Properties

Label 288.2.i.f.193.4
Level $288$
Weight $2$
Character 288.193
Analytic conductor $2.300$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.170772624.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 6 x^{5} + 6 x^{4} - 12 x^{3} + 20 x^{2} - 24 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.4
Root \(-1.02187 - 0.977642i\) of defining polynomial
Character \(\chi\) \(=\) 288.193
Dual form 288.2.i.f.97.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.35760 + 1.07561i) q^{3} +(-1.18614 + 2.05446i) q^{5} +(1.10489 + 1.91373i) q^{7} +(0.686141 + 2.92048i) q^{9} +O(q^{10})\) \(q+(1.35760 + 1.07561i) q^{3} +(-1.18614 + 2.05446i) q^{5} +(1.10489 + 1.91373i) q^{7} +(0.686141 + 2.92048i) q^{9} +(-2.96790 - 5.14055i) q^{11} +(-2.18614 + 3.78651i) q^{13} +(-3.82009 + 1.51330i) q^{15} +3.37228 q^{17} +3.72601 q^{19} +(-0.558422 + 3.78651i) q^{21} +(1.10489 - 1.91373i) q^{23} +(-0.313859 - 0.543620i) q^{25} +(-2.20979 + 4.70285i) q^{27} +(-0.186141 - 0.322405i) q^{29} +(4.83090 - 8.36737i) q^{31} +(1.50000 - 10.1711i) q^{33} -5.24224 q^{35} +4.00000 q^{37} +(-7.04069 + 2.78912i) q^{39} +(-0.500000 + 0.866025i) q^{41} +(2.96790 + 5.14055i) q^{43} +(-6.81386 - 2.05446i) q^{45} +(1.10489 + 1.91373i) q^{47} +(1.05842 - 1.83324i) q^{49} +(4.57820 + 3.62725i) q^{51} -4.00000 q^{53} +14.0814 q^{55} +(5.05842 + 4.00772i) q^{57} +(5.17769 - 8.96801i) q^{59} +(-7.55842 - 13.0916i) q^{61} +(-4.83090 + 4.53991i) q^{63} +(-5.18614 - 8.98266i) q^{65} +(-5.17769 + 8.96801i) q^{67} +(3.55842 - 1.40965i) q^{69} -4.41957 q^{71} +4.62772 q^{73} +(0.158627 - 1.07561i) q^{75} +(6.55842 - 11.3595i) q^{77} +(-4.83090 - 8.36737i) q^{79} +(-8.05842 + 4.00772i) q^{81} +(-7.04069 - 12.1948i) q^{83} +(-4.00000 + 6.92820i) q^{85} +(0.0940770 - 0.637910i) q^{87} +1.25544 q^{89} -9.66181 q^{91} +(15.5584 - 6.16337i) q^{93} +(-4.41957 + 7.65492i) q^{95} +(-4.50000 - 7.79423i) q^{97} +(12.9765 - 12.1948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{5} - 6q^{9} + O(q^{10}) \) \( 8q + 2q^{5} - 6q^{9} - 6q^{13} + 4q^{17} + 30q^{21} - 14q^{25} + 10q^{29} + 12q^{33} + 32q^{37} - 4q^{41} - 66q^{45} - 26q^{49} - 32q^{53} + 6q^{57} - 26q^{61} - 30q^{65} - 6q^{69} + 60q^{73} + 18q^{77} - 30q^{81} - 32q^{85} + 56q^{89} + 90q^{93} - 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.35760 + 1.07561i 0.783809 + 0.621002i
\(4\) 0 0
\(5\) −1.18614 + 2.05446i −0.530458 + 0.918781i 0.468910 + 0.883246i \(0.344647\pi\)
−0.999368 + 0.0355348i \(0.988687\pi\)
\(6\) 0 0
\(7\) 1.10489 + 1.91373i 0.417610 + 0.723322i 0.995699 0.0926519i \(-0.0295344\pi\)
−0.578088 + 0.815974i \(0.696201\pi\)
\(8\) 0 0
\(9\) 0.686141 + 2.92048i 0.228714 + 0.973494i
\(10\) 0 0
\(11\) −2.96790 5.14055i −0.894855 1.54993i −0.833984 0.551789i \(-0.813945\pi\)
−0.0608712 0.998146i \(-0.519388\pi\)
\(12\) 0 0
\(13\) −2.18614 + 3.78651i −0.606326 + 1.05019i 0.385514 + 0.922702i \(0.374024\pi\)
−0.991840 + 0.127486i \(0.959309\pi\)
\(14\) 0 0
\(15\) −3.82009 + 1.51330i −0.986342 + 0.390733i
\(16\) 0 0
\(17\) 3.37228 0.817898 0.408949 0.912557i \(-0.365895\pi\)
0.408949 + 0.912557i \(0.365895\pi\)
\(18\) 0 0
\(19\) 3.72601 0.854805 0.427403 0.904061i \(-0.359429\pi\)
0.427403 + 0.904061i \(0.359429\pi\)
\(20\) 0 0
\(21\) −0.558422 + 3.78651i −0.121858 + 0.826284i
\(22\) 0 0
\(23\) 1.10489 1.91373i 0.230386 0.399041i −0.727536 0.686070i \(-0.759334\pi\)
0.957922 + 0.287029i \(0.0926677\pi\)
\(24\) 0 0
\(25\) −0.313859 0.543620i −0.0627719 0.108724i
\(26\) 0 0
\(27\) −2.20979 + 4.70285i −0.425274 + 0.905065i
\(28\) 0 0
\(29\) −0.186141 0.322405i −0.0345655 0.0598691i 0.848225 0.529636i \(-0.177671\pi\)
−0.882791 + 0.469767i \(0.844338\pi\)
\(30\) 0 0
\(31\) 4.83090 8.36737i 0.867656 1.50282i 0.00327038 0.999995i \(-0.498959\pi\)
0.864386 0.502830i \(-0.167708\pi\)
\(32\) 0 0
\(33\) 1.50000 10.1711i 0.261116 1.77056i
\(34\) 0 0
\(35\) −5.24224 −0.886099
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) −7.04069 + 2.78912i −1.12741 + 0.446617i
\(40\) 0 0
\(41\) −0.500000 + 0.866025i −0.0780869 + 0.135250i −0.902424 0.430848i \(-0.858214\pi\)
0.824338 + 0.566099i \(0.191548\pi\)
\(42\) 0 0
\(43\) 2.96790 + 5.14055i 0.452600 + 0.783927i 0.998547 0.0538934i \(-0.0171631\pi\)
−0.545946 + 0.837820i \(0.683830\pi\)
\(44\) 0 0
\(45\) −6.81386 2.05446i −1.01575 0.306260i
\(46\) 0 0
\(47\) 1.10489 + 1.91373i 0.161165 + 0.279146i 0.935287 0.353891i \(-0.115141\pi\)
−0.774122 + 0.633037i \(0.781808\pi\)
\(48\) 0 0
\(49\) 1.05842 1.83324i 0.151203 0.261892i
\(50\) 0 0
\(51\) 4.57820 + 3.62725i 0.641076 + 0.507916i
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 14.0814 1.89873
\(56\) 0 0
\(57\) 5.05842 + 4.00772i 0.670004 + 0.530836i
\(58\) 0 0
\(59\) 5.17769 8.96801i 0.674077 1.16754i −0.302661 0.953098i \(-0.597875\pi\)
0.976738 0.214437i \(-0.0687918\pi\)
\(60\) 0 0
\(61\) −7.55842 13.0916i −0.967757 1.67620i −0.702019 0.712159i \(-0.747718\pi\)
−0.265738 0.964045i \(-0.585616\pi\)
\(62\) 0 0
\(63\) −4.83090 + 4.53991i −0.608637 + 0.571975i
\(64\) 0 0
\(65\) −5.18614 8.98266i −0.643262 1.11416i
\(66\) 0 0
\(67\) −5.17769 + 8.96801i −0.632555 + 1.09562i 0.354473 + 0.935066i \(0.384660\pi\)
−0.987028 + 0.160551i \(0.948673\pi\)
\(68\) 0 0
\(69\) 3.55842 1.40965i 0.428384 0.169701i
\(70\) 0 0
\(71\) −4.41957 −0.524507 −0.262253 0.964999i \(-0.584466\pi\)
−0.262253 + 0.964999i \(0.584466\pi\)
\(72\) 0 0
\(73\) 4.62772 0.541634 0.270817 0.962631i \(-0.412706\pi\)
0.270817 + 0.962631i \(0.412706\pi\)
\(74\) 0 0
\(75\) 0.158627 1.07561i 0.0183167 0.124200i
\(76\) 0 0
\(77\) 6.55842 11.3595i 0.747402 1.29454i
\(78\) 0 0
\(79\) −4.83090 8.36737i −0.543519 0.941403i −0.998698 0.0510030i \(-0.983758\pi\)
0.455179 0.890400i \(-0.349575\pi\)
\(80\) 0 0
\(81\) −8.05842 + 4.00772i −0.895380 + 0.445302i
\(82\) 0 0
\(83\) −7.04069 12.1948i −0.772816 1.33856i −0.936014 0.351963i \(-0.885514\pi\)
0.163198 0.986593i \(-0.447819\pi\)
\(84\) 0 0
\(85\) −4.00000 + 6.92820i −0.433861 + 0.751469i
\(86\) 0 0
\(87\) 0.0940770 0.637910i 0.0100861 0.0683912i
\(88\) 0 0
\(89\) 1.25544 0.133076 0.0665380 0.997784i \(-0.478805\pi\)
0.0665380 + 0.997784i \(0.478805\pi\)
\(90\) 0 0
\(91\) −9.66181 −1.01283
\(92\) 0 0
\(93\) 15.5584 6.16337i 1.61333 0.639111i
\(94\) 0 0
\(95\) −4.41957 + 7.65492i −0.453439 + 0.785379i
\(96\) 0 0
\(97\) −4.50000 7.79423i −0.456906 0.791384i 0.541890 0.840450i \(-0.317709\pi\)
−0.998796 + 0.0490655i \(0.984376\pi\)
\(98\) 0 0
\(99\) 12.9765 12.1948i 1.30419 1.22563i
\(100\) 0 0
\(101\) 7.55842 + 13.0916i 0.752091 + 1.30266i 0.946808 + 0.321800i \(0.104288\pi\)
−0.194716 + 0.980860i \(0.562379\pi\)
\(102\) 0 0
\(103\) −1.10489 + 1.91373i −0.108868 + 0.188566i −0.915312 0.402745i \(-0.868056\pi\)
0.806444 + 0.591311i \(0.201389\pi\)
\(104\) 0 0
\(105\) −7.11684 5.63858i −0.694533 0.550269i
\(106\) 0 0
\(107\) 3.72601 0.360207 0.180104 0.983648i \(-0.442357\pi\)
0.180104 + 0.983648i \(0.442357\pi\)
\(108\) 0 0
\(109\) 17.4891 1.67515 0.837577 0.546319i \(-0.183971\pi\)
0.837577 + 0.546319i \(0.183971\pi\)
\(110\) 0 0
\(111\) 5.43039 + 4.30243i 0.515430 + 0.408368i
\(112\) 0 0
\(113\) −5.81386 + 10.0699i −0.546922 + 0.947296i 0.451561 + 0.892240i \(0.350867\pi\)
−0.998483 + 0.0550564i \(0.982466\pi\)
\(114\) 0 0
\(115\) 2.62112 + 4.53991i 0.244420 + 0.423349i
\(116\) 0 0
\(117\) −12.5584 3.78651i −1.16103 0.350063i
\(118\) 0 0
\(119\) 3.72601 + 6.45364i 0.341563 + 0.591604i
\(120\) 0 0
\(121\) −12.1168 + 20.9870i −1.10153 + 1.90791i
\(122\) 0 0
\(123\) −1.61030 + 0.637910i −0.145196 + 0.0575184i
\(124\) 0 0
\(125\) −10.3723 −0.927725
\(126\) 0 0
\(127\) −7.45202 −0.661260 −0.330630 0.943760i \(-0.607261\pi\)
−0.330630 + 0.943760i \(0.607261\pi\)
\(128\) 0 0
\(129\) −1.50000 + 10.1711i −0.132068 + 0.895515i
\(130\) 0 0
\(131\) −4.83090 + 8.36737i −0.422078 + 0.731061i −0.996143 0.0877494i \(-0.972033\pi\)
0.574065 + 0.818810i \(0.305366\pi\)
\(132\) 0 0
\(133\) 4.11684 + 7.13058i 0.356976 + 0.618300i
\(134\) 0 0
\(135\) −7.04069 10.1182i −0.605966 0.870832i
\(136\) 0 0
\(137\) 6.24456 + 10.8159i 0.533509 + 0.924065i 0.999234 + 0.0391351i \(0.0124603\pi\)
−0.465725 + 0.884930i \(0.654206\pi\)
\(138\) 0 0
\(139\) 1.45167 2.51437i 0.123129 0.213266i −0.797871 0.602829i \(-0.794040\pi\)
0.921000 + 0.389562i \(0.127374\pi\)
\(140\) 0 0
\(141\) −0.558422 + 3.78651i −0.0470276 + 0.318881i
\(142\) 0 0
\(143\) 25.9530 2.17030
\(144\) 0 0
\(145\) 0.883156 0.0733421
\(146\) 0 0
\(147\) 3.40876 1.35036i 0.281150 0.111376i
\(148\) 0 0
\(149\) 5.81386 10.0699i 0.476290 0.824958i −0.523341 0.852123i \(-0.675315\pi\)
0.999631 + 0.0271650i \(0.00864795\pi\)
\(150\) 0 0
\(151\) −1.10489 1.91373i −0.0899149 0.155737i 0.817560 0.575843i \(-0.195326\pi\)
−0.907475 + 0.420106i \(0.861993\pi\)
\(152\) 0 0
\(153\) 2.31386 + 9.84868i 0.187064 + 0.796219i
\(154\) 0 0
\(155\) 11.4603 + 19.8498i 0.920510 + 1.59437i
\(156\) 0 0
\(157\) 1.55842 2.69927i 0.124376 0.215425i −0.797113 0.603830i \(-0.793641\pi\)
0.921489 + 0.388405i \(0.126974\pi\)
\(158\) 0 0
\(159\) −5.43039 4.30243i −0.430658 0.341205i
\(160\) 0 0
\(161\) 4.88316 0.384847
\(162\) 0 0
\(163\) −8.83915 −0.692335 −0.346168 0.938173i \(-0.612517\pi\)
−0.346168 + 0.938173i \(0.612517\pi\)
\(164\) 0 0
\(165\) 19.1168 + 15.1460i 1.48824 + 1.17912i
\(166\) 0 0
\(167\) −4.83090 + 8.36737i −0.373827 + 0.647487i −0.990151 0.140006i \(-0.955288\pi\)
0.616324 + 0.787493i \(0.288621\pi\)
\(168\) 0 0
\(169\) −3.05842 5.29734i −0.235263 0.407488i
\(170\) 0 0
\(171\) 2.55657 + 10.8817i 0.195506 + 0.832148i
\(172\) 0 0
\(173\) 0.186141 + 0.322405i 0.0141520 + 0.0245120i 0.873015 0.487694i \(-0.162162\pi\)
−0.858863 + 0.512206i \(0.828828\pi\)
\(174\) 0 0
\(175\) 0.693562 1.20128i 0.0524284 0.0908086i
\(176\) 0 0
\(177\) 16.6753 6.60580i 1.25339 0.496522i
\(178\) 0 0
\(179\) −8.83915 −0.660669 −0.330334 0.943864i \(-0.607162\pi\)
−0.330334 + 0.943864i \(0.607162\pi\)
\(180\) 0 0
\(181\) −8.23369 −0.612005 −0.306003 0.952031i \(-0.598992\pi\)
−0.306003 + 0.952031i \(0.598992\pi\)
\(182\) 0 0
\(183\) 3.82009 25.9030i 0.282389 1.91480i
\(184\) 0 0
\(185\) −4.74456 + 8.21782i −0.348827 + 0.604186i
\(186\) 0 0
\(187\) −10.0086 17.3354i −0.731901 1.26769i
\(188\) 0 0
\(189\) −11.4416 + 0.967215i −0.832252 + 0.0703546i
\(190\) 0 0
\(191\) 8.55691 + 14.8210i 0.619157 + 1.07241i 0.989640 + 0.143572i \(0.0458587\pi\)
−0.370483 + 0.928839i \(0.620808\pi\)
\(192\) 0 0
\(193\) −0.500000 + 0.866025i −0.0359908 + 0.0623379i −0.883460 0.468507i \(-0.844792\pi\)
0.847469 + 0.530845i \(0.178125\pi\)
\(194\) 0 0
\(195\) 2.62112 17.7731i 0.187702 1.27276i
\(196\) 0 0
\(197\) 0.744563 0.0530479 0.0265239 0.999648i \(-0.491556\pi\)
0.0265239 + 0.999648i \(0.491556\pi\)
\(198\) 0 0
\(199\) −20.7107 −1.46815 −0.734073 0.679071i \(-0.762383\pi\)
−0.734073 + 0.679071i \(0.762383\pi\)
\(200\) 0 0
\(201\) −16.6753 + 6.60580i −1.17618 + 0.465937i
\(202\) 0 0
\(203\) 0.411331 0.712446i 0.0288698 0.0500039i
\(204\) 0 0
\(205\) −1.18614 2.05446i −0.0828437 0.143489i
\(206\) 0 0
\(207\) 6.34713 + 1.91373i 0.441156 + 0.133014i
\(208\) 0 0
\(209\) −11.0584 19.1537i −0.764927 1.32489i
\(210\) 0 0
\(211\) −2.62112 + 4.53991i −0.180445 + 0.312540i −0.942032 0.335522i \(-0.891087\pi\)
0.761587 + 0.648063i \(0.224421\pi\)
\(212\) 0 0
\(213\) −6.00000 4.75372i −0.411113 0.325720i
\(214\) 0 0
\(215\) −14.0814 −0.960342
\(216\) 0 0
\(217\) 21.3505 1.44937
\(218\) 0 0
\(219\) 6.28258 + 4.97760i 0.424537 + 0.336355i
\(220\) 0 0
\(221\) −7.37228 + 12.7692i −0.495913 + 0.858947i
\(222\) 0 0
\(223\) 1.10489 + 1.91373i 0.0739891 + 0.128153i 0.900646 0.434553i \(-0.143094\pi\)
−0.826657 + 0.562706i \(0.809760\pi\)
\(224\) 0 0
\(225\) 1.37228 1.28962i 0.0914854 0.0859747i
\(226\) 0 0
\(227\) 4.48412 + 7.76673i 0.297622 + 0.515496i 0.975591 0.219594i \(-0.0704733\pi\)
−0.677970 + 0.735090i \(0.737140\pi\)
\(228\) 0 0
\(229\) 2.18614 3.78651i 0.144464 0.250219i −0.784709 0.619865i \(-0.787187\pi\)
0.929173 + 0.369645i \(0.120521\pi\)
\(230\) 0 0
\(231\) 21.1221 8.36737i 1.38973 0.550533i
\(232\) 0 0
\(233\) 2.86141 0.187457 0.0937285 0.995598i \(-0.470121\pi\)
0.0937285 + 0.995598i \(0.470121\pi\)
\(234\) 0 0
\(235\) −5.24224 −0.341966
\(236\) 0 0
\(237\) 2.44158 16.5557i 0.158598 1.07541i
\(238\) 0 0
\(239\) 8.55691 14.8210i 0.553501 0.958692i −0.444518 0.895770i \(-0.646625\pi\)
0.998018 0.0629214i \(-0.0200418\pi\)
\(240\) 0 0
\(241\) −0.127719 0.221215i −0.00822708 0.0142497i 0.861883 0.507108i \(-0.169285\pi\)
−0.870110 + 0.492858i \(0.835952\pi\)
\(242\) 0 0
\(243\) −15.2508 3.22682i −0.978341 0.207001i
\(244\) 0 0
\(245\) 2.51087 + 4.34896i 0.160414 + 0.277845i
\(246\) 0 0
\(247\) −8.14558 + 14.1086i −0.518291 + 0.897706i
\(248\) 0 0
\(249\) 3.55842 24.1287i 0.225506 1.52909i
\(250\) 0 0
\(251\) 11.1780 0.705551 0.352776 0.935708i \(-0.385238\pi\)
0.352776 + 0.935708i \(0.385238\pi\)
\(252\) 0 0
\(253\) −13.1168 −0.824649
\(254\) 0 0
\(255\) −12.8824 + 5.10328i −0.806728 + 0.319580i
\(256\) 0 0
\(257\) 3.24456 5.61975i 0.202390 0.350550i −0.746908 0.664928i \(-0.768462\pi\)
0.949298 + 0.314377i \(0.101796\pi\)
\(258\) 0 0
\(259\) 4.41957 + 7.65492i 0.274619 + 0.475654i
\(260\) 0 0
\(261\) 0.813859 0.764836i 0.0503766 0.0473421i
\(262\) 0 0
\(263\) −8.55691 14.8210i −0.527642 0.913903i −0.999481 0.0322179i \(-0.989743\pi\)
0.471839 0.881685i \(-0.343590\pi\)
\(264\) 0 0
\(265\) 4.74456 8.21782i 0.291456 0.504817i
\(266\) 0 0
\(267\) 1.70438 + 1.35036i 0.104306 + 0.0826405i
\(268\) 0 0
\(269\) 9.48913 0.578562 0.289281 0.957244i \(-0.406584\pi\)
0.289281 + 0.957244i \(0.406584\pi\)
\(270\) 0 0
\(271\) −14.9040 −0.905356 −0.452678 0.891674i \(-0.649531\pi\)
−0.452678 + 0.891674i \(0.649531\pi\)
\(272\) 0 0
\(273\) −13.1168 10.3923i −0.793868 0.628971i
\(274\) 0 0
\(275\) −1.86301 + 3.22682i −0.112343 + 0.194585i
\(276\) 0 0
\(277\) −6.55842 11.3595i −0.394057 0.682527i 0.598923 0.800807i \(-0.295596\pi\)
−0.992980 + 0.118279i \(0.962262\pi\)
\(278\) 0 0
\(279\) 27.7514 + 8.36737i 1.66143 + 0.500941i
\(280\) 0 0
\(281\) −12.9307 22.3966i −0.771381 1.33607i −0.936806 0.349849i \(-0.886233\pi\)
0.165425 0.986222i \(-0.447100\pi\)
\(282\) 0 0
\(283\) 2.62112 4.53991i 0.155809 0.269870i −0.777544 0.628828i \(-0.783535\pi\)
0.933353 + 0.358959i \(0.116868\pi\)
\(284\) 0 0
\(285\) −14.2337 + 5.63858i −0.843131 + 0.334001i
\(286\) 0 0
\(287\) −2.20979 −0.130440
\(288\) 0 0
\(289\) −5.62772 −0.331042
\(290\) 0 0
\(291\) 2.27434 15.4217i 0.133324 0.904033i
\(292\) 0 0
\(293\) 10.1861 17.6429i 0.595081 1.03071i −0.398455 0.917188i \(-0.630453\pi\)
0.993535 0.113522i \(-0.0362132\pi\)
\(294\) 0 0
\(295\) 12.2829 + 21.2747i 0.715140 + 1.23866i
\(296\) 0 0
\(297\) 30.7337 2.59808i 1.78335 0.150756i
\(298\) 0 0
\(299\) 4.83090 + 8.36737i 0.279378 + 0.483898i
\(300\) 0 0
\(301\) −6.55842 + 11.3595i −0.378021 + 0.654752i
\(302\) 0 0
\(303\) −3.82009 + 25.9030i −0.219458 + 1.48809i
\(304\) 0 0
\(305\) 35.8614 2.05342
\(306\) 0 0
\(307\) 28.8563 1.64692 0.823459 0.567376i \(-0.192041\pi\)
0.823459 + 0.567376i \(0.192041\pi\)
\(308\) 0 0
\(309\) −3.55842 + 1.40965i −0.202432 + 0.0801919i
\(310\) 0 0
\(311\) −6.34713 + 10.9935i −0.359913 + 0.623387i −0.987946 0.154800i \(-0.950527\pi\)
0.628033 + 0.778186i \(0.283860\pi\)
\(312\) 0 0
\(313\) −9.61684 16.6569i −0.543576 0.941502i −0.998695 0.0510708i \(-0.983737\pi\)
0.455119 0.890431i \(-0.349597\pi\)
\(314\) 0 0
\(315\) −3.59691 15.3098i −0.202663 0.862612i
\(316\) 0 0
\(317\) −4.18614 7.25061i −0.235117 0.407235i 0.724190 0.689601i \(-0.242214\pi\)
−0.959307 + 0.282366i \(0.908881\pi\)
\(318\) 0 0
\(319\) −1.10489 + 1.91373i −0.0618621 + 0.107148i
\(320\) 0 0
\(321\) 5.05842 + 4.00772i 0.282334 + 0.223689i
\(322\) 0 0
\(323\) 12.5652 0.699144
\(324\) 0 0
\(325\) 2.74456 0.152241
\(326\) 0 0
\(327\) 23.7432 + 18.8114i 1.31300 + 1.04027i
\(328\) 0 0
\(329\) −2.44158 + 4.22894i −0.134609 + 0.233149i
\(330\) 0 0
\(331\) −16.7025 28.9296i −0.918052 1.59011i −0.802370 0.596827i \(-0.796428\pi\)
−0.115682 0.993286i \(-0.536905\pi\)
\(332\) 0 0
\(333\) 2.74456 + 11.6819i 0.150401 + 0.640166i
\(334\) 0 0
\(335\) −12.2829 21.2747i −0.671088 1.16236i
\(336\) 0 0
\(337\) 4.50000 7.79423i 0.245131 0.424579i −0.717038 0.697034i \(-0.754502\pi\)
0.962168 + 0.272456i \(0.0878358\pi\)
\(338\) 0 0
\(339\) −18.7241 + 7.41744i −1.01696 + 0.402860i
\(340\) 0 0
\(341\) −57.3505 −3.10571
\(342\) 0 0
\(343\) 20.1463 1.08780
\(344\) 0 0
\(345\) −1.32473 + 8.98266i −0.0713213 + 0.483610i
\(346\) 0 0
\(347\) −5.17769 + 8.96801i −0.277953 + 0.481428i −0.970876 0.239583i \(-0.922989\pi\)
0.692923 + 0.721011i \(0.256323\pi\)
\(348\) 0 0
\(349\) 11.5584 + 20.0198i 0.618708 + 1.07163i 0.989722 + 0.143007i \(0.0456770\pi\)
−0.371014 + 0.928627i \(0.620990\pi\)
\(350\) 0 0
\(351\) −12.9765 18.6485i −0.692634 0.995382i
\(352\) 0 0
\(353\) 9.61684 + 16.6569i 0.511853 + 0.886555i 0.999906 + 0.0137411i \(0.00437407\pi\)
−0.488053 + 0.872814i \(0.662293\pi\)
\(354\) 0 0
\(355\) 5.24224 9.07982i 0.278229 0.481907i
\(356\) 0 0
\(357\) −1.88316 + 12.7692i −0.0996672 + 0.675816i
\(358\) 0 0
\(359\) −22.3561 −1.17991 −0.589954 0.807437i \(-0.700854\pi\)
−0.589954 + 0.807437i \(0.700854\pi\)
\(360\) 0 0
\(361\) −5.11684 −0.269308
\(362\) 0 0
\(363\) −39.0235 + 15.4589i −2.04820 + 0.811383i
\(364\) 0 0
\(365\) −5.48913 + 9.50744i −0.287314 + 0.497642i
\(366\) 0 0
\(367\) −13.6700 23.6772i −0.713571 1.23594i −0.963508 0.267679i \(-0.913743\pi\)
0.249937 0.968262i \(-0.419590\pi\)
\(368\) 0 0
\(369\) −2.87228 0.866025i −0.149525 0.0450835i
\(370\) 0 0
\(371\) −4.41957 7.65492i −0.229453 0.397424i
\(372\) 0 0
\(373\) 8.55842 14.8236i 0.443138 0.767538i −0.554782 0.831996i \(-0.687198\pi\)
0.997920 + 0.0644576i \(0.0205317\pi\)
\(374\) 0 0
\(375\) −14.0814 11.1565i −0.727159 0.576119i
\(376\) 0 0
\(377\) 1.62772 0.0838318
\(378\) 0 0
\(379\) 8.14558 0.418411 0.209205 0.977872i \(-0.432912\pi\)
0.209205 + 0.977872i \(0.432912\pi\)
\(380\) 0 0
\(381\) −10.1168 8.01544i −0.518302 0.410644i
\(382\) 0 0
\(383\) 11.4603 19.8498i 0.585592 1.01428i −0.409209 0.912441i \(-0.634195\pi\)
0.994801 0.101835i \(-0.0324713\pi\)
\(384\) 0 0
\(385\) 15.5584 + 26.9480i 0.792931 + 1.37340i
\(386\) 0 0
\(387\) −12.9765 + 12.1948i −0.659632 + 0.619898i
\(388\) 0 0
\(389\) 9.67527 + 16.7581i 0.490555 + 0.849667i 0.999941 0.0108715i \(-0.00346057\pi\)
−0.509385 + 0.860538i \(0.670127\pi\)
\(390\) 0 0
\(391\) 3.72601 6.45364i 0.188432 0.326375i
\(392\) 0 0
\(393\) −15.5584 + 6.16337i −0.784819 + 0.310901i
\(394\) 0 0
\(395\) 22.9205 1.15326
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) −2.08069 + 14.1086i −0.104165 + 0.706312i
\(400\) 0 0
\(401\) −13.9891 + 24.2299i −0.698584 + 1.20998i 0.270374 + 0.962755i \(0.412853\pi\)
−0.968958 + 0.247227i \(0.920481\pi\)
\(402\) 0 0
\(403\) 21.1221 + 36.5845i 1.05217 + 1.82240i
\(404\) 0 0
\(405\) 1.32473 21.3094i 0.0658266 1.05887i
\(406\) 0 0
\(407\) −11.8716 20.5622i −0.588453 1.01923i
\(408\) 0 0
\(409\) 9.12772 15.8097i 0.451337 0.781738i −0.547133 0.837046i \(-0.684281\pi\)
0.998469 + 0.0553079i \(0.0176140\pi\)
\(410\) 0 0
\(411\) −3.15605 + 21.4003i −0.155677 + 1.05560i
\(412\) 0 0
\(413\) 22.8832 1.12601
\(414\) 0 0
\(415\) 33.4050 1.63979
\(416\) 0 0
\(417\) 4.67527 1.85208i 0.228949 0.0906966i
\(418\) 0 0
\(419\) −2.62112 + 4.53991i −0.128050 + 0.221789i −0.922921 0.384989i \(-0.874205\pi\)
0.794871 + 0.606778i \(0.207538\pi\)
\(420\) 0 0
\(421\) 11.1861 + 19.3750i 0.545179 + 0.944278i 0.998596 + 0.0529792i \(0.0168717\pi\)
−0.453416 + 0.891299i \(0.649795\pi\)
\(422\) 0 0
\(423\) −4.83090 + 4.53991i −0.234887 + 0.220738i
\(424\) 0 0
\(425\) −1.05842 1.83324i −0.0513410 0.0889252i
\(426\) 0 0
\(427\) 16.7025 28.9296i 0.808291 1.40000i
\(428\) 0 0
\(429\) 35.2337 + 27.9152i 1.70110 + 1.34776i
\(430\) 0 0
\(431\) −7.45202 −0.358951 −0.179476 0.983762i \(-0.557440\pi\)
−0.179476 + 0.983762i \(0.557440\pi\)
\(432\) 0 0
\(433\) −18.1168 −0.870640 −0.435320 0.900276i \(-0.643365\pi\)
−0.435320 + 0.900276i \(0.643365\pi\)
\(434\) 0 0
\(435\) 1.19897 + 0.949929i 0.0574862 + 0.0455456i
\(436\) 0 0
\(437\) 4.11684 7.13058i 0.196935 0.341102i
\(438\) 0 0
\(439\) 11.4603 + 19.8498i 0.546969 + 0.947377i 0.998480 + 0.0551120i \(0.0175516\pi\)
−0.451512 + 0.892265i \(0.649115\pi\)
\(440\) 0 0
\(441\) 6.08017 + 1.83324i 0.289532 + 0.0872972i
\(442\) 0 0
\(443\) −4.48412 7.76673i −0.213047 0.369008i 0.739620 0.673025i \(-0.235005\pi\)
−0.952667 + 0.304017i \(0.901672\pi\)
\(444\) 0 0
\(445\) −1.48913 + 2.57924i −0.0705913 + 0.122268i
\(446\) 0 0
\(447\) 18.7241 7.41744i 0.885621 0.350833i
\(448\) 0 0
\(449\) −18.1168 −0.854987 −0.427493 0.904018i \(-0.640603\pi\)
−0.427493 + 0.904018i \(0.640603\pi\)
\(450\) 0 0
\(451\) 5.93580 0.279506
\(452\) 0 0
\(453\) 0.558422 3.78651i 0.0262370 0.177906i
\(454\) 0 0
\(455\) 11.4603 19.8498i 0.537265 0.930571i
\(456\) 0 0
\(457\) 12.9891 + 22.4978i 0.607606 + 1.05240i 0.991634 + 0.129083i \(0.0412032\pi\)
−0.384028 + 0.923321i \(0.625463\pi\)
\(458\) 0 0
\(459\) −7.45202 + 15.8593i −0.347831 + 0.740251i
\(460\) 0 0
\(461\) 14.5584 + 25.2159i 0.678053 + 1.17442i 0.975566 + 0.219705i \(0.0705095\pi\)
−0.297513 + 0.954718i \(0.596157\pi\)
\(462\) 0 0
\(463\) −18.9123 + 32.7570i −0.878928 + 1.52235i −0.0264102 + 0.999651i \(0.508408\pi\)
−0.852518 + 0.522697i \(0.824926\pi\)
\(464\) 0 0
\(465\) −5.79211 + 39.2747i −0.268603 + 1.82132i
\(466\) 0 0
\(467\) −36.3083 −1.68015 −0.840075 0.542470i \(-0.817489\pi\)
−0.840075 + 0.542470i \(0.817489\pi\)
\(468\) 0 0
\(469\) −22.8832 −1.05665
\(470\) 0 0
\(471\) 5.01906 1.98827i 0.231266 0.0916145i
\(472\) 0 0
\(473\) 17.6168 30.5133i 0.810023 1.40300i
\(474\) 0 0
\(475\) −1.16944 2.02554i −0.0536577 0.0929379i
\(476\) 0 0
\(477\) −2.74456 11.6819i −0.125665 0.534879i
\(478\) 0 0
\(479\) −1.10489 1.91373i −0.0504839 0.0874406i 0.839679 0.543083i \(-0.182743\pi\)
−0.890163 + 0.455642i \(0.849410\pi\)
\(480\) 0 0
\(481\) −8.74456 + 15.1460i −0.398718 + 0.690599i
\(482\) 0 0
\(483\) 6.62936 + 5.25236i 0.301646 + 0.238990i
\(484\) 0 0
\(485\) 21.3505 0.969478
\(486\) 0 0
\(487\) −7.45202 −0.337683 −0.168842 0.985643i \(-0.554003\pi\)
−0.168842 + 0.985643i \(0.554003\pi\)
\(488\) 0 0
\(489\) −12.0000 9.50744i −0.542659 0.429941i
\(490\) 0 0
\(491\) 0.0645501 0.111804i 0.00291310 0.00504564i −0.864565 0.502521i \(-0.832406\pi\)
0.867478 + 0.497475i \(0.165739\pi\)
\(492\) 0 0
\(493\) −0.627719 1.08724i −0.0282710 0.0489669i
\(494\) 0 0
\(495\) 9.66181 + 41.1244i 0.434266 + 1.84840i
\(496\) 0 0
\(497\) −4.88316 8.45787i −0.219039 0.379388i
\(498\) 0 0
\(499\) 12.6297 21.8753i 0.565383 0.979273i −0.431631 0.902050i \(-0.642062\pi\)
0.997014 0.0772222i \(-0.0246051\pi\)
\(500\) 0 0
\(501\) −15.5584 + 6.16337i −0.695099 + 0.275359i
\(502\) 0 0
\(503\) −10.4845 −0.467479 −0.233740 0.972299i \(-0.575096\pi\)
−0.233740 + 0.972299i \(0.575096\pi\)
\(504\) 0 0
\(505\) −35.8614 −1.59581
\(506\) 0 0
\(507\) 1.54575 10.4813i 0.0686492 0.465492i
\(508\) 0 0
\(509\) 6.67527 11.5619i 0.295876 0.512472i −0.679312 0.733849i \(-0.737722\pi\)
0.975188 + 0.221377i \(0.0710552\pi\)
\(510\) 0 0
\(511\) 5.11313 + 8.85621i 0.226192 + 0.391776i
\(512\) 0 0
\(513\) −8.23369 + 17.5229i −0.363526 + 0.773654i
\(514\) 0 0
\(515\) −2.62112 4.53991i −0.115500 0.200052i
\(516\) 0 0
\(517\) 6.55842 11.3595i 0.288439 0.499591i
\(518\) 0 0
\(519\) −0.0940770 + 0.637910i −0.00412952 + 0.0280012i
\(520\) 0 0
\(521\) −16.3505 −0.716330 −0.358165 0.933658i \(-0.616597\pi\)
−0.358165 + 0.933658i \(0.616597\pi\)
\(522\) 0 0
\(523\) 19.3236 0.844963 0.422481 0.906372i \(-0.361159\pi\)
0.422481 + 0.906372i \(0.361159\pi\)
\(524\) 0 0
\(525\) 2.23369 0.884861i 0.0974861 0.0386185i
\(526\) 0 0
\(527\) 16.2912 28.2171i 0.709654 1.22916i
\(528\) 0 0
\(529\) 9.05842 + 15.6896i 0.393844 + 0.682159i
\(530\) 0 0
\(531\) 29.7435 + 8.96801i 1.29076 + 0.389179i
\(532\) 0 0
\(533\) −2.18614 3.78651i −0.0946923 0.164012i
\(534\) 0 0
\(535\) −4.41957 + 7.65492i −0.191075 + 0.330951i
\(536\) 0 0
\(537\) −12.0000 9.50744i −0.517838 0.410276i
\(538\) 0 0
\(539\) −12.5652 −0.541220
\(540\) 0 0
\(541\) 8.74456 0.375958 0.187979 0.982173i \(-0.439806\pi\)
0.187979 + 0.982173i \(0.439806\pi\)
\(542\) 0 0
\(543\) −11.1780 8.85621i −0.479695 0.380056i
\(544\) 0 0
\(545\) −20.7446 + 35.9306i −0.888599 + 1.53910i
\(546\) 0 0
\(547\) 0.758112 + 1.31309i 0.0324145 + 0.0561436i 0.881778 0.471665i \(-0.156347\pi\)
−0.849363 + 0.527809i \(0.823014\pi\)
\(548\) 0 0
\(549\) 33.0475 31.0569i 1.41043 1.32548i
\(550\) 0 0
\(551\) −0.693562 1.20128i −0.0295467 0.0511765i
\(552\) 0 0
\(553\) 10.6753 18.4901i 0.453958 0.786279i
\(554\) 0 0
\(555\) −15.2804 + 6.05321i −0.648615 + 0.256945i
\(556\) 0 0
\(557\) −18.7446 −0.794233 −0.397116 0.917768i \(-0.629989\pi\)
−0.397116 + 0.917768i \(0.629989\pi\)
\(558\) 0 0
\(559\) −25.9530 −1.09769
\(560\) 0 0
\(561\) 5.05842 34.2998i 0.213567 1.44814i
\(562\) 0 0
\(563\) 11.1135 19.2491i 0.468377 0.811254i −0.530969 0.847391i \(-0.678172\pi\)
0.999347 + 0.0361375i \(0.0115054\pi\)
\(564\) 0 0
\(565\) −13.7921 23.8886i −0.580238 1.00500i
\(566\) 0 0
\(567\) −16.5734 10.9935i −0.696017 0.461686i
\(568\) 0 0
\(569\) 19.8723 + 34.4198i 0.833089 + 1.44295i 0.895577 + 0.444907i \(0.146763\pi\)
−0.0624872 + 0.998046i \(0.519903\pi\)
\(570\) 0 0
\(571\) −0.0645501 + 0.111804i −0.00270134 + 0.00467885i −0.867373 0.497659i \(-0.834193\pi\)
0.864672 + 0.502338i \(0.167527\pi\)
\(572\) 0 0
\(573\) −4.32473 + 29.3248i −0.180668 + 1.22506i
\(574\) 0 0
\(575\) −1.38712 −0.0578471
\(576\) 0 0
\(577\) 18.1168 0.754214 0.377107 0.926170i \(-0.376919\pi\)
0.377107 + 0.926170i \(0.376919\pi\)
\(578\) 0 0
\(579\) −1.61030 + 0.637910i −0.0669218 + 0.0265107i
\(580\) 0 0
\(581\) 15.5584 26.9480i 0.645472 1.11799i
\(582\) 0 0
\(583\) 11.8716 + 20.5622i 0.491671 + 0.851599i
\(584\) 0 0
\(585\) 22.6753 21.3094i 0.937507 0.881035i
\(586\) 0 0
\(587\) −5.87125 10.1693i −0.242332 0.419732i 0.719046 0.694963i \(-0.244579\pi\)
−0.961378 + 0.275231i \(0.911246\pi\)
\(588\) 0 0
\(589\) 18.0000 31.1769i 0.741677 1.28462i
\(590\) 0 0
\(591\) 1.01082 + 0.800857i 0.0415794 + 0.0329428i
\(592\) 0 0
\(593\) −17.7228 −0.727789 −0.363894 0.931440i \(-0.618553\pi\)
−0.363894 + 0.931440i \(0.618553\pi\)
\(594\) 0 0
\(595\) −17.6783 −0.724739
\(596\) 0 0
\(597\) −28.1168 22.2766i −1.15075 0.911721i
\(598\) 0 0
\(599\) −13.6700 + 23.6772i −0.558543 + 0.967425i 0.439075 + 0.898450i \(0.355306\pi\)
−0.997618 + 0.0689747i \(0.978027\pi\)
\(600\) 0 0
\(601\) 1.38316 + 2.39570i 0.0564201 + 0.0977225i 0.892856 0.450342i \(-0.148698\pi\)
−0.836436 + 0.548065i \(0.815365\pi\)
\(602\) 0 0
\(603\) −29.7435 8.96801i −1.21125 0.365206i
\(604\) 0 0
\(605\) −28.7446 49.7870i −1.16863 2.02413i
\(606\) 0 0
\(607\) 18.9123 32.7570i 0.767626 1.32957i −0.171221 0.985233i \(-0.554771\pi\)
0.938847 0.344335i \(-0.111895\pi\)
\(608\) 0 0
\(609\) 1.32473 0.524785i 0.0536809 0.0212654i
\(610\) 0 0
\(611\) −9.66181 −0.390875
\(612\) 0 0
\(613\) 36.4674 1.47290 0.736452 0.676490i \(-0.236500\pi\)
0.736452 + 0.676490i \(0.236500\pi\)
\(614\) 0 0
\(615\) 0.599485 4.06494i 0.0241736 0.163914i
\(616\) 0 0
\(617\) 18.8723 32.6878i 0.759769 1.31596i −0.183199 0.983076i \(-0.558645\pi\)
0.942968 0.332883i \(-0.108022\pi\)
\(618\) 0 0
\(619\) 0.758112 + 1.31309i 0.0304711 + 0.0527775i 0.880859 0.473379i \(-0.156966\pi\)
−0.850388 + 0.526157i \(0.823633\pi\)
\(620\) 0 0
\(621\) 6.55842 + 9.42509i 0.263180 + 0.378216i
\(622\) 0 0
\(623\) 1.38712 + 2.40257i 0.0555740 + 0.0962569i
\(624\) 0 0
\(625\) 13.8723 24.0275i 0.554891 0.961100i
\(626\) 0 0
\(627\) 5.58902 37.8976i 0.223204 1.51348i
\(628\) 0 0
\(629\) 13.4891 0.537847
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −8.44158 + 3.34408i −0.335523 + 0.132915i
\(634\) 0 0
\(635\) 8.83915 15.3098i 0.350771 0.607553i
\(636\) 0 0
\(637\) 4.62772 + 8.01544i 0.183357 + 0.317583i
\(638\) 0 0
\(639\) −3.03245 12.9073i −0.119962 0.510604i
\(640\) 0 0
\(641\) −6.87228 11.9031i −0.271439 0.470146i 0.697792 0.716301i \(-0.254166\pi\)
−0.969230 + 0.246155i \(0.920833\pi\)
\(642\) 0 0
\(643\) −8.90370 + 15.4217i −0.351127 + 0.608171i −0.986447 0.164079i \(-0.947535\pi\)
0.635320 + 0.772249i \(0.280868\pi\)
\(644\) 0 0
\(645\) −19.1168 15.1460i −0.752725 0.596374i
\(646\) 0 0
\(647\) 40.0344 1.57391 0.786956 0.617009i \(-0.211656\pi\)
0.786956 + 0.617009i \(0.211656\pi\)
\(648\) 0 0
\(649\) −61.4674 −2.41281
\(650\) 0 0
\(651\) 28.9854 + 22.9648i 1.13603 + 0.900060i
\(652\) 0 0
\(653\) −20.5584 + 35.6082i −0.804513 + 1.39346i 0.112106 + 0.993696i \(0.464240\pi\)
−0.916619 + 0.399762i \(0.869093\pi\)
\(654\) 0 0
\(655\) −11.4603 19.8498i −0.447790 0.775594i
\(656\) 0 0
\(657\) 3.17527 + 13.5152i 0.123879 + 0.527277i
\(658\) 0 0
\(659\) 15.8798 + 27.5047i 0.618591 + 1.07143i 0.989743 + 0.142858i \(0.0456294\pi\)
−0.371153 + 0.928572i \(0.621037\pi\)
\(660\) 0 0
\(661\) 1.55842 2.69927i 0.0606156 0.104989i −0.834125 0.551575i \(-0.814027\pi\)
0.894741 + 0.446586i \(0.147360\pi\)
\(662\) 0 0
\(663\) −23.7432 + 9.40571i −0.922109 + 0.365287i
\(664\) 0 0
\(665\) −19.5326 −0.757443
\(666\) 0 0
\(667\) −0.822662 −0.0318536
\(668\) 0 0
\(669\) −0.558422 + 3.78651i −0.0215898 + 0.146395i
\(670\) 0 0
\(671\) −44.8653 + 77.7089i −1.73200 + 2.99992i
\(672\) 0 0
\(673\) −11.6753 20.2222i −0.450048 0.779507i 0.548340 0.836255i \(-0.315260\pi\)
−0.998388 + 0.0567487i \(0.981927\pi\)
\(674\) 0 0
\(675\) 3.25013 0.274750i 0.125098 0.0105751i
\(676\) 0 0
\(677\) −0.675266 1.16959i −0.0259526 0.0449512i 0.852757 0.522307i \(-0.174929\pi\)
−0.878710 + 0.477356i \(0.841595\pi\)
\(678\) 0 0
\(679\) 9.94404 17.2236i 0.381617 0.660980i
\(680\) 0 0
\(681\) −2.26631 + 15.3672i −0.0868453 + 0.588874i
\(682\) 0 0
\(683\) 36.3083 1.38930 0.694650 0.719348i \(-0.255559\pi\)
0.694650 + 0.719348i \(0.255559\pi\)
\(684\) 0 0
\(685\) −29.6277 −1.13202
\(686\) 0 0
\(687\) 7.04069 2.78912i 0.268619 0.106412i
\(688\) 0 0
\(689\) 8.74456 15.1460i 0.333141 0.577018i
\(690\) 0 0
\(691\) −23.3319 40.4120i −0.887586 1.53734i −0.842721 0.538350i \(-0.819048\pi\)
−0.0448646 0.998993i \(-0.514286\pi\)
\(692\) 0 0
\(693\) 37.6753 + 11.3595i 1.43117 + 0.431512i
\(694\) 0 0
\(695\) 3.44378 + 5.96480i 0.130630 + 0.226258i
\(696\) 0 0
\(697\) −1.68614 + 2.92048i −0.0638671 + 0.110621i
\(698\) 0 0
\(699\) 3.88464 + 3.07775i 0.146930 + 0.116411i
\(700\) 0 0
\(701\) 34.7446 1.31228 0.656142 0.754637i \(-0.272187\pi\)
0.656142 + 0.754637i \(0.272187\pi\)
\(702\) 0 0
\(703\) 14.9040 0.562117
\(704\) 0 0
\(705\) −7.11684 5.63858i −0.268036 0.212361i
\(706\) 0 0
\(707\) −16.7025 + 28.9296i −0.628162 + 1.08801i
\(708\) 0 0
\(709\) 6.30298 + 10.9171i 0.236714 + 0.410000i 0.959769 0.280790i \(-0.0905964\pi\)
−0.723056 + 0.690790i \(0.757263\pi\)
\(710\) 0 0
\(711\) 21.1221 19.8498i 0.792140 0.744424i
\(712\) 0 0
\(713\) −10.6753 18.4901i −0.399792 0.692460i
\(714\) 0 0
\(715\) −30.7839 + 53.3192i −1.15125 + 1.99403i
\(716\) 0 0
\(717\) 27.5584 10.9171i 1.02919 0.407706i
\(718\) 0 0
\(719\) 32.5823 1.21512 0.607558 0.794275i \(-0.292149\pi\)
0.607558 + 0.794275i \(0.292149\pi\)
\(720\) 0 0
\(721\) −4.88316 −0.181858
\(722\) 0 0
\(723\) 0.0645501 0.437696i 0.00240064 0.0162781i
\(724\) 0 0
\(725\) −0.116844 + 0.202380i −0.00433948 + 0.00751619i
\(726\) 0 0
\(727\) −17.3961 30.1309i −0.645184 1.11749i −0.984259 0.176732i \(-0.943447\pi\)
0.339075 0.940759i \(-0.389886\pi\)
\(728\) 0 0
\(729\) −17.2337 20.7846i −0.638285 0.769800i
\(730\) 0 0
\(731\) 10.0086 + 17.3354i 0.370181 + 0.641172i
\(732\) 0 0
\(733\) −11.4416 + 19.8174i −0.422604 + 0.731972i −0.996193 0.0871711i \(-0.972217\pi\)
0.573589 + 0.819143i \(0.305551\pi\)
\(734\) 0 0
\(735\) −1.26902 + 8.60485i −0.0468084 + 0.317395i
\(736\) 0 0
\(737\) 61.4674 2.26418
\(738\) 0 0
\(739\) −15.5976 −0.573767 −0.286884 0.957965i \(-0.592619\pi\)
−0.286884 + 0.957965i \(0.592619\pi\)
\(740\) 0 0
\(741\) −26.2337 + 10.3923i −0.963719 + 0.381771i
\(742\) 0 0
\(743\) 13.7991 23.9008i 0.506242 0.876836i −0.493732 0.869614i \(-0.664368\pi\)
0.999974 0.00722236i \(-0.00229897\pi\)
\(744\) 0 0
\(745\) 13.7921 + 23.8886i 0.505304 + 0.875212i
\(746\) 0 0
\(747\) 30.7839 28.9296i 1.12632 1.05848i
\(748\) 0 0
\(749\) 4.11684 + 7.13058i 0.150426 + 0.260546i
\(750\) 0 0
\(751\) 11.4603 19.8498i 0.418191 0.724328i −0.577567 0.816344i \(-0.695998\pi\)
0.995758 + 0.0920156i \(0.0293310\pi\)
\(752\) 0 0
\(753\) 15.1753 + 12.0232i 0.553017 + 0.438149i
\(754\) 0 0
\(755\) 5.24224 0.190784
\(756\) 0 0
\(757\) −34.4674 −1.25274 −0.626369 0.779527i \(-0.715460\pi\)
−0.626369 + 0.779527i \(0.715460\pi\)
\(758\) 0 0
\(759\) −17.8074 14.1086i −0.646367 0.512108i
\(760\) 0 0
\(761\) −10.1861 + 17.6429i −0.369247 + 0.639555i −0.989448 0.144888i \(-0.953718\pi\)
0.620201 + 0.784443i \(0.287051\pi\)
\(762\) 0 0
\(763\) 19.3236 + 33.4695i 0.699562 + 1.21168i
\(764\) 0 0
\(765\) −22.9783 6.92820i −0.830780 0.250490i
\(766\) 0 0
\(767\) 22.6383 + 39.2107i 0.817421 + 1.41582i
\(768\) 0 0
\(769\) 7.44158 12.8892i 0.268350 0.464796i −0.700086 0.714059i \(-0.746855\pi\)
0.968436 + 0.249263i \(0.0801882\pi\)
\(770\) 0 0
\(771\) 10.4494 4.13948i 0.376328 0.149080i
\(772\) 0 0
\(773\) −18.7446 −0.674195 −0.337098 0.941470i \(-0.609445\pi\)
−0.337098 + 0.941470i \(0.609445\pi\)
\(774\) 0 0
\(775\) −6.06490 −0.217858
\(776\) 0 0
\(777\) −2.23369 + 15.1460i −0.0801331 + 0.543361i
\(778\) 0 0
\(779\) −1.86301 + 3.22682i −0.0667491 + 0.115613i
\(780\) 0 0
\(781\) 13.1168 + 22.7190i 0.469358 + 0.812951i
\(782\) 0 0
\(783\) 1.92756 0.162946i 0.0688852 0.00582322i
\(784\) 0 0
\(785\) 3.69702 + 6.40342i 0.131952 + 0.228548i
\(786\) 0 0
\(787\) −21.1221 + 36.5845i −0.752921 + 1.30410i 0.193481 + 0.981104i \(0.438022\pi\)
−0.946402 + 0.322993i \(0.895311\pi\)
\(788\) 0 0
\(789\) 4.32473 29.3248i 0.153965 1.04399i
\(790\) 0 0
\(791\) −25.6948 −0.913601
\(792\) 0 0
\(793\) 66.0951 2.34711
\(794\) 0 0
\(795\) 15.2804 6.05321i 0.541938 0.214685i
\(796\) 0 0