106\) 0 0
\(107\) 1.09086i 0.105458i 0.998609 + 0.0527288i \(0.0167919\pi\)
−0.998609 + 0.0527288i \(0.983208\pi\)
\(108\) 0 0
\(109\) 2.31356 0.221599 0.110800 0.993843i \(-0.464659\pi\)
0.110800 + 0.993843i \(0.464659\pi\)
\(110\) 0 0
\(111\) 3.69407 + 4.11718i 0.350626 + 0.390785i
\(112\) 0 0
\(113\) 13.8868 + 8.01754i 1.30636 + 0.754227i 0.981487 0.191531i \(-0.0613453\pi\)
0.324872 + 0.945758i \(0.394679\pi\)
\(114\) 0 0
\(115\) −7.44183 + 4.29654i −0.693954 + 0.400655i
\(116\) 0 0
\(117\) −9.68915 + 13.2381i −0.895763 + 1.22386i
\(118\) 0 0
\(119\) −4.05797 5.49113i −0.371994 0.503371i
\(120\) 0 0
\(121\) −2.56895 + 4.44955i −0.233541 + 0.404505i
\(122\) 0 0
\(123\) 13.6917 2.88516i 1.23454 0.260146i
\(124\) 0 0
\(125\) −9.99041 −0.893569
\(126\) 0 0
\(127\) −3.06425 −0.271909 −0.135954 0.990715i \(-0.543410\pi\)
−0.135954 + 0.990715i \(0.543410\pi\)
\(128\) 0 0
\(129\) −4.54791 + 13.9140i −0.400421 + 1.22506i
\(130\) 0 0
\(131\) 5.73151 9.92727i 0.500765 0.867350i −0.499235 0.866467i \(-0.666386\pi\)
1.00000 0.000883062i \(-0.000281087\pi\)
\(132\) 0 0
\(133\) 0.856873 0.633234i 0.0743003 0.0549083i
\(134\) 0 0
\(135\) 1.25111 + 12.5378i 0.107679 + 1.07908i
\(136\) 0 0
\(137\) 1.71002 0.987278i 0.146096 0.0843488i −0.425170 0.905114i \(-0.639786\pi\)
0.571266 + 0.820765i \(0.306452\pi\)
\(138\) 0 0
\(139\) −5.37804 3.10501i −0.456159 0.263364i 0.254269 0.967134i \(-0.418165\pi\)
−0.710428 + 0.703770i \(0.751499\pi\)
\(140\) 0 0
\(141\) 2.42982 7.43383i 0.204628 0.626041i
\(142\) 0 0
\(143\) 13.2399 1.10717
\(144\) 0 0
\(145\) 17.6900i 1.46907i
\(146\) 0 0
\(147\) 11.0037 5.09110i 0.907567 0.419906i
\(148\) 0 0
\(149\) 10.5389 + 6.08462i 0.863378 + 0.498472i 0.865142 0.501527i \(-0.167228\pi\)
−0.00176397 + 0.999998i \(0.500561\pi\)
\(150\) 0 0
\(151\) −5.31784 9.21076i −0.432759 0.749561i 0.564350 0.825535i \(-0.309127\pi\)
−0.997110 + 0.0759740i \(0.975793\pi\)
\(152\) 0 0
\(153\) 0.836270 7.69677i 0.0676084 0.622247i
\(154\) 0 0
\(155\) −8.82006 + 5.09226i −0.708444 + 0.409021i
\(156\) 0 0
\(157\) −3.06154 1.76758i −0.244337 0.141068i 0.372831 0.927899i \(-0.378387\pi\)
−0.617169 + 0.786831i \(0.711720\pi\)
\(158\) 0 0
\(159\) −18.0859 + 16.2273i −1.43431 + 1.28691i
\(160\) 0 0
\(161\) 1.05561 + 9.31618i 0.0831939 + 0.734218i
\(162\) 0 0
\(163\) 6.33150 0.495921 0.247961 0.968770i \(-0.420240\pi\)
0.247961 + 0.968770i \(0.420240\pi\)
\(164\) 0 0
\(165\) 7.56895 6.79111i 0.589242 0.528687i
\(166\) 0 0
\(167\) 8.39779 14.5454i 0.649840 1.12556i −0.333320 0.942814i \(-0.608169\pi\)
0.983161 0.182743i \(-0.0584976\pi\)
\(168\) 0 0
\(169\) 8.45146 + 14.6384i 0.650112 + 1.12603i
\(170\) 0 0
\(171\) 1.20106 + 0.130497i 0.0918470 + 0.00997937i
\(172\) 0 0
\(173\) 8.30850 + 14.3907i 0.631684 + 1.09411i 0.987207 + 0.159441i \(0.0509692\pi\)
−0.355524 + 0.934667i \(0.615697\pi\)
\(174\) 0 0
\(175\) 0.929754 2.13468i 0.0702828 0.161367i
\(176\) 0 0
\(177\) −0.264069 + 0.0556457i −0.0198487 + 0.00418259i
\(178\) 0 0
\(179\) 14.5587i 1.08817i 0.839030 + 0.544086i \(0.183123\pi\)
−0.839030 + 0.544086i \(0.816877\pi\)
\(180\) 0 0
\(181\) 4.02355i 0.299068i 0.988757 + 0.149534i \(0.0477774\pi\)
−0.988757 + 0.149534i \(0.952223\pi\)
\(182\) 0 0
\(183\) −19.4452 6.35587i −1.43743 0.469839i
\(184\) 0 0
\(185\) 3.87205 6.70659i 0.284679 0.493078i
\(186\) 0 0
\(187\) −5.41119 + 3.12415i −0.395705 + 0.228461i
\(188\) 0 0
\(189\) 13.0869 + 4.21104i 0.951932 + 0.306308i
\(190\) 0 0
\(191\) 7.28998 4.20887i 0.527485 0.304543i −0.212507 0.977160i \(-0.568163\pi\)
0.739992 + 0.672616i \(0.234829\pi\)
\(192\) 0 0
\(193\) 4.31784 7.47871i 0.310805 0.538330i −0.667732 0.744402i \(-0.732735\pi\)
0.978537 + 0.206072i \(0.0660681\pi\)
\(194\) 0 0
\(195\) 21.8306 + 7.13555i 1.56332 + 0.510987i
\(196\) 0 0
\(197\) 23.3303i 1.66221i −0.556112 0.831107i \(-0.687708\pi\)
0.556112 0.831107i \(-0.312292\pi\)
\(198\) 0 0
\(199\) 14.1383i 1.00223i −0.865379 0.501117i \(-0.832923\pi\)
0.865379 0.501117i \(-0.167077\pi\)
\(200\) 0 0
\(201\) −8.59896 + 1.81201i −0.606524 + 0.127809i
\(202\) 0 0
\(203\) −17.6957 7.70732i −1.24199 0.540948i
\(204\) 0 0
\(205\) −9.79468 16.9649i −0.684090 1.18488i
\(206\) 0 0
\(207\) −6.27896 + 8.57881i −0.436418 + 0.596268i
\(208\) 0 0
\(209\) −0.487514 0.844399i −0.0337221 0.0584083i
\(210\) 0 0
\(211\) −6.75786 + 11.7050i −0.465230 + 0.805802i −0.999212 0.0396938i \(-0.987362\pi\)
0.533982 + 0.845496i \(0.320695\pi\)
\(212\) 0 0
\(213\) −11.2674 + 10.1095i −0.772029 + 0.692690i
\(214\) 0 0
\(215\) 20.4938 1.39766
\(216\) 0 0
\(217\) 1.25111 + 11.0415i 0.0849310 + 0.749548i
\(218\) 0 0
\(219\) −11.3484 + 10.1822i −0.766857 + 0.688050i
\(220\) 0 0
\(221\) −12.2215 7.05606i −0.822104 0.474642i
\(222\) 0 0
\(223\) −13.4054 + 7.73961i −0.897692 + 0.518283i −0.876451 0.481492i \(-0.840095\pi\)
−0.0212411 + 0.999774i \(0.506762\pi\)
\(224\) 0 0
\(225\) 2.41562 1.06537i 0.161041 0.0710245i
\(226\) 0 0
\(227\) −7.50835 13.0048i −0.498347 0.863162i 0.501651 0.865070i \(-0.332726\pi\)
−0.999998 + 0.00190793i \(0.999393\pi\)
\(228\) 0 0
\(229\) −16.9685 9.79677i −1.12131 0.647389i −0.179575 0.983744i \(-0.557472\pi\)
−0.941735 + 0.336355i \(0.890806\pi\)
\(230\) 0 0
\(231\) −3.49560 10.5302i −0.229994 0.692836i
\(232\) 0 0
\(233\) 19.5471i 1.28057i −0.768136 0.640287i \(-0.778815\pi\)
0.768136 0.640287i \(-0.221185\pi\)
\(234\) 0 0
\(235\) −10.9492 −0.714249
\(236\) 0 0
\(237\) 6.09772 18.6555i 0.396090 1.21180i
\(238\) 0 0
\(239\) 7.36210 + 4.25051i 0.476215 + 0.274943i 0.718838 0.695178i \(-0.244674\pi\)
−0.242623 + 0.970121i \(0.578008\pi\)
\(240\) 0 0
\(241\) −7.21480 + 4.16547i −0.464746 + 0.268321i −0.714038 0.700107i \(-0.753136\pi\)
0.249292 + 0.968428i \(0.419802\pi\)
\(242\) 0 0
\(243\) 7.67554 + 13.5678i 0.492386 + 0.870377i
\(244\) 0 0
\(245\) −11.5610 12.4284i −0.738605 0.794022i
\(246\) 0 0
\(247\) 1.10108 1.90712i 0.0700598 0.121347i
\(248\) 0 0
\(249\) −8.08191 + 24.7259i −0.512170 + 1.56694i
\(250\) 0 0
\(251\) −13.5763 −0.856928 −0.428464 0.903559i \(-0.640945\pi\)
−0.428464 + 0.903559i \(0.640945\pi\)
\(252\) 0 0
\(253\) 8.57997 0.539418
\(254\) 0 0
\(255\) −10.6060 + 2.23494i −0.664174 + 0.139957i
\(256\) 0 0
\(257\) −2.99030 + 5.17935i −0.186530 + 0.323079i −0.944091 0.329685i \(-0.893057\pi\)
0.757561 + 0.652764i \(0.226391\pi\)
\(258\) 0 0
\(259\) −5.02174 6.79528i −0.312036 0.422238i
\(260\) 0 0
\(261\) −8.83150 20.0246i −0.546656 1.23949i
\(262\) 0 0
\(263\) −2.91506 + 1.68301i −0.179750 + 0.103779i −0.587175 0.809460i \(-0.699760\pi\)
0.407425 + 0.913239i \(0.366427\pi\)
\(264\) 0 0
\(265\) 29.4607 + 17.0091i 1.80976 + 1.04486i
\(266\) 0 0
\(267\) −18.1219 20.1975i −1.10904 1.23607i
\(268\) 0 0
\(269\) 12.2822 0.748862 0.374431 0.927255i \(-0.377838\pi\)
0.374431 + 0.927255i \(0.377838\pi\)
\(270\) 0 0
\(271\) 29.4244i 1.78741i −0.448659 0.893703i \(-0.648098\pi\)
0.448659 0.893703i \(-0.351902\pi\)
\(272\) 0 0
\(273\) 16.6492 18.7288i 1.00765 1.13352i
\(274\) 0 0
\(275\) −1.84527 1.06537i −0.111274 0.0642440i
\(276\) 0 0
\(277\) 4.60108 + 7.96930i 0.276452 + 0.478829i 0.970500 0.241100i \(-0.0775080\pi\)
−0.694049 + 0.719928i \(0.744175\pi\)
\(278\) 0 0
\(279\) −7.44183 + 10.1676i −0.445531 + 0.608719i
\(280\) 0 0
\(281\) 1.05254 0.607682i 0.0627891 0.0362513i −0.468277 0.883582i \(-0.655125\pi\)
0.531066 + 0.847331i \(0.321792\pi\)
\(282\) 0 0
\(283\) 10.5776 + 6.10696i 0.628771 + 0.363021i 0.780276 0.625435i \(-0.215079\pi\)
−0.151505 + 0.988457i \(0.548412\pi\)
\(284\) 0 0
\(285\) −0.348755 1.65503i −0.0206585 0.0980357i
\(286\) 0 0
\(287\) −21.2378 + 2.40644i −1.25363 + 0.142048i
\(288\) 0 0
\(289\) −10.3400 −0.608238
\(290\) 0 0
\(291\) 9.46166 + 3.09264i 0.554652 + 0.181294i
\(292\) 0 0
\(293\) −3.15082 + 5.45739i −0.184073 + 0.318824i −0.943264 0.332044i \(-0.892262\pi\)
0.759191 + 0.650868i \(0.225595\pi\)
\(294\) 0 0
\(295\) 0.188909 + 0.327199i 0.0109987 + 0.0190503i
\(296\) 0 0
\(297\) 5.17748 11.4661i 0.300428 0.665328i
\(298\) 0 0
\(299\) 9.68915 + 16.7821i 0.560338 + 0.970534i
\(300\) 0 0
\(301\) 8.92889 20.5004i 0.514652 1.18162i
\(302\) 0 0
\(303\) 5.20727 15.9312i 0.299150 0.915223i
\(304\) 0 0
\(305\) 28.6408i 1.63997i
\(306\) 0 0
\(307\) 28.7264i 1.63950i 0.572721 + 0.819750i \(0.305888\pi\)
−0.572721 + 0.819750i \(0.694112\pi\)
\(308\) 0 0
\(309\) 6.88128 + 32.6554i 0.391462 + 1.85770i
\(310\) 0 0
\(311\) −8.86623 + 15.3568i −0.502758 + 0.870802i 0.497237 + 0.867615i \(0.334348\pi\)
−0.999995 + 0.00318766i \(0.998985\pi\)
\(312\) 0 0
\(313\) 23.4526 13.5404i 1.32562 0.765348i 0.341003 0.940062i \(-0.389233\pi\)
0.984619 + 0.174714i \(0.0559001\pi\)
\(314\) 0 0
\(315\) −0.0885507 19.2467i −0.00498926 1.08443i
\(316\) 0 0
\(317\) −4.65389 + 2.68692i −0.261388 + 0.150913i −0.624968 0.780651i \(-0.714888\pi\)
0.363579 + 0.931563i \(0.381555\pi\)
\(318\) 0 0
\(319\) −8.83150 + 15.2966i −0.494469 + 0.856446i
\(320\) 0 0
\(321\) 1.40633 1.26181i 0.0784940 0.0704274i
\(322\) 0 0
\(323\) 1.03926i 0.0578262i
\(324\) 0 0
\(325\) 4.81237i 0.266942i
\(326\) 0 0
\(327\) −2.67612 2.98263i −0.147990 0.164940i
\(328\) 0 0
\(329\) −4.77045 + 10.9528i −0.263003 + 0.603845i
\(330\) 0 0
\(331\) 3.72104 + 6.44502i 0.204527 + 0.354250i 0.949982 0.312305i \(-0.101101\pi\)
−0.745455 + 0.666556i \(0.767768\pi\)
\(332\) 0 0
\(333\) 1.03488 9.52475i 0.0567113 0.521953i
\(334\) 0 0
\(335\) 6.15149 + 10.6547i 0.336092 + 0.582128i
\(336\) 0 0
\(337\) −5.31784 + 9.21076i −0.289681 + 0.501742i −0.973734 0.227690i \(-0.926883\pi\)
0.684053 + 0.729433i \(0.260216\pi\)
\(338\) 0 0
\(339\) −5.72679 27.1767i −0.311037 1.47604i
\(340\) 0 0
\(341\) 10.1690 0.550681
\(342\) 0 0
\(343\) −17.4694 + 6.14981i −0.943259 + 0.332058i
\(344\) 0 0
\(345\) 14.1471 + 4.62412i 0.761655 + 0.248954i
\(346\) 0 0
\(347\) −1.63842 0.945944i −0.0879552 0.0507809i 0.455377 0.890299i \(-0.349504\pi\)
−0.543332 + 0.839518i \(0.682838\pi\)
\(348\) 0 0
\(349\) 16.1105 9.30140i 0.862375 0.497892i −0.00243201 0.999997i \(-0.500774\pi\)
0.864807 + 0.502105i \(0.167441\pi\)
\(350\) 0 0
\(351\) 28.2740 2.82139i 1.50915 0.150595i
\(352\) 0 0
\(353\) 1.94505 + 3.36893i 0.103525 + 0.179310i 0.913134 0.407659i \(-0.133655\pi\)
−0.809610 + 0.586968i \(0.800321\pi\)
\(354\) 0 0
\(355\) 18.3538 + 10.5966i 0.974118 + 0.562407i
\(356\) 0 0
\(357\) −2.38525 + 11.5832i −0.126241 + 0.613046i
\(358\) 0 0
\(359\) 8.62553i 0.455238i 0.973750 + 0.227619i \(0.0730940\pi\)
−0.973750 + 0.227619i \(0.926906\pi\)
\(360\) 0 0
\(361\) 18.8378 0.991465
\(362\) 0 0
\(363\) 8.70786 1.83496i 0.457044 0.0963103i
\(364\) 0 0
\(365\) 18.4858 + 10.6728i 0.967592 + 0.558639i
\(366\) 0 0
\(367\) 15.8701 9.16260i 0.828412 0.478284i −0.0248966 0.999690i \(-0.507926\pi\)
0.853309 + 0.521406i \(0.174592\pi\)
\(368\) 0 0
\(369\) −19.5568 14.3139i −1.01809 0.745154i
\(370\) 0 0
\(371\) 29.8503 22.0595i 1.54975 1.14527i
\(372\) 0 0
\(373\) 3.84791 6.66478i 0.199237 0.345089i −0.749044 0.662520i \(-0.769487\pi\)
0.948281 + 0.317431i \(0.102820\pi\)
\(374\) 0 0
\(375\) 11.5560 + 12.8796i 0.596749 + 0.665099i
\(376\) 0 0
\(377\) −39.8928 −2.05458
\(378\) 0 0
\(379\) −7.52510 −0.386539 −0.193269 0.981146i \(-0.561909\pi\)
−0.193269 + 0.981146i \(0.561909\pi\)
\(380\) 0 0
\(381\) 3.54445 + 3.95042i 0.181588 + 0.202386i
\(382\) 0 0
\(383\) 1.70467 2.95258i 0.0871047 0.150870i −0.819181 0.573534i \(-0.805572\pi\)
0.906286 + 0.422665i \(0.138905\pi\)
\(384\) 0 0
\(385\) −12.4923 + 9.23189i −0.636668 + 0.470501i
\(386\) 0 0
\(387\) 23.1984 10.2312i 1.17924 0.520083i
\(388\) 0 0
\(389\) 8.33425 4.81178i 0.422563 0.243967i −0.273610 0.961841i \(-0.588218\pi\)
0.696173 + 0.717874i \(0.254884\pi\)
\(390\) 0 0
\(391\) −7.92000 4.57261i −0.400532 0.231247i
\(392\) 0 0
\(393\) −19.4279 + 4.09392i −0.980007 + 0.206511i
\(394\) 0 0
\(395\) −27.4775 −1.38254
\(396\) 0 0
\(397\) 23.4807i 1.17846i 0.807964 + 0.589232i \(0.200570\pi\)
−0.807964 + 0.589232i \(0.799430\pi\)
\(398\) 0 0
\(399\) −1.80752 0.372210i −0.0904889 0.0186338i
\(400\) 0 0
\(401\) −22.2019 12.8183i −1.10871 0.640113i −0.170214 0.985407i \(-0.554446\pi\)
−0.938495 + 0.345294i \(0.887779\pi\)
\(402\) 0 0
\(403\) 11.4836 + 19.8902i 0.572038 + 0.990799i
\(404\) 0 0
\(405\) 14.7165 16.1155i 0.731267 0.800785i
\(406\) 0 0
\(407\) −6.69635 + 3.86614i −0.331926 + 0.191637i
\(408\) 0 0
\(409\) −13.3646 7.71603i −0.660835 0.381533i 0.131760 0.991282i \(-0.457937\pi\)
−0.792595 + 0.609748i \(0.791270\pi\)
\(410\) 0 0
\(411\) −3.25078 1.06255i −0.160349 0.0524118i
\(412\) 0 0
\(413\) 0.409610 0.0464127i 0.0201556 0.00228382i
\(414\) 0 0
\(415\) 36.4186 1.78772
\(416\) 0 0
\(417\) 2.21786 + 10.5249i 0.108609 + 0.515408i
\(418\) 0 0
\(419\) −7.10643 + 12.3087i −0.347172 + 0.601319i −0.985746 0.168241i \(-0.946191\pi\)
0.638574 + 0.769560i \(0.279525\pi\)
\(420\) 0 0
\(421\) −0.849964 1.47218i −0.0414247 0.0717497i 0.844570 0.535446i \(-0.179856\pi\)
−0.885994 + 0.463696i \(0.846523\pi\)
\(422\) 0 0
\(423\) −12.3942 + 5.46626i −0.602629 + 0.265779i
\(424\) 0 0
\(425\) 1.13555 + 1.96684i 0.0550825 + 0.0954057i
\(426\) 0 0
\(427\) 28.6500 + 12.4784i 1.38647 + 0.603874i
\(428\) 0 0
\(429\) −15.3147 17.0688i −0.739399 0.824088i
\(430\) 0 0
\(431\) 32.6628i 1.57331i 0.617392 + 0.786656i \(0.288189\pi\)
−0.617392 + 0.786656i \(0.711811\pi\)
\(432\) 0 0
\(433\) 13.6919i 0.657992i 0.944331 + 0.328996i \(0.106710\pi\)
−0.944331 + 0.328996i \(0.893290\pi\)
\(434\) 0 0
\(435\) −22.8059 + 20.4622i −1.09346 + 0.981087i
\(436\) 0 0
\(437\) 0.713542 1.23589i 0.0341333 0.0591207i
\(438\) 0 0
\(439\) 7.64139 4.41176i 0.364704 0.210562i −0.306438 0.951890i \(-0.599137\pi\)
0.671142 + 0.741329i \(0.265804\pi\)
\(440\) 0 0
\(441\) −19.2915 8.29696i −0.918641 0.395094i
\(442\) 0 0
\(443\) 21.3562 12.3300i 1.01466 0.585816i 0.102109 0.994773i \(-0.467441\pi\)
0.912554 + 0.408957i \(0.134107\pi\)
\(444\) 0 0
\(445\) −18.9950 + 32.9004i −0.900451 + 1.55963i
\(446\) 0 0
\(447\) −4.34614 20.6248i −0.205566 0.975520i
\(448\) 0 0
\(449\) 4.61306i 0.217704i 0.994058 + 0.108852i \(0.0347174\pi\)
−0.994058 + 0.108852i \(0.965283\pi\)
\(450\) 0 0
\(451\) 19.5595i 0.921019i
\(452\) 0 0
\(453\) −5.72328 + 17.5099i −0.268903 + 0.822687i
\(454\) 0 0
\(455\) −32.1645 14.0092i −1.50790 0.656760i
\(456\) 0 0
\(457\) −3.85935 6.68460i −0.180533 0.312692i 0.761529 0.648131i \(-0.224449\pi\)
−0.942062 + 0.335438i \(0.891116\pi\)
\(458\) 0 0
\(459\) −10.8900 + 7.82480i −0.508300 + 0.365231i
\(460\) 0 0
\(461\) −9.28621 16.0842i −0.432502 0.749115i 0.564586 0.825374i \(-0.309036\pi\)
−0.997088 + 0.0762589i \(0.975702\pi\)
\(462\) 0 0
\(463\) 17.7046 30.6653i 0.822804 1.42514i −0.0807828 0.996732i \(-0.525742\pi\)
0.903586 0.428406i \(-0.140925\pi\)
\(464\) 0 0
\(465\) 16.7672 + 5.48051i 0.777559 + 0.254153i
\(466\) 0 0
\(467\) −15.8433 −0.733141 −0.366571 0.930390i \(-0.619468\pi\)
−0.366571 + 0.930390i \(0.619468\pi\)
\(468\) 0 0
\(469\) 13.3382 1.51135i 0.615903 0.0697877i
\(470\) 0 0
\(471\) 1.26255 + 5.99149i 0.0581753 + 0.276073i
\(472\) 0 0
\(473\) −17.7210 10.2312i −0.814814 0.470433i
\(474\) 0 0
\(475\) −0.306919 + 0.177200i −0.0140824 + 0.00813048i
\(476\) 0 0
\(477\) 41.8403 + 4.54603i 1.91574 + 0.208149i
\(478\) 0 0
\(479\) 13.2512 + 22.9518i 0.605465 + 1.04870i 0.991978 + 0.126412i \(0.0403461\pi\)
−0.386513 + 0.922284i \(0.626321\pi\)
\(480\) 0 0
\(481\) −15.1241 8.73188i −0.689598 0.398139i
\(482\) 0 0
\(483\) 10.7893 12.1370i 0.490932 0.552252i
\(484\) 0 0
\(485\) 13.9360i 0.632802i
\(486\) 0 0
\(487\) −7.00939 −0.317626 −0.158813 0.987309i \(-0.550767\pi\)
−0.158813 + 0.987309i \(0.550767\pi\)
\(488\) 0 0
\(489\) −7.32370 8.16254i −0.331189 0.369123i
\(490\) 0 0
\(491\) −16.4508 9.49785i −0.742413 0.428632i 0.0805333 0.996752i \(-0.474338\pi\)
−0.822946 + 0.568120i \(0.807671\pi\)
\(492\) 0 0
\(493\) 16.3044 9.41333i 0.734312 0.423955i
\(494\) 0 0
\(495\) −17.5101 1.90251i −0.787022 0.0855116i
\(496\) 0 0
\(497\) 18.5965 13.7429i 0.834167 0.616454i
\(498\) 0 0
\(499\) −0.628929 + 1.08934i −0.0281547 + 0.0487654i −0.879759 0.475419i \(-0.842296\pi\)
0.851605 + 0.524184i \(0.175630\pi\)
\(500\) 0 0
\(501\) −28.4657 + 5.99840i −1.27175 + 0.267989i
\(502\) 0 0
\(503\) 37.9507 1.69214 0.846070 0.533072i \(-0.178963\pi\)
0.846070 + 0.533072i \(0.178963\pi\)
\(504\) 0 0
\(505\) −23.4650 −1.04418
\(506\) 0 0
\(507\) 9.09582 27.8279i 0.403960 1.23588i
\(508\) 0 0
\(509\) −2.90471 + 5.03110i −0.128749 + 0.223000i −0.923192 0.384339i \(-0.874429\pi\)
0.794443 + 0.607338i \(0.207763\pi\)
\(510\) 0 0
\(511\) 18.7303 13.8418i 0.828578 0.612323i
\(512\) 0 0
\(513\) −1.22104 1.69934i −0.0539100 0.0750278i
\(514\) 0 0
\(515\) 40.4622 23.3609i 1.78298 1.02940i
\(516\) 0 0
\(517\) 9.46784 + 5.46626i 0.416395 + 0.240406i
\(518\) 0 0
\(519\) 8.94197 27.3572i 0.392509 1.20085i
\(520\) 0 0
\(521\) 13.6999 0.600203 0.300102 0.953907i \(-0.402979\pi\)
0.300102 + 0.953907i \(0.402979\pi\)
\(522\) 0 0
\(523\) 24.4881i 1.07079i −0.844602 0.535394i \(-0.820163\pi\)
0.844602 0.535394i \(-0.179837\pi\)
\(524\) 0 0
\(525\) −3.82747 + 1.27057i −0.167045 + 0.0554521i
\(526\) 0 0
\(527\) −9.38679 5.41946i −0.408895 0.236076i
\(528\) 0 0
\(529\) −5.22104 9.04310i −0.227002 0.393178i
\(530\) 0 0
\(531\) 0.377189 + 0.276071i 0.0163686 + 0.0119805i
\(532\) 0 0
\(533\) −38.2576 + 22.0880i −1.65712 + 0.956739i
\(534\) 0 0
\(535\) −2.29082 1.32261i −0.0990408 0.0571812i
\(536\) 0 0
\(537\) 18.7691 16.8402i 0.809945 0.726709i
\(538\) 0 0
\(539\) 3.79211 + 16.5186i 0.163338 + 0.711505i
\(540\) 0 0
\(541\) −37.1608 −1.59767 −0.798833 0.601552i \(-0.794549\pi\)
−0.798833 + 0.601552i \(0.794549\pi\)
\(542\) 0 0
\(543\) 5.18714 4.65408i 0.222602 0.199726i
\(544\) 0 0
\(545\) −2.80506 + 4.85850i −0.120155 + 0.208115i
\(546\) 0 0
\(547\) −3.31826 5.74739i −0.141878 0.245741i 0.786326 0.617812i \(-0.211981\pi\)
−0.928204 + 0.372072i \(0.878648\pi\)
\(548\) 0 0
\(549\) 14.2985 + 32.4206i 0.610247 + 1.38368i
\(550\) 0 0
\(551\) 1.46892 + 2.54424i 0.0625781 + 0.108388i
\(552\) 0 0
\(553\) −11.9716 + 27.4864i −0.509085 + 1.16884i
\(554\) 0 0
\(555\) −13.1249 + 2.76574i −0.557123 + 0.117399i
\(556\) 0 0
\(557\) 24.6188i 1.04313i 0.853211 + 0.521565i \(0.174652\pi\)
−0.853211 + 0.521565i \(0.825348\pi\)
\(558\) 0 0
\(559\) 46.2156i 1.95471i
\(560\) 0 0
\(561\) 10.2868 + 3.36235i 0.434310 + 0.141958i
\(562\) 0 0
\(563\) −6.28555 + 10.8869i −0.264904 + 0.458828i −0.967539 0.252724i \(-0.918674\pi\)
0.702634 + 0.711551i \(0.252007\pi\)
\(564\) 0 0
\(565\) −33.6738 + 19.4416i −1.41667 + 0.817913i
\(566\) 0 0
\(567\) −9.70889 21.7425i −0.407735 0.913100i
\(568\) 0 0
\(569\) −12.8872 + 7.44043i −0.540260 + 0.311919i −0.745184 0.666859i \(-0.767638\pi\)
0.204924 + 0.978778i \(0.434305\pi\)
\(570\) 0 0
\(571\) 8.45573 14.6458i 0.353861 0.612906i −0.633061 0.774102i \(-0.718202\pi\)
0.986922 + 0.161196i \(0.0515351\pi\)
\(572\) 0 0
\(573\) −13.8585 4.52977i −0.578945 0.189234i
\(574\) 0 0
\(575\) 3.11861i 0.130055i
\(576\) 0 0
\(577\) 20.9013i 0.870133i 0.900398 + 0.435067i \(0.143275\pi\)
−0.900398 + 0.435067i \(0.856725\pi\)
\(578\) 0 0
\(579\) −14.6360 + 3.08416i −0.608252 + 0.128173i
\(580\) 0 0
\(581\) 15.8672 36.4304i 0.658281 1.51139i
\(582\) 0 0
\(583\) −16.9832 29.4157i −0.703371 1.21827i
\(584\) 0 0
\(585\) −16.0525 36.3977i −0.663691 1.50486i
\(586\) 0 0
\(587\) −14.8542 25.7283i −0.613100 1.06192i −0.990715 0.135957i \(-0.956589\pi\)
0.377615 0.925963i \(-0.376744\pi\)
\(588\) 0 0
\(589\) 0.845690 1.46478i 0.0348461 0.0603551i
\(590\) 0 0
\(591\) −30.0773 + 26.9864i −1.23721 + 1.11007i
\(592\) 0 0
\(593\) −11.7921 −0.484241 −0.242121 0.970246i \(-0.577843\pi\)
−0.242121 + 0.970246i \(0.577843\pi\)
\(594\) 0 0
\(595\) 16.4515 1.86411i 0.674444 0.0764210i
\(596\) 0 0
\(597\) −18.2270 + 16.3538i −0.745980 + 0.669318i
\(598\) 0 0
\(599\) −27.7991 16.0498i −1.13584 0.655778i −0.190443 0.981698i \(-0.560992\pi\)
−0.945397 + 0.325921i \(0.894326\pi\)
\(600\) 0 0
\(601\) −16.1636 + 9.33208i −0.659329 + 0.380664i −0.792021 0.610494i \(-0.790971\pi\)
0.132692 + 0.991157i \(0.457638\pi\)
\(602\) 0 0
\(603\) 12.2825 + 8.98978i 0.500183 + 0.366092i
\(604\) 0 0
\(605\) −6.22939 10.7896i −0.253261 0.438661i
\(606\) 0 0
\(607\) 12.0104 + 6.93419i 0.487486 + 0.281450i 0.723531 0.690292i \(-0.242518\pi\)
−0.236045 + 0.971742i \(0.575851\pi\)
\(608\) 0 0
\(609\) 10.5325 + 31.7283i 0.426800 + 1.28570i
\(610\) 0 0
\(611\) 24.6917i 0.998918i
\(612\) 0 0
\(613\) −20.9021 −0.844227 −0.422114 0.906543i \(-0.638712\pi\)
−0.422114 + 0.906543i \(0.638712\pi\)
\(614\) 0 0
\(615\) −10.5415 + 32.2507i −0.425072 + 1.30047i
\(616\) 0 0
\(617\) 15.2904 + 8.82792i 0.615569 + 0.355399i 0.775142 0.631787i \(-0.217678\pi\)
−0.159573 + 0.987186i \(0.551012\pi\)
\(618\) 0 0
\(619\) 4.78789 2.76429i 0.192441 0.111106i −0.400684 0.916216i \(-0.631227\pi\)
0.593125 + 0.805110i \(0.297894\pi\)
\(620\) 0 0
\(621\) 18.3227 1.82837i 0.735264 0.0733701i
\(622\) 0 0
\(623\) 24.6350 + 33.3354i 0.986982 + 1.33556i
\(624\) 0 0
\(625\) 14.3129 24.7906i 0.572515 0.991624i
\(626\) 0 0
\(627\) −0.524684 + 1.60522i −0.0209538 + 0.0641065i
\(628\) 0 0
\(629\) 8.24169 0.328618
\(630\) 0 0
\(631\) 24.3544 0.969533 0.484766 0.874644i \(-0.338905\pi\)
0.484766 + 0.874644i \(0.338905\pi\)
\(632\) 0 0
\(633\) 22.9068 4.82702i 0.910465 0.191857i
\(634\) 0 0
\(635\) 3.71522 6.43496i 0.147434 0.255363i
\(636\) 0 0
\(637\) −28.0274 + 26.0712i −1.11048 + 1.03298i
\(638\) 0 0
\(639\) 26.0662 + 2.83215i 1.03116 + 0.112038i
\(640\) 0 0
\(641\) 25.3174 14.6170i 0.999978 0.577337i 0.0917361 0.995783i \(-0.470758\pi\)
0.908242 + 0.418446i \(0.137425\pi\)
\(642\) 0 0
\(643\) −34.6535 20.0072i −1.36660 0.789008i −0.376109 0.926575i \(-0.622738\pi\)
−0.990492 + 0.137567i \(0.956072\pi\)
\(644\) 0 0
\(645\) −23.7053 26.4205i −0.933396 1.04031i
\(646\) 0 0
\(647\) −7.56553 −0.297432 −0.148716 0.988880i \(-0.547514\pi\)
−0.148716 + 0.988880i \(0.547514\pi\)
\(648\) 0 0
\(649\) 0.377240i 0.0148080i
\(650\) 0 0
\(651\) 12.7875 14.3848i 0.501183 0.563784i
\(652\) 0 0
\(653\) 33.9375 + 19.5938i 1.32808 + 0.766766i 0.985002 0.172542i \(-0.0551980\pi\)
0.343076 + 0.939308i \(0.388531\pi\)
\(654\) 0 0
\(655\) 13.8982 + 24.0724i 0.543049 + 0.940588i
\(656\) 0 0
\(657\) 26.2537 + 2.85252i 1.02425 + 0.111287i
\(658\) 0 0
\(659\) −22.8594 + 13.1979i −0.890474 + 0.514115i −0.874098 0.485751i \(-0.838546\pi\)
−0.0163765 + 0.999866i \(0.505213\pi\)
\(660\) 0 0
\(661\) −27.3501 15.7906i −1.06380 0.614184i −0.137317 0.990527i \(-0.543848\pi\)
−0.926480 + 0.376343i \(0.877181\pi\)
\(662\) 0 0
\(663\) 5.04003 + 23.9177i 0.195738 + 0.928885i
\(664\) 0 0
\(665\) 0.290888 + 2.56720i 0.0112802 + 0.0995517i
\(666\) 0 0
\(667\) −25.8522 −1.00100
\(668\) 0 0
\(669\) 25.4840 + 8.32970i 0.985269 + 0.322045i
\(670\) 0 0
\(671\) 14.2985 24.7658i 0.551989 0.956073i
\(672\) 0 0
\(673\) −7.21676 12.4998i −0.278186 0.481832i 0.692748 0.721180i \(-0.256400\pi\)
−0.970934 + 0.239348i \(0.923066\pi\)
\(674\) 0 0
\(675\) −4.16764 1.88189i −0.160412 0.0724340i
\(676\) 0 0
\(677\) −17.2099 29.8084i −0.661430 1.14563i −0.980240 0.197812i \(-0.936616\pi\)
0.318809 0.947819i \(-0.396717\pi\)
\(678\) 0 0
\(679\) −13.9405 6.07175i −0.534988 0.233013i
\(680\) 0 0
\(681\) −8.08081 + 24.7226i −0.309657 + 0.947370i
\(682\) 0 0
\(683\) 19.0172i 0.727674i −0.931463 0.363837i \(-0.881467\pi\)
0.931463 0.363837i \(-0.118533\pi\)
\(684\) 0 0
\(685\) 4.78806i 0.182942i
\(686\) 0 0
\(687\) 6.99767 + 33.2077i 0.266978 + 1.26695i
\(688\) 0 0
\(689\) 38.3574 66.4369i 1.46130 2.53104i
\(690\) 0 0
\(691\) −16.7795 + 9.68764i −0.638321 + 0.368535i −0.783968 0.620802i \(-0.786807\pi\)
0.145646 + 0.989337i \(0.453474\pi\)
\(692\) 0 0
\(693\) −9.53208 + 16.6869i −0.362094 + 0.633882i
\(694\) 0 0
\(695\) 13.0411 7.52928i 0.494677 0.285602i
\(696\) 0 0
\(697\) 10.4240 18.0549i 0.394838 0.683880i
\(698\) 0 0
\(699\) −25.2001 + 22.6103i −0.953154 + 0.855201i
\(700\) 0 0
\(701\) 23.0297i 0.869819i −0.900474 0.434910i \(-0.856780\pi\)
0.900474 0.434910i \(-0.143220\pi\)
\(702\) 0 0
\(703\) 1.28609i 0.0485058i
\(704\) 0 0
\(705\) 12.6651 + 14.1157i 0.476995 + 0.531628i
\(706\) 0 0
\(707\) −10.2234 + 23.4725i −0.384490 + 0.882775i
\(708\) 0 0
\(709\) 20.4119 + 35.3544i 0.766585 + 1.32776i 0.939405 + 0.342810i \(0.111379\pi\)
−0.172820 + 0.984953i \(0.555288\pi\)
\(710\) 0 0
\(711\) −31.1038 + 13.7178i −1.16648 + 0.514457i
\(712\) 0 0
\(713\) 7.44183 + 12.8896i 0.278699 + 0.482720i
\(714\) 0 0
\(715\) −16.0525 + 27.8038i −0.600331 + 1.03980i
\(716\) 0 0
\(717\) −3.03607 14.4078i −0.113384 0.538069i
\(718\) 0 0
\(719\) 42.3156 1.57811 0.789054 0.614324i \(-0.210571\pi\)
0.789054 + 0.614324i \(0.210571\pi\)
\(720\) 0 0
\(721\) −5.73950 50.6533i −0.213750 1.88643i
\(722\) 0 0
\(723\) 13.7155 + 4.48306i 0.510086 + 0.166727i
\(724\) 0 0
\(725\) 5.55995 + 3.21004i 0.206491 + 0.119218i
\(726\) 0 0
\(727\) 4.58754 2.64862i 0.170142 0.0982318i −0.412511 0.910953i \(-0.635348\pi\)
0.582653 + 0.812721i \(0.302015\pi\)
\(728\) 0 0
\(729\) 8.61321 25.5893i 0.319008 0.947752i
\(730\) 0 0
\(731\) 10.9053 + 18.8885i 0.403347 + 0.698617i
\(732\) 0 0
\(733\) 16.1513 + 9.32497i 0.596563 + 0.344426i 0.767688 0.640824i \(-0.221407\pi\)
−0.171125 + 0.985249i \(0.554740\pi\)
\(734\) 0 0
\(735\) −2.64995 + 29.2804i −0.0977449 + 1.08002i
\(736\) 0 0
\(737\) 12.2842i 0.452494i
\(738\) 0 0
\(739\) 41.1837 1.51497 0.757483 0.652855i \(-0.226429\pi\)
0.757483 + 0.652855i \(0.226429\pi\)
\(740\) 0 0
\(741\) −3.73227 + 0.786480i −0.137108 + 0.0288921i
\(742\) 0 0
\(743\) 20.5831 + 11.8837i 0.755122 + 0.435970i 0.827542 0.561404i \(-0.189739\pi\)
−0.0724196 + 0.997374i \(0.523072\pi\)
\(744\) 0 0
\(745\) −25.5555 + 14.7545i −0.936281 + 0.540562i
\(746\) 0 0
\(747\) 41.2249 18.1815i 1.50834 0.665227i
\(748\) 0 0
\(749\) −2.32111 + 1.71531i −0.0848116 + 0.0626762i
\(750\) 0 0
\(751\) −9.06151 + 15.6950i −0.330659 + 0.572718i −0.982641 0.185516i \(-0.940604\pi\)
0.651982 + 0.758234i \(0.273938\pi\)
\(752\) 0 0
\(753\) 15.7038 + 17.5025i 0.572279 + 0.637826i
\(754\) 0 0
\(755\) 25.7902 0.938603
\(756\) 0 0
\(757\) 37.1059 1.34864 0.674319 0.738440i \(-0.264437\pi\)
0.674319 + 0.738440i \(0.264437\pi\)
\(758\) 0 0
\(759\) −9.92453 11.0613i −0.360237 0.401498i
\(760\) 0 0
\(761\) 5.90537 10.2284i 0.214070 0.370779i −0.738915 0.673799i \(-0.764661\pi\)
0.952984 + 0.303020i \(0.0979948\pi\)
\(762\) 0 0
\(763\) 3.63793 + 4.92275i 0.131702 + 0.178215i
\(764\) 0 0
\(765\) 15.1493 + 11.0880i 0.547725 + 0.400889i
\(766\) 0 0
\(767\) 0.737868 0.426009i 0.0266429 0.0153823i
\(768\) 0 0
\(769\) −3.14015 1.81297i −0.113237 0.0653773i 0.442312 0.896861i \(-0.354158\pi\)
−0.555549 + 0.831484i \(0.687492\pi\)
\(770\) 0 0
\(771\) 10.1361 2.13592i 0.365043 0.0769233i
\(772\) 0 0
\(773\) 12.1111 0.435605 0.217802 0.975993i \(-0.430111\pi\)
0.217802 + 0.975993i \(0.430111\pi\)
\(774\) 0 0
\(775\) 3.69618i 0.132771i
\(776\) 0 0
\(777\) −2.95174 + 14.3342i −0.105893 + 0.514235i
\(778\) 0 0
\(779\) 2.81742 + 1.62664i 0.100944 + 0.0582803i
\(780\) 0 0
\(781\) −10.5804 18.3258i −0.378596 0.655748i
\(782\) 0 0
\(783\) −15.6002 + 34.5482i −0.557505 + 1.23465i
\(784\) 0 0
\(785\) 7.42386 4.28617i 0.264969 0.152980i
\(786\) 0 0
\(787\) 17.5995 + 10.1611i 0.627354 + 0.362203i 0.779727 0.626120i \(-0.215358\pi\)
−0.152372 + 0.988323i \(0.548691\pi\)
\(788\) 0 0
\(789\) 5.54160 + 1.81133i 0.197286 + 0.0644850i
\(790\) 0 0
\(791\) 4.77657 + 42.1551i 0.169835 + 1.49886i
\(792\) 0 0
\(793\) 64.5880 2.29359
\(794\) 0 0
\(795\) −12.1493 57.6552i −0.430893 2.04482i
\(796\) 0 0