Properties

Label 252.2.x.a.41.7
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 41.7
Root \(-1.69483 + 0.357142i\) of defining polynomial
Character \(\chi\) \(=\) 252.41
Dual form 252.2.x.a.209.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.15671 + 1.28920i) q^{3} +(1.21244 - 2.10001i) q^{5} +(1.05649 + 2.42566i) q^{7} +(-0.324049 + 2.98245i) q^{9} +O(q^{10})\) \(q+(1.15671 + 1.28920i) q^{3} +(1.21244 - 2.10001i) q^{5} +(1.05649 + 2.42566i) q^{7} +(-0.324049 + 2.98245i) q^{9} +(2.09680 - 1.21059i) q^{11} +(-4.73574 - 2.73418i) q^{13} +(4.10976 - 0.866025i) q^{15} +2.58069 q^{17} +0.402708i q^{19} +(-1.90510 + 4.16781i) q^{21} +(3.06895 + 1.77186i) q^{23} +(-0.440020 - 0.762137i) q^{25} +(-4.21979 + 3.03206i) q^{27} +(-6.31784 + 3.64761i) q^{29} +(-3.63732 - 2.10001i) q^{31} +(3.98607 + 1.30289i) q^{33} +(6.37484 + 0.722330i) q^{35} -3.19360 q^{37} +(-1.95298 - 9.26794i) q^{39} +(4.03924 - 6.99618i) q^{41} +(-4.22573 - 7.31918i) q^{43} +(5.87027 + 4.29654i) q^{45} +(-2.25769 - 3.91043i) q^{47} +(-4.76766 + 5.12537i) q^{49} +(2.98510 + 3.32701i) q^{51} -14.0288i q^{53} -5.87106i q^{55} +(-0.519169 + 0.465816i) q^{57} +(-0.0779043 + 0.134934i) q^{59} +(-10.2288 + 5.90561i) q^{61} +(-7.57676 + 2.36489i) q^{63} +(-11.4836 + 6.63005i) q^{65} +(2.53682 - 4.39390i) q^{67} +(1.26561 + 6.00600i) q^{69} -8.73987i q^{71} +8.80274i q^{73} +(0.473569 - 1.44884i) q^{75} +(5.15173 + 3.80715i) q^{77} +(5.66575 + 9.81337i) q^{79} +(-8.78998 - 1.93292i) q^{81} +(7.50937 + 13.0066i) q^{83} +(3.12893 - 5.41946i) q^{85} +(-12.0104 - 3.92571i) q^{87} -15.6668 q^{89} +(1.62893 - 14.3759i) q^{91} +(-1.50000 - 7.11831i) q^{93} +(0.845690 + 0.488259i) q^{95} +(4.97713 - 2.87355i) q^{97} +(2.93105 + 6.64589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + O(q^{10}) \) \( 16q - q^{7} + 6q^{11} - 12q^{15} + 9q^{21} + 6q^{23} - 8q^{25} - 12q^{29} + 4q^{37} + 18q^{39} + 4q^{43} - 5q^{49} - 18q^{51} - 42q^{57} - 27q^{63} - 24q^{65} + 14q^{67} - 21q^{77} + 20q^{79} - 36q^{81} + 6q^{85} - 18q^{91} - 24q^{93} - 60q^{95} + 90q^{99} + O(q^{100}) \)

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 \(-0.650917\pi\)
0.998776 0.0494574i \(-0.0157492\pi\)
\(6\) 0 0
\(7\) 1.05649 + 2.42566i 0.399316 + 0.916813i
\(8\) 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 −0.330790 0.943704i \(-0.607315\pi\)
−0.982667 + 0.185380i \(0.940648\pi\)
\(14\) 0 0
\(15\) 4.10976 0.866025i 1.06114 0.223607i
\(16\) 0 0
\(17\) 2.58069 0.625909 0.312954 0.949768i \(-0.398681\pi\)
0.312954 + 0.949768i \(0.398681\pi\)
\(18\) 0 0
\(19\) 0.402708i 0.0923876i 0.998932 + 0.0461938i \(0.0147092\pi\)
−0.998932 + 0.0461938i \(0.985291\pi\)
\(20\) 0 0
\(21\) −1.90510 + 4.16781i −0.415726 + 0.909490i
\(22\) 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 0.136431 0.990650i \(-0.456437\pi\)
−0.789712 + 0.613477i \(0.789770\pi\)
\(32\) 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 \(-0.616050\pi\)
0.987384 0.158346i \(-0.0506163\pi\)
\(42\) 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 0.653059 0.757307i \(-0.273485\pi\)
−0.982377 + 0.186912i \(0.940152\pi\)
\(48\) 0 0
\(49\) −4.76766 + 5.12537i −0.681094 + 0.732196i
\(50\) 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 −0.871052 0.491191i \(-0.836562\pi\)
0.860910 + 0.508758i \(0.169895\pi\)
\(60\) 0 0
\(61\) −10.2288 + 5.90561i −1.30967 + 0.756136i −0.982040 0.188672i \(-0.939582\pi\)
−0.327626 + 0.944808i \(0.606248\pi\)
\(62\) 0 0
\(63\) −7.57676 + 2.36489i −0.954582 + 0.297949i
\(64\) 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 \(0.172261\pi\)
−0.857105 + 0.515141i \(0.827739\pi\)
\(74\) 0 0
\(75\) 0.473569 1.44884i 0.0546830 0.167298i
\(76\) 0 0
\(77\) 5.15173 + 3.80715i 0.587094 + 0.433865i
\(78\) 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 \(0.141742\pi\)
−0.0782227 + 0.996936i \(0.524925\pi\)
\(84\) 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 \(-0.811852\pi\)
−0.830338 + 0.557260i \(0.811852\pi\)
\(90\) 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 −0.225569 0.974227i \(-0.572424\pi\)
0.730921 + 0.682462i \(0.239091\pi\)
\(98\) 0 0
\(99\) 2.93105 + 6.64589i 0.294582 + 0.667937i
\(100\) 0 0
\(101\) −4.83838 8.38031i −0.481436 0.833872i 0.518337 0.855177i \(-0.326551\pi\)
−0.999773 + 0.0213045i \(0.993218\pi\)
\(102\) 0 0
\(103\) 16.6863 + 9.63382i 1.64415 + 0.949249i 0.979337 + 0.202237i \(0.0648212\pi\)
0.664811 + 0.747012i \(0.268512\pi\)
\(104\) 0 0
\(105\) 6.44260 + 9.05393i 0.628734 + 0.883573i
\(106\) 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
\(119\) 2.72647 + 6.25987i 0.249935 + 0.573842i
\(120\) 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 \(0.333614\pi\)
−1.00000 0.000883062i \(0.999719\pi\)
\(132\) 0 0
\(133\) −0.976833 + 0.425457i −0.0847022 + 0.0368918i
\(134\) 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 0.710428 0.703770i \(-0.248501\pi\)
−0.254269 + 0.967134i \(0.581835\pi\)
\(140\) 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
\(147\) −12.1224 0.217875i −0.999839 0.0179700i
\(148\) 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 0.617169 0.786831i \(-0.288280\pi\)
−0.372831 + 0.927899i \(0.621613\pi\)
\(158\) 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 \(0.391831\pi\)
−0.983161 + 0.182743i \(0.941502\pi\)
\(168\) 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 \(-0.949031\pi\)
0.355524 0.934667i \(-0.384303\pi\)
\(174\) 0 0
\(175\) 1.38381 1.87253i 0.104606 0.141550i
\(176\) 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 \(-0.952223\pi\)
0.988757 0.149534i \(-0.0477774\pi\)
\(182\) 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
\(189\) −11.8129 7.03243i −0.859263 0.511534i
\(190\) 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 \(0.167077\pi\)
−0.865379 + 0.501117i \(0.832923\pi\)
\(200\) 0 0
\(201\) 8.59896 1.81201i 0.606524 0.127809i
\(202\) 0 0
\(203\) −15.5226 11.4713i −1.08947 0.805125i
\(204\) 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 0.0212411 0.999774i \(-0.493238\pi\)
0.876451 + 0.481492i \(0.159905\pi\)
\(224\) 0 0
\(225\) 2.41562 1.06537i 0.161041 0.0710245i
\(226\) 0 0
\(227\) 7.50835 + 13.0048i 0.498347 + 0.863162i 0.999998 0.00190793i \(-0.000607314\pi\)
−0.501651 + 0.865070i \(0.667274\pi\)
\(228\) 0 0
\(229\) 16.9685 + 9.79677i 1.12131 + 0.647389i 0.941735 0.336355i \(-0.109194\pi\)
0.179575 + 0.983744i \(0.442528\pi\)
\(230\) 0 0
\(231\) 1.05089 + 11.0454i 0.0691432 + 0.726731i
\(232\) 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 −0.249292 0.968428i \(-0.580198\pi\)
0.714038 + 0.700107i \(0.246864\pi\)
\(242\) 0 0
\(243\) −7.67554 13.5678i −0.492386 0.870377i
\(244\) 0 0
\(245\) 4.98283 + 16.2263i 0.318341 + 1.03666i
\(246\) 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 \(-0.359055\pi\)
0.428464 + 0.903559i \(0.359055\pi\)
\(252\) 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 −0.757561 0.652764i \(-0.773609\pi\)
0.944091 + 0.329685i \(0.106943\pi\)
\(258\) 0 0
\(259\) −3.37401 7.74660i −0.209651 0.481350i
\(260\) 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 \(-0.622162\pi\)
−0.374431 + 0.927255i \(0.622162\pi\)
\(270\) 0 0
\(271\) 29.4244i 1.78741i 0.448659 + 0.893703i \(0.351902\pi\)
−0.448659 + 0.893703i \(0.648098\pi\)
\(272\) 0 0
\(273\) 20.4176 14.5287i 1.23573 0.879320i
\(274\) 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 0.151505 0.988457i \(-0.451588\pi\)
−0.780276 + 0.625435i \(0.784921\pi\)
\(284\) 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 −0.759191 0.650868i \(-0.774405\pi\)
0.943264 + 0.332044i \(0.107738\pi\)
\(294\) 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
\(301\) 13.2894 17.9828i 0.765988 1.03651i
\(302\) 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 \(-0.694112\pi\)
0.572721 0.819750i \(-0.305888\pi\)
\(308\) 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 \(-0.665652\pi\)
0.999995 0.00318766i \(-0.00101467\pi\)
\(312\) 0 0
\(313\) −23.4526 + 13.5404i −1.32562 + 0.765348i −0.984619 0.174714i \(-0.944100\pi\)
−0.341003 + 0.940062i \(0.610767\pi\)
\(314\) 0 0
\(315\) −4.22007 + 18.7785i −0.237774 + 1.05805i
\(316\) 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
\(329\) 7.10015 9.60771i 0.391444 0.529690i
\(330\) 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 −0.864807 0.502105i \(-0.832559\pi\)
0.00243201 + 0.999997i \(0.499226\pi\)
\(350\) 0 0
\(351\) 28.2740 2.82139i 1.50915 0.150595i
\(352\) 0 0
\(353\) −1.94505 3.36893i −0.103525 0.179310i 0.809610 0.586968i \(-0.199679\pi\)
−0.913134 + 0.407659i \(0.866345\pi\)
\(354\) 0 0
\(355\) −18.3538 10.5966i −0.974118 0.562407i
\(356\) 0 0
\(357\) −4.91646 + 10.7558i −0.260207 + 0.569258i
\(358\) 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 −0.853309 0.521406i \(-0.825408\pi\)
0.0248966 + 0.999690i \(0.492074\pi\)
\(368\) 0 0
\(369\) 19.5568 + 14.3139i 1.01809 + 0.745154i
\(370\) 0 0
\(371\) 34.0292 14.8213i 1.76671 0.769486i
\(372\) 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 −0.906286 0.422665i \(-0.861095\pi\)
0.819181 + 0.573534i \(0.194428\pi\)
\(384\) 0 0
\(385\) 14.2412 6.20272i 0.725799 0.316120i
\(386\) 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 \(-0.799430\pi\)
0.807964 0.589232i \(-0.200570\pi\)
\(398\) 0 0
\(399\) −1.67841 0.767199i −0.0840256 0.0384080i
\(400\) 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 0.792595 0.609748i \(-0.208730\pi\)
−0.131760 + 0.991282i \(0.542063\pi\)
\(410\) 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 −0.638574 0.769560i \(-0.720475\pi\)
0.985746 + 0.168241i \(0.0538088\pi\)
\(420\) 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
\(427\) −25.1317 18.5724i −1.21621 0.898782i
\(428\) 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 \(-0.893290\pi\)
0.944331 0.328996i \(-0.106710\pi\)
\(434\) 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 −0.671142 0.741329i \(-0.734196\pi\)
0.306438 + 0.951890i \(0.400863\pi\)
\(440\) 0 0
\(441\) −13.7412 15.8802i −0.654343 0.756198i
\(442\) 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
\(455\) −28.2146 20.8507i −1.32272 0.977496i
\(456\) 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 0.997088 0.0762589i \(-0.0242975\pi\)
−0.564586 + 0.825374i \(0.690964\pi\)
\(462\) 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 \(-0.380532\pi\)
0.366571 + 0.930390i \(0.380532\pi\)
\(468\) 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 \(-0.959654\pi\)
0.386513 0.922284i \(-0.373679\pi\)
\(480\) 0 0
\(481\) 15.1241 + 8.73188i 0.689598 + 0.398139i
\(482\) 0 0
\(483\) −13.2314 + 9.41522i −0.602050 + 0.428407i
\(484\) 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
\(497\) 21.2000 9.23359i 0.950948 0.414183i
\(498\) 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 \(-0.821037\pi\)
−0.846070 + 0.533072i \(0.821037\pi\)
\(504\) 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 −0.794443 0.607338i \(-0.792237\pi\)
0.923192 + 0.384339i \(0.125571\pi\)
\(510\) 0 0
\(511\) −21.3524 + 9.30001i −0.944577 + 0.411408i
\(512\) 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 \(-0.597021\pi\)
−0.300102 + 0.953907i \(0.597021\pi\)
\(522\) 0 0
\(523\) 24.4881i 1.07079i 0.844602 + 0.535394i \(0.179837\pi\)
−0.844602 + 0.535394i \(0.820163\pi\)
\(524\) 0 0
\(525\) 4.01472 0.381972i 0.175217 0.0166706i
\(526\) 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
\(553\) −17.8181 + 24.1109i −0.757702 + 1.02530i
\(554\) 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 −0.702634 0.711551i \(-0.747993\pi\)
0.967539 + 0.252724i \(0.0813263\pi\)
\(564\) 0 0
\(565\) 33.6738 19.4416i 1.41667 0.817913i
\(566\) 0 0
\(567\) −4.59793 23.3636i −0.193095 0.981180i
\(568\) 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 \(-0.856725\pi\)
0.900398 0.435067i \(-0.143275\pi\)
\(578\) 0 0
\(579\) 14.6360 3.08416i 0.608252 0.128173i
\(580\) 0 0
\(581\) −23.6160 + 31.9565i −0.979759 + 1.32578i
\(582\) 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 \(0.0434109\pi\)
−0.377615 + 0.925963i \(0.623256\pi\)
\(588\) 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 \(-0.422157\pi\)
0.242121 + 0.970246i \(0.422157\pi\)
\(594\) 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 −0.132692 0.991157i \(-0.542362\pi\)
0.792021 + 0.610494i \(0.209029\pi\)
\(602\) 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 0.236045 0.971742i \(-0.424149\pi\)
−0.723531 + 0.690292i \(0.757482\pi\)
\(608\) 0 0
\(609\) −3.16641 33.2806i −0.128309 1.34860i
\(610\) 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 −0.593125 0.805110i \(-0.702106\pi\)
0.400684 + 0.916216i \(0.368773\pi\)
\(620\) 0 0
\(621\) −18.3227 + 1.82837i −0.735264 + 0.0733701i
\(622\) 0 0
\(623\) −16.5518 38.0023i −0.663134 1.52253i
\(624\) 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
\(637\) 36.5920 11.2368i 1.44983 0.445218i
\(638\) 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 0.990492 0.137567i \(-0.0439284\pi\)
0.376109 + 0.926575i \(0.377262\pi\)
\(644\) 0 0
\(645\) −23.7053 26.4205i −0.933396 1.04031i
\(646\) 0 0
\(647\) 7.56553 0.297432 0.148716 0.988880i \(-0.452486\pi\)
0.148716 + 0.988880i \(0.452486\pi\)
\(648\) 0 0
\(649\) 0.377240i 0.0148080i
\(650\) 0 0
\(651\) 15.6819 11.1589i 0.614621 0.437352i
\(652\) 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 0.926480 0.376343i \(-0.122819\pi\)
0.137317 + 0.990527i \(0.456152\pi\)
\(662\) 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 \(0.0633837\pi\)
−0.318809 + 0.947819i \(0.603283\pi\)
\(678\) 0 0
\(679\) 12.2285 + 9.03696i 0.469289 + 0.346807i
\(680\) 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 −0.145646 0.989337i \(-0.546526\pi\)
0.783968 + 0.620802i \(0.213193\pi\)
\(692\) 0 0
\(693\) −13.0240 + 14.1311i −0.494743 + 0.536794i
\(694\) 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
\(707\) 15.2161 20.5900i 0.572260 0.774366i
\(708\) 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 \(-0.789429\pi\)
−0.789054 + 0.614324i \(0.789429\pi\)
\(720\) 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 −0.582653 0.812721i \(-0.697985\pi\)
0.412511 + 0.910953i \(0.364652\pi\)
\(728\) 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 0.171125 0.985249i \(-0.445260\pi\)
−0.767688 + 0.640824i \(0.778593\pi\)
\(734\) 0 0
\(735\) −15.1552 + 25.1930i −0.559009 + 0.929256i
\(736\) 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
\(749\) −2.64606 + 1.15249i −0.0966850 + 0.0421109i
\(750\) 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 −0.952984 0.303020i \(-0.902005\pi\)
0.738915 + 0.673799i \(0.235339\pi\)
\(762\) 0 0
\(763\) 2.44426 + 5.61192i 0.0884880 + 0.203165i
\(764\) 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 0.555549 0.831484i \(-0.312508\pi\)
−0.442312 + 0.896861i \(0.645842\pi\)
\(770\) 0 0
\(771\) 10.1361 2.13592i 0.365043 0.0769233i
\(772\) 0 0
\(773\) −12.1111 −0.435605 −0.217802 0.975993i \(-0.569889\pi\)
−0.217802 + 0.975993i \(0.569889\pi\)
\(774\) 0 0
\(775\) 3.69618i 0.132771i
\(776\) 0 0
\(777\) 6.08413 13.3103i 0.218267 0.477505i
\(778\) 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 0.152372 0.988323i \(-0.451309\pi\)
−0.779727 + 0.626120i \(0.784642\pi\)
\(788\) 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