Properties

Label 576.2.bb.d.529.1
Level $576$
Weight $2$
Character 576.529
Analytic conductor $4.599$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 529.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.529
Dual form 576.2.bb.d.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{3} +(-3.73205 - 1.00000i) q^{5} +(0.633975 + 0.366025i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{3} +(-3.73205 - 1.00000i) q^{5} +(0.633975 + 0.366025i) q^{7} +(1.50000 + 2.59808i) q^{9} +(0.767949 + 2.86603i) q^{11} +(-1.63397 + 6.09808i) q^{13} +(-4.73205 - 4.73205i) q^{15} -2.26795 q^{17} +(0.633975 + 0.633975i) q^{19} +(0.633975 + 1.09808i) q^{21} +(1.09808 - 0.633975i) q^{23} +(8.59808 + 4.96410i) q^{25} +5.19615i q^{27} +(-2.36603 + 0.633975i) q^{29} +(3.73205 + 6.46410i) q^{31} +(-1.33013 + 4.96410i) q^{33} +(-2.00000 - 2.00000i) q^{35} +(1.26795 - 1.26795i) q^{37} +(-7.73205 + 7.73205i) q^{39} +(-2.59808 + 1.50000i) q^{41} +(-0.330127 - 1.23205i) q^{43} +(-3.00000 - 11.1962i) q^{45} +(4.83013 - 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(-3.40192 - 1.96410i) q^{51} +(-0.535898 + 0.535898i) q^{53} -11.4641i q^{55} +(0.401924 + 1.50000i) q^{57} +(-4.96410 - 1.33013i) q^{59} +(-3.00000 + 0.803848i) q^{61} +2.19615i q^{63} +(12.1962 - 21.1244i) q^{65} +(-1.40192 + 5.23205i) q^{67} +2.19615 q^{69} +10.9282i q^{71} -9.73205i q^{73} +(8.59808 + 14.8923i) q^{75} +(-0.562178 + 2.09808i) q^{77} +(6.00000 - 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(1.36603 - 0.366025i) q^{83} +(8.46410 + 2.26795i) q^{85} +(-4.09808 - 1.09808i) q^{87} -2.00000i q^{89} +(-3.26795 + 3.26795i) q^{91} +12.9282i q^{93} +(-1.73205 - 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +(-6.29423 + 6.29423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} - 8 q^{5} + 6 q^{7} + 6 q^{9} + O(q^{10}) \) \( 4 q + 6 q^{3} - 8 q^{5} + 6 q^{7} + 6 q^{9} + 10 q^{11} - 10 q^{13} - 12 q^{15} - 16 q^{17} + 6 q^{19} + 6 q^{21} - 6 q^{23} + 24 q^{25} - 6 q^{29} + 8 q^{31} + 12 q^{33} - 8 q^{35} + 12 q^{37} - 24 q^{39} + 16 q^{43} - 12 q^{45} + 2 q^{47} - 6 q^{49} - 24 q^{51} - 16 q^{53} + 12 q^{57} - 6 q^{59} - 12 q^{61} + 28 q^{65} - 16 q^{67} - 12 q^{69} + 24 q^{75} + 22 q^{77} + 24 q^{79} - 18 q^{81} + 2 q^{83} + 20 q^{85} - 6 q^{87} - 20 q^{91} - 20 q^{97} + 6 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 0 0
\(5\) −3.73205 1.00000i −1.66902 0.447214i −0.704177 0.710025i \(-0.748684\pi\)
−0.964847 + 0.262811i \(0.915350\pi\)
\(6\) 0 0
\(7\) 0.633975 + 0.366025i 0.239620 + 0.138345i 0.615002 0.788526i \(-0.289155\pi\)
−0.375382 + 0.926870i \(0.622489\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 0.767949 + 2.86603i 0.231545 + 0.864139i 0.979676 + 0.200587i \(0.0642851\pi\)
−0.748130 + 0.663552i \(0.769048\pi\)
\(12\) 0 0
\(13\) −1.63397 + 6.09808i −0.453183 + 1.69130i 0.240192 + 0.970725i \(0.422790\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) −4.73205 4.73205i −1.22181 1.22181i
\(16\) 0 0
\(17\) −2.26795 −0.550058 −0.275029 0.961436i \(-0.588688\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) 0 0
\(19\) 0.633975 + 0.633975i 0.145444 + 0.145444i 0.776079 0.630635i \(-0.217206\pi\)
−0.630635 + 0.776079i \(0.717206\pi\)
\(20\) 0 0
\(21\) 0.633975 + 1.09808i 0.138345 + 0.239620i
\(22\) 0 0
\(23\) 1.09808 0.633975i 0.228965 0.132193i −0.381130 0.924522i \(-0.624465\pi\)
0.610094 + 0.792329i \(0.291132\pi\)
\(24\) 0 0
\(25\) 8.59808 + 4.96410i 1.71962 + 0.992820i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −2.36603 + 0.633975i −0.439360 + 0.117726i −0.471717 0.881750i \(-0.656365\pi\)
0.0323566 + 0.999476i \(0.489699\pi\)
\(30\) 0 0
\(31\) 3.73205 + 6.46410i 0.670296 + 1.16099i 0.977820 + 0.209447i \(0.0671662\pi\)
−0.307524 + 0.951540i \(0.599500\pi\)
\(32\) 0 0
\(33\) −1.33013 + 4.96410i −0.231545 + 0.864139i
\(34\) 0 0
\(35\) −2.00000 2.00000i −0.338062 0.338062i
\(36\) 0 0
\(37\) 1.26795 1.26795i 0.208450 0.208450i −0.595159 0.803608i \(-0.702911\pi\)
0.803608 + 0.595159i \(0.202911\pi\)
\(38\) 0 0
\(39\) −7.73205 + 7.73205i −1.23812 + 1.23812i
\(40\) 0 0
\(41\) −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) 0 0
\(43\) −0.330127 1.23205i −0.0503439 0.187886i 0.936175 0.351535i \(-0.114340\pi\)
−0.986519 + 0.163649i \(0.947674\pi\)
\(44\) 0 0
\(45\) −3.00000 11.1962i −0.447214 1.66902i
\(46\) 0 0
\(47\) 4.83013 8.36603i 0.704546 1.22031i −0.262309 0.964984i \(-0.584484\pi\)
0.966855 0.255326i \(-0.0821828\pi\)
\(48\) 0 0
\(49\) −3.23205 5.59808i −0.461722 0.799725i
\(50\) 0 0
\(51\) −3.40192 1.96410i −0.476365 0.275029i
\(52\) 0 0
\(53\) −0.535898 + 0.535898i −0.0736113 + 0.0736113i −0.742954 0.669343i \(-0.766576\pi\)
0.669343 + 0.742954i \(0.266576\pi\)
\(54\) 0 0
\(55\) 11.4641i 1.54582i
\(56\) 0 0
\(57\) 0.401924 + 1.50000i 0.0532361 + 0.198680i
\(58\) 0 0
\(59\) −4.96410 1.33013i −0.646271 0.173168i −0.0792287 0.996856i \(-0.525246\pi\)
−0.567042 + 0.823689i \(0.691912\pi\)
\(60\) 0 0
\(61\) −3.00000 + 0.803848i −0.384111 + 0.102922i −0.445707 0.895179i \(-0.647048\pi\)
0.0615961 + 0.998101i \(0.480381\pi\)
\(62\) 0 0
\(63\) 2.19615i 0.276689i
\(64\) 0 0
\(65\) 12.1962 21.1244i 1.51275 2.62015i
\(66\) 0 0
\(67\) −1.40192 + 5.23205i −0.171272 + 0.639197i 0.825884 + 0.563840i \(0.190676\pi\)
−0.997157 + 0.0753572i \(0.975990\pi\)
\(68\) 0 0
\(69\) 2.19615 0.264386
\(70\) 0 0
\(71\) 10.9282i 1.29694i 0.761241 + 0.648470i \(0.224591\pi\)
−0.761241 + 0.648470i \(0.775409\pi\)
\(72\) 0 0
\(73\) 9.73205i 1.13905i −0.821974 0.569525i \(-0.807127\pi\)
0.821974 0.569525i \(-0.192873\pi\)
\(74\) 0 0
\(75\) 8.59808 + 14.8923i 0.992820 + 1.71962i
\(76\) 0 0
\(77\) −0.562178 + 2.09808i −0.0640661 + 0.239098i
\(78\) 0 0
\(79\) 6.00000 10.3923i 0.675053 1.16923i −0.301401 0.953498i \(-0.597454\pi\)
0.976453 0.215728i \(-0.0692125\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 1.36603 0.366025i 0.149941 0.0401765i −0.183068 0.983100i \(-0.558603\pi\)
0.333009 + 0.942924i \(0.391936\pi\)
\(84\) 0 0
\(85\) 8.46410 + 2.26795i 0.918061 + 0.245994i
\(86\) 0 0
\(87\) −4.09808 1.09808i −0.439360 0.117726i
\(88\) 0 0
\(89\) 2.00000i 0.212000i −0.994366 0.106000i \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 0 0
\(91\) −3.26795 + 3.26795i −0.342574 + 0.342574i
\(92\) 0 0
\(93\) 12.9282i 1.34059i
\(94\) 0 0
\(95\) −1.73205 3.00000i −0.177705 0.307794i
\(96\) 0 0
\(97\) −4.13397 + 7.16025i −0.419742 + 0.727014i −0.995913 0.0903150i \(-0.971213\pi\)
0.576172 + 0.817329i \(0.304546\pi\)
\(98\) 0 0
\(99\) −6.29423 + 6.29423i −0.632594 + 0.632594i
\(100\) 0 0
\(101\) −2.00000 7.46410i −0.199007 0.742706i −0.991193 0.132426i \(-0.957723\pi\)
0.792186 0.610280i \(-0.208943\pi\)
\(102\) 0 0
\(103\) 7.90192 4.56218i 0.778600 0.449525i −0.0573341 0.998355i \(-0.518260\pi\)
0.835934 + 0.548830i \(0.184927\pi\)
\(104\) 0 0
\(105\) −1.26795 4.73205i −0.123739 0.461801i
\(106\) 0 0
\(107\) 13.4904 13.4904i 1.30416 1.30416i 0.378607 0.925558i \(-0.376403\pi\)
0.925558 0.378607i \(-0.123597\pi\)
\(108\) 0 0
\(109\) 7.26795 + 7.26795i 0.696143 + 0.696143i 0.963576 0.267433i \(-0.0861754\pi\)
−0.267433 + 0.963576i \(0.586175\pi\)
\(110\) 0 0
\(111\) 3.00000 0.803848i 0.284747 0.0762978i
\(112\) 0 0
\(113\) 6.92820 + 12.0000i 0.651751 + 1.12887i 0.982698 + 0.185216i \(0.0592984\pi\)
−0.330947 + 0.943649i \(0.607368\pi\)
\(114\) 0 0
\(115\) −4.73205 + 1.26795i −0.441266 + 0.118237i
\(116\) 0 0
\(117\) −18.2942 + 4.90192i −1.69130 + 0.453183i
\(118\) 0 0
\(119\) −1.43782 0.830127i −0.131805 0.0760976i
\(120\) 0 0
\(121\) 1.90192 1.09808i 0.172902 0.0998251i
\(122\) 0 0
\(123\) −5.19615 −0.468521
\(124\) 0 0
\(125\) −13.4641 13.4641i −1.20427 1.20427i
\(126\) 0 0
\(127\) 6.19615 0.549820 0.274910 0.961470i \(-0.411352\pi\)
0.274910 + 0.961470i \(0.411352\pi\)
\(128\) 0 0
\(129\) 0.571797 2.13397i 0.0503439 0.187886i
\(130\) 0 0
\(131\) −0.830127 + 3.09808i −0.0725285 + 0.270680i −0.992662 0.120926i \(-0.961414\pi\)
0.920133 + 0.391606i \(0.128080\pi\)
\(132\) 0 0
\(133\) 0.169873 + 0.633975i 0.0147299 + 0.0549726i
\(134\) 0 0
\(135\) 5.19615 19.3923i 0.447214 1.66902i
\(136\) 0 0
\(137\) 14.2583 + 8.23205i 1.21817 + 0.703312i 0.964527 0.263986i \(-0.0850372\pi\)
0.253645 + 0.967297i \(0.418371\pi\)
\(138\) 0 0
\(139\) 9.06218 + 2.42820i 0.768644 + 0.205958i 0.621772 0.783198i \(-0.286413\pi\)
0.146872 + 0.989156i \(0.453080\pi\)
\(140\) 0 0
\(141\) 14.4904 8.36603i 1.22031 0.704546i
\(142\) 0 0
\(143\) −18.7321 −1.56645
\(144\) 0 0
\(145\) 9.46410 0.785951
\(146\) 0 0
\(147\) 11.1962i 0.923443i
\(148\) 0 0
\(149\) 3.09808 + 0.830127i 0.253804 + 0.0680067i 0.383478 0.923550i \(-0.374726\pi\)
−0.129674 + 0.991557i \(0.541393\pi\)
\(150\) 0 0
\(151\) 2.36603 + 1.36603i 0.192544 + 0.111166i 0.593173 0.805075i \(-0.297875\pi\)
−0.400629 + 0.916240i \(0.631208\pi\)
\(152\) 0 0
\(153\) −3.40192 5.89230i −0.275029 0.476365i
\(154\) 0 0
\(155\) −7.46410 27.8564i −0.599531 2.23748i
\(156\) 0 0
\(157\) −1.26795 + 4.73205i −0.101193 + 0.377659i −0.997886 0.0649959i \(-0.979297\pi\)
0.896692 + 0.442655i \(0.145963\pi\)
\(158\) 0 0
\(159\) −1.26795 + 0.339746i −0.100555 + 0.0269436i
\(160\) 0 0
\(161\) 0.928203 0.0731527
\(162\) 0 0
\(163\) 7.00000 + 7.00000i 0.548282 + 0.548282i 0.925944 0.377661i \(-0.123272\pi\)
−0.377661 + 0.925944i \(0.623272\pi\)
\(164\) 0 0
\(165\) 9.92820 17.1962i 0.772910 1.33872i
\(166\) 0 0
\(167\) −0.464102 + 0.267949i −0.0359133 + 0.0207345i −0.517849 0.855472i \(-0.673267\pi\)
0.481936 + 0.876206i \(0.339934\pi\)
\(168\) 0 0
\(169\) −23.2583 13.4282i −1.78910 1.03294i
\(170\) 0 0
\(171\) −0.696152 + 2.59808i −0.0532361 + 0.198680i
\(172\) 0 0
\(173\) −12.5622 + 3.36603i −0.955085 + 0.255914i −0.702519 0.711665i \(-0.747941\pi\)
−0.252566 + 0.967580i \(0.581275\pi\)
\(174\) 0 0
\(175\) 3.63397 + 6.29423i 0.274703 + 0.475799i
\(176\) 0 0
\(177\) −6.29423 6.29423i −0.473103 0.473103i
\(178\) 0 0
\(179\) −11.9282 11.9282i −0.891556 0.891556i 0.103114 0.994670i \(-0.467119\pi\)
−0.994670 + 0.103114i \(0.967119\pi\)
\(180\) 0 0
\(181\) 13.3923 13.3923i 0.995442 0.995442i −0.00454748 0.999990i \(-0.501448\pi\)
0.999990 + 0.00454748i \(0.00144751\pi\)
\(182\) 0 0
\(183\) −5.19615 1.39230i −0.384111 0.102922i
\(184\) 0 0
\(185\) −6.00000 + 3.46410i −0.441129 + 0.254686i
\(186\) 0 0
\(187\) −1.74167 6.50000i −0.127364 0.475327i
\(188\) 0 0
\(189\) −1.90192 + 3.29423i −0.138345 + 0.239620i
\(190\) 0 0
\(191\) −7.02628 + 12.1699i −0.508404 + 0.880581i 0.491549 + 0.870850i \(0.336431\pi\)
−0.999953 + 0.00973114i \(0.996902\pi\)
\(192\) 0 0
\(193\) −9.13397 15.8205i −0.657478 1.13879i −0.981266 0.192656i \(-0.938290\pi\)
0.323789 0.946129i \(-0.395043\pi\)
\(194\) 0 0
\(195\) 36.5885 21.1244i 2.62015 1.51275i
\(196\) 0 0
\(197\) −3.66025 + 3.66025i −0.260782 + 0.260782i −0.825372 0.564590i \(-0.809034\pi\)
0.564590 + 0.825372i \(0.309034\pi\)
\(198\) 0 0
\(199\) 0.875644i 0.0620728i −0.999518 0.0310364i \(-0.990119\pi\)
0.999518 0.0310364i \(-0.00988078\pi\)
\(200\) 0 0
\(201\) −6.63397 + 6.63397i −0.467924 + 0.467924i
\(202\) 0 0
\(203\) −1.73205 0.464102i −0.121566 0.0325735i
\(204\) 0 0
\(205\) 11.1962 3.00000i 0.781973 0.209529i
\(206\) 0 0
\(207\) 3.29423 + 1.90192i 0.228965 + 0.132193i
\(208\) 0 0
\(209\) −1.33013 + 2.30385i −0.0920068 + 0.159360i
\(210\) 0 0
\(211\) 1.09808 4.09808i 0.0755947 0.282123i −0.917773 0.397106i \(-0.870015\pi\)
0.993367 + 0.114983i \(0.0366812\pi\)
\(212\) 0 0
\(213\) −9.46410 + 16.3923i −0.648470 + 1.12318i
\(214\) 0 0
\(215\) 4.92820i 0.336101i
\(216\) 0 0
\(217\) 5.46410i 0.370927i
\(218\) 0 0
\(219\) 8.42820 14.5981i 0.569525 0.986447i
\(220\) 0 0
\(221\) 3.70577 13.8301i 0.249277 0.930315i
\(222\) 0 0
\(223\) −11.0263 + 19.0981i −0.738374 + 1.27890i 0.214853 + 0.976646i \(0.431073\pi\)
−0.953227 + 0.302255i \(0.902260\pi\)
\(224\) 0 0
\(225\) 29.7846i 1.98564i
\(226\) 0 0
\(227\) 14.4282 3.86603i 0.957633 0.256597i 0.254035 0.967195i \(-0.418242\pi\)
0.703598 + 0.710598i \(0.251575\pi\)
\(228\) 0 0
\(229\) 6.83013 + 1.83013i 0.451347 + 0.120938i 0.477330 0.878724i \(-0.341605\pi\)
−0.0259823 + 0.999662i \(0.508271\pi\)
\(230\) 0 0
\(231\) −2.66025 + 2.66025i −0.175032 + 0.175032i
\(232\) 0 0
\(233\) 7.19615i 0.471436i 0.971822 + 0.235718i \(0.0757441\pi\)
−0.971822 + 0.235718i \(0.924256\pi\)
\(234\) 0 0
\(235\) −26.3923 + 26.3923i −1.72164 + 1.72164i
\(236\) 0 0
\(237\) 18.0000 10.3923i 1.16923 0.675053i
\(238\) 0 0
\(239\) 13.0981 + 22.6865i 0.847244 + 1.46747i 0.883658 + 0.468133i \(0.155073\pi\)
−0.0364139 + 0.999337i \(0.511593\pi\)
\(240\) 0 0
\(241\) −6.40192 + 11.0885i −0.412384 + 0.714270i −0.995150 0.0983699i \(-0.968637\pi\)
0.582766 + 0.812640i \(0.301971\pi\)
\(242\) 0 0
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 0 0
\(245\) 6.46410 + 24.1244i 0.412976 + 1.54125i
\(246\) 0 0
\(247\) −4.90192 + 2.83013i −0.311902 + 0.180077i
\(248\) 0 0
\(249\) 2.36603 + 0.633975i 0.149941 + 0.0401765i
\(250\) 0 0
\(251\) −2.83013 + 2.83013i −0.178636 + 0.178636i −0.790761 0.612125i \(-0.790315\pi\)
0.612125 + 0.790761i \(0.290315\pi\)
\(252\) 0 0
\(253\) 2.66025 + 2.66025i 0.167249 + 0.167249i
\(254\) 0 0
\(255\) 10.7321 + 10.7321i 0.672067 + 0.672067i
\(256\) 0 0
\(257\) −4.42820 7.66987i −0.276224 0.478434i 0.694219 0.719763i \(-0.255750\pi\)
−0.970443 + 0.241330i \(0.922416\pi\)
\(258\) 0 0
\(259\) 1.26795 0.339746i 0.0787865 0.0211108i
\(260\) 0 0
\(261\) −5.19615 5.19615i −0.321634 0.321634i
\(262\) 0 0
\(263\) 23.4904 + 13.5622i 1.44848 + 0.836280i 0.998391 0.0567045i \(-0.0180593\pi\)
0.450088 + 0.892984i \(0.351393\pi\)
\(264\) 0 0
\(265\) 2.53590 1.46410i 0.155779 0.0899390i
\(266\) 0 0
\(267\) 1.73205 3.00000i 0.106000 0.183597i
\(268\) 0 0
\(269\) 4.73205 + 4.73205i 0.288518 + 0.288518i 0.836494 0.547976i \(-0.184601\pi\)
−0.547976 + 0.836494i \(0.684601\pi\)
\(270\) 0 0
\(271\) −20.3923 −1.23874 −0.619372 0.785098i \(-0.712613\pi\)
−0.619372 + 0.785098i \(0.712613\pi\)
\(272\) 0 0
\(273\) −7.73205 + 2.07180i −0.467965 + 0.125391i
\(274\) 0 0
\(275\) −7.62436 + 28.4545i −0.459766 + 1.71587i
\(276\) 0 0
\(277\) −4.22243 15.7583i −0.253701 0.946826i −0.968808 0.247811i \(-0.920289\pi\)
0.715107 0.699015i \(-0.246378\pi\)
\(278\) 0 0
\(279\) −11.1962 + 19.3923i −0.670296 + 1.16099i
\(280\) 0 0
\(281\) −8.66025 5.00000i −0.516627 0.298275i 0.218926 0.975741i \(-0.429745\pi\)
−0.735554 + 0.677466i \(0.763078\pi\)
\(282\) 0 0
\(283\) −27.7583 7.43782i −1.65006 0.442133i −0.690431 0.723398i \(-0.742579\pi\)
−0.959630 + 0.281265i \(0.909246\pi\)
\(284\) 0 0
\(285\) 6.00000i 0.355409i
\(286\) 0 0
\(287\) −2.19615 −0.129635
\(288\) 0 0
\(289\) −11.8564 −0.697436
\(290\) 0 0
\(291\) −12.4019 + 7.16025i −0.727014 + 0.419742i
\(292\) 0 0
\(293\) 13.5622 + 3.63397i 0.792311 + 0.212299i 0.632205 0.774801i \(-0.282150\pi\)
0.160106 + 0.987100i \(0.448817\pi\)
\(294\) 0 0
\(295\) 17.1962 + 9.92820i 1.00120 + 0.578042i
\(296\) 0 0
\(297\) −14.8923 + 3.99038i −0.864139 + 0.231545i
\(298\) 0 0
\(299\) 2.07180 + 7.73205i 0.119815 + 0.447156i
\(300\) 0 0
\(301\) 0.241670 0.901924i 0.0139296 0.0519860i
\(302\) 0 0
\(303\) 3.46410 12.9282i 0.199007 0.742706i
\(304\) 0 0
\(305\) 12.0000 0.687118
\(306\) 0 0
\(307\) 16.0263 + 16.0263i 0.914668 + 0.914668i 0.996635 0.0819670i \(-0.0261202\pi\)
−0.0819670 + 0.996635i \(0.526120\pi\)
\(308\) 0 0
\(309\) 15.8038 0.899049
\(310\) 0 0
\(311\) −13.9019 + 8.02628i −0.788306 + 0.455129i −0.839366 0.543567i \(-0.817073\pi\)
0.0510600 + 0.998696i \(0.483740\pi\)
\(312\) 0 0
\(313\) 24.6506 + 14.2321i 1.39334 + 0.804443i 0.993683 0.112223i \(-0.0357972\pi\)
0.399653 + 0.916666i \(0.369131\pi\)
\(314\) 0 0
\(315\) 2.19615 8.19615i 0.123739 0.461801i
\(316\) 0 0
\(317\) 31.4904 8.43782i 1.76868 0.473915i 0.780231 0.625492i \(-0.215102\pi\)
0.988445 + 0.151577i \(0.0484351\pi\)
\(318\) 0 0
\(319\) −3.63397 6.29423i −0.203464 0.352409i
\(320\) 0 0
\(321\) 31.9186 8.55256i 1.78152 0.477357i
\(322\) 0 0
\(323\) −1.43782 1.43782i −0.0800026 0.0800026i
\(324\) 0 0
\(325\) −44.3205 + 44.3205i −2.45846 + 2.45846i
\(326\) 0 0
\(327\) 4.60770 + 17.1962i 0.254806 + 0.950949i
\(328\) 0 0
\(329\) 6.12436 3.53590i 0.337647 0.194940i
\(330\) 0 0
\(331\) −5.09808 19.0263i −0.280216 1.04578i −0.952265 0.305273i \(-0.901252\pi\)
0.672049 0.740506i \(-0.265414\pi\)
\(332\) 0 0
\(333\) 5.19615 + 1.39230i 0.284747 + 0.0762978i
\(334\) 0 0
\(335\) 10.4641 18.1244i 0.571715 0.990239i
\(336\) 0 0
\(337\) −11.8923 20.5981i −0.647815 1.12205i −0.983644 0.180126i \(-0.942350\pi\)
0.335829 0.941923i \(-0.390984\pi\)
\(338\) 0 0
\(339\) 24.0000i 1.30350i
\(340\) 0 0
\(341\) −15.6603 + 15.6603i −0.848050 + 0.848050i
\(342\) 0 0
\(343\) 9.85641i 0.532196i
\(344\) 0 0
\(345\) −8.19615 2.19615i −0.441266 0.118237i
\(346\) 0 0
\(347\) 24.7224 + 6.62436i 1.32717 + 0.355614i 0.851659 0.524096i \(-0.175597\pi\)
0.475510 + 0.879710i \(0.342263\pi\)
\(348\) 0 0
\(349\) −7.73205 + 2.07180i −0.413887 + 0.110901i −0.459753 0.888047i \(-0.652062\pi\)
0.0458657 + 0.998948i \(0.485395\pi\)
\(350\) 0 0
\(351\) −31.6865 8.49038i −1.69130 0.453183i
\(352\) 0 0
\(353\) −10.1603 + 17.5981i −0.540776 + 0.936651i 0.458084 + 0.888909i \(0.348536\pi\)
−0.998860 + 0.0477421i \(0.984797\pi\)
\(354\) 0 0
\(355\) 10.9282 40.7846i 0.580009 2.16462i
\(356\) 0 0
\(357\) −1.43782 2.49038i −0.0760976 0.131805i
\(358\) 0 0
\(359\) 14.7321i 0.777528i −0.921337 0.388764i \(-0.872902\pi\)
0.921337 0.388764i \(-0.127098\pi\)
\(360\) 0 0
\(361\) 18.1962i 0.957692i
\(362\) 0 0
\(363\) 3.80385 0.199650
\(364\) 0 0
\(365\) −9.73205 + 36.3205i −0.509399 + 1.90110i
\(366\) 0 0
\(367\) 10.1244 17.5359i 0.528487 0.915366i −0.470961 0.882154i \(-0.656093\pi\)
0.999448 0.0332125i \(-0.0105738\pi\)
\(368\) 0 0
\(369\) −7.79423 4.50000i −0.405751 0.234261i
\(370\) 0 0
\(371\) −0.535898 + 0.143594i −0.0278225 + 0.00745501i
\(372\) 0 0
\(373\) −5.63397 1.50962i −0.291716 0.0781651i 0.109993 0.993932i \(-0.464917\pi\)
−0.401709 + 0.915767i \(0.631584\pi\)
\(374\) 0 0
\(375\) −8.53590 31.8564i −0.440792 1.64506i
\(376\) 0 0
\(377\) 15.4641i 0.796442i
\(378\) 0 0
\(379\) 18.7583 18.7583i 0.963551 0.963551i −0.0358080 0.999359i \(-0.511400\pi\)
0.999359 + 0.0358080i \(0.0114005\pi\)
\(380\) 0 0
\(381\) 9.29423 + 5.36603i 0.476158 + 0.274910i
\(382\) 0 0
\(383\) 3.26795 + 5.66025i 0.166984 + 0.289225i 0.937358 0.348367i \(-0.113264\pi\)
−0.770374 + 0.637593i \(0.779930\pi\)
\(384\) 0 0
\(385\) 4.19615 7.26795i 0.213856 0.370409i
\(386\) 0 0
\(387\) 2.70577 2.70577i 0.137542 0.137542i
\(388\) 0 0
\(389\) −2.75833 10.2942i −0.139853 0.521938i −0.999931 0.0117752i \(-0.996252\pi\)
0.860078 0.510163i \(-0.170415\pi\)
\(390\) 0 0
\(391\) −2.49038 + 1.43782i −0.125944 + 0.0727138i
\(392\) 0 0
\(393\) −3.92820 + 3.92820i −0.198152 + 0.198152i
\(394\) 0 0
\(395\) −32.7846 + 32.7846i −1.64957 + 1.64957i
\(396\) 0 0
\(397\) −12.7321 12.7321i −0.639003 0.639003i 0.311306 0.950310i \(-0.399233\pi\)
−0.950310 + 0.311306i \(0.899233\pi\)
\(398\) 0 0
\(399\) −0.294229 + 1.09808i −0.0147299 + 0.0549726i
\(400\) 0 0
\(401\) 13.7942 + 23.8923i 0.688851 + 1.19312i 0.972210 + 0.234111i \(0.0752179\pi\)
−0.283359 + 0.959014i \(0.591449\pi\)
\(402\) 0 0
\(403\) −45.5167 + 12.1962i −2.26735 + 0.607534i
\(404\) 0 0
\(405\) 24.5885 24.5885i 1.22181 1.22181i
\(406\) 0 0
\(407\) 4.60770 + 2.66025i 0.228395 + 0.131864i
\(408\) 0 0
\(409\) −26.1340 + 15.0885i −1.29224 + 0.746076i −0.979051 0.203614i \(-0.934731\pi\)
−0.313191 + 0.949690i \(0.601398\pi\)
\(410\) 0 0
\(411\) 14.2583 + 24.6962i 0.703312 + 1.21817i
\(412\) 0 0
\(413\) −2.66025 2.66025i −0.130903 0.130903i
\(414\) 0 0
\(415\) −5.46410 −0.268222
\(416\) 0 0
\(417\) 11.4904 + 11.4904i 0.562686 + 0.562686i
\(418\) 0 0
\(419\) 8.36603 31.2224i 0.408707 1.52532i −0.388408 0.921488i \(-0.626975\pi\)
0.797115 0.603828i \(-0.206359\pi\)
\(420\) 0 0
\(421\) 0.588457 + 2.19615i 0.0286797 + 0.107034i 0.978782 0.204905i \(-0.0656884\pi\)
−0.950102 + 0.311938i \(0.899022\pi\)
\(422\) 0 0
\(423\) 28.9808 1.40909
\(424\) 0 0
\(425\) −19.5000 11.2583i −0.945889 0.546109i
\(426\) 0 0
\(427\) −2.19615 0.588457i −0.106279 0.0284774i
\(428\) 0 0
\(429\) −28.0981 16.2224i −1.35659 0.783226i
\(430\) 0 0
\(431\) 5.80385 0.279562 0.139781 0.990182i \(-0.455360\pi\)
0.139781 + 0.990182i \(0.455360\pi\)
\(432\) 0 0
\(433\) −2.26795 −0.108991 −0.0544953 0.998514i \(-0.517355\pi\)
−0.0544953 + 0.998514i \(0.517355\pi\)
\(434\) 0 0
\(435\) 14.1962 + 8.19615i 0.680653 + 0.392975i
\(436\) 0 0
\(437\) 1.09808 + 0.294229i 0.0525281 + 0.0140749i
\(438\) 0 0
\(439\) 4.85641 + 2.80385i 0.231784 + 0.133820i 0.611395 0.791326i \(-0.290609\pi\)
−0.379611 + 0.925146i \(0.623942\pi\)
\(440\) 0 0
\(441\) 9.69615 16.7942i 0.461722 0.799725i
\(442\) 0 0
\(443\) 5.25833 + 19.6244i 0.249831 + 0.932381i 0.970894 + 0.239511i \(0.0769873\pi\)
−0.721063 + 0.692870i \(0.756346\pi\)
\(444\) 0 0
\(445\) −2.00000 + 7.46410i −0.0948091 + 0.353832i
\(446\) 0 0
\(447\) 3.92820 + 3.92820i 0.185798 + 0.185798i
\(448\) 0 0
\(449\) −20.6603 −0.975018 −0.487509 0.873118i \(-0.662094\pi\)
−0.487509 + 0.873118i \(0.662094\pi\)
\(450\) 0 0
\(451\) −6.29423 6.29423i −0.296384 0.296384i
\(452\) 0 0
\(453\) 2.36603 + 4.09808i 0.111166 + 0.192544i
\(454\) 0 0
\(455\) 15.4641 8.92820i 0.724968 0.418561i
\(456\) 0 0
\(457\) 20.2583 + 11.6962i 0.947645 + 0.547123i 0.892348 0.451347i \(-0.149056\pi\)
0.0552962 + 0.998470i \(0.482390\pi\)
\(458\) 0 0
\(459\) 11.7846i 0.550058i
\(460\) 0 0
\(461\) 2.56218 0.686533i 0.119333 0.0319751i −0.198659 0.980069i \(-0.563658\pi\)
0.317991 + 0.948094i \(0.396992\pi\)
\(462\) 0 0
\(463\) 9.19615 + 15.9282i 0.427381 + 0.740246i 0.996640 0.0819125i \(-0.0261028\pi\)
−0.569258 + 0.822159i \(0.692769\pi\)
\(464\) 0 0
\(465\) 12.9282 48.2487i 0.599531 2.23748i
\(466\) 0 0
\(467\) −4.36603 4.36603i −0.202036 0.202036i 0.598836 0.800872i \(-0.295630\pi\)
−0.800872 + 0.598836i \(0.795630\pi\)
\(468\) 0 0
\(469\) −2.80385 + 2.80385i −0.129470 + 0.129470i
\(470\) 0 0
\(471\) −6.00000 + 6.00000i −0.276465 + 0.276465i
\(472\) 0 0
\(473\) 3.27757 1.89230i 0.150703 0.0870083i
\(474\) 0 0
\(475\) 2.30385 + 8.59808i 0.105708 + 0.394507i
\(476\) 0 0
\(477\) −2.19615 0.588457i −0.100555 0.0269436i
\(478\) 0 0
\(479\) −12.8301 + 22.2224i −0.586223 + 1.01537i 0.408498 + 0.912759i \(0.366053\pi\)
−0.994722 + 0.102610i \(0.967281\pi\)
\(480\) 0 0
\(481\) 5.66025 + 9.80385i 0.258085 + 0.447017i
\(482\) 0 0
\(483\) 1.39230 + 0.803848i 0.0633521 + 0.0365763i
\(484\) 0 0
\(485\) 22.5885 22.5885i 1.02569 1.02569i
\(486\) 0 0
\(487\) 16.1962i 0.733918i −0.930237 0.366959i \(-0.880399\pi\)
0.930237 0.366959i \(-0.119601\pi\)
\(488\) 0 0
\(489\) 4.43782 + 16.5622i 0.200685 + 0.748968i
\(490\) 0 0
\(491\) 25.7224 + 6.89230i 1.16084 + 0.311045i 0.787300 0.616570i \(-0.211478\pi\)
0.373537 + 0.927615i \(0.378145\pi\)
\(492\) 0 0
\(493\) 5.36603 1.43782i 0.241674 0.0647563i
\(494\) 0 0
\(495\) 29.7846 17.1962i 1.33872 0.772910i
\(496\) 0 0
\(497\) −4.00000 + 6.92820i −0.179425 + 0.310772i
\(498\) 0 0
\(499\) 1.69615 6.33013i 0.0759302 0.283375i −0.917512 0.397707i \(-0.869806\pi\)
0.993443 + 0.114332i \(0.0364727\pi\)
\(500\) 0 0
\(501\) −0.928203 −0.0414691
\(502\) 0 0
\(503\) 27.7128i 1.23565i −0.786314 0.617827i \(-0.788013\pi\)
0.786314 0.617827i \(-0.211987\pi\)
\(504\) 0 0
\(505\) 29.8564i 1.32859i
\(506\) 0 0
\(507\) −23.2583 40.2846i −1.03294 1.78910i
\(508\) 0 0
\(509\) −4.53590 + 16.9282i −0.201050 + 0.750329i 0.789567 + 0.613664i \(0.210305\pi\)
−0.990617 + 0.136665i \(0.956362\pi\)
\(510\) 0 0
\(511\) 3.56218 6.16987i 0.157581 0.272939i
\(512\) 0 0
\(513\) −3.29423 + 3.29423i −0.145444 + 0.145444i
\(514\) 0 0
\(515\) −34.0526 + 9.12436i −1.50054 + 0.402067i
\(516\) 0 0
\(517\) 27.6865 + 7.41858i 1.21765 + 0.326269i
\(518\) 0 0
\(519\) −21.7583 5.83013i −0.955085 0.255914i
\(520\) 0 0
\(521\) 13.0000i 0.569540i 0.958596 + 0.284770i \(0.0919173\pi\)
−0.958596 + 0.284770i \(0.908083\pi\)
\(522\) 0 0
\(523\) 14.4641 14.4641i 0.632471 0.632471i −0.316216 0.948687i \(-0.602412\pi\)
0.948687 + 0.316216i \(0.102412\pi\)
\(524\) 0 0
\(525\) 12.5885i 0.549405i
\(526\) 0 0
\(527\) −8.46410 14.6603i −0.368702 0.638611i
\(528\) 0 0
\(529\) −10.6962 + 18.5263i −0.465050 + 0.805490i
\(530\) 0 0
\(531\) −3.99038 14.8923i −0.173168 0.646271i
\(532\) 0 0
\(533\) −4.90192 18.2942i −0.212326 0.792411i
\(534\) 0 0
\(535\) −63.8372 + 36.8564i −2.75992 + 1.59344i
\(536\) 0 0
\(537\) −7.56218 28.2224i −0.326332 1.21789i
\(538\) 0 0
\(539\) 13.5622 13.5622i 0.584164 0.584164i
\(540\) 0 0
\(541\) −8.19615 8.19615i −0.352380 0.352380i 0.508614 0.860994i \(-0.330158\pi\)
−0.860994 + 0.508614i \(0.830158\pi\)
\(542\) 0 0
\(543\) 31.6865 8.49038i 1.35980 0.364357i
\(544\) 0 0
\(545\) −19.8564 34.3923i −0.850555 1.47320i
\(546\) 0 0
\(547\) 31.2583 8.37564i 1.33651 0.358117i 0.481371 0.876517i \(-0.340139\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(548\) 0 0
\(549\) −6.58846 6.58846i −0.281189 0.281189i
\(550\) 0 0
\(551\) −1.90192 1.09808i −0.0810247 0.0467796i
\(552\) 0 0
\(553\) 7.60770 4.39230i 0.323512 0.186780i
\(554\) 0 0
\(555\) −12.0000 −0.509372
\(556\) 0 0
\(557\) −25.1962 25.1962i −1.06760 1.06760i −0.997543 0.0700519i \(-0.977684\pi\)
−0.0700519 0.997543i \(-0.522316\pi\)
\(558\) 0 0
\(559\) 8.05256 0.340587
\(560\) 0 0
\(561\) 3.01666 11.2583i 0.127364 0.475327i
\(562\) 0 0
\(563\) −1.00962 + 3.76795i −0.0425504 + 0.158800i −0.983932 0.178543i \(-0.942862\pi\)
0.941382 + 0.337343i \(0.109528\pi\)
\(564\) 0 0
\(565\) −13.8564 51.7128i −0.582943 2.17557i
\(566\) 0 0
\(567\) −5.70577 + 3.29423i −0.239620 + 0.138345i
\(568\) 0 0
\(569\) 23.5981 + 13.6244i 0.989283 + 0.571163i 0.905060 0.425284i \(-0.139826\pi\)
0.0842230 + 0.996447i \(0.473159\pi\)
\(570\) 0 0
\(571\) 19.8923 + 5.33013i 0.832467 + 0.223059i 0.649790 0.760114i \(-0.274857\pi\)
0.182677 + 0.983173i \(0.441524\pi\)
\(572\) 0 0
\(573\) −21.0788 + 12.1699i −0.880581 + 0.508404i
\(574\) 0 0
\(575\) 12.5885 0.524975
\(576\) 0 0
\(577\) 35.7846 1.48973 0.744866 0.667214i \(-0.232513\pi\)
0.744866 + 0.667214i \(0.232513\pi\)
\(578\) 0 0
\(579\) 31.6410i 1.31496i
\(580\) 0 0
\(581\) 1.00000 + 0.267949i 0.0414870 + 0.0111164i
\(582\) 0 0
\(583\) −1.94744 1.12436i −0.0806548 0.0465661i
\(584\) 0 0
\(585\) 73.1769 3.02549
\(586\) 0 0
\(587\) 1.00962 + 3.76795i 0.0416714 + 0.155520i 0.983626 0.180219i \(-0.0576807\pi\)
−0.941955 + 0.335739i \(0.891014\pi\)
\(588\) 0 0
\(589\) −1.73205 + 6.46410i −0.0713679 + 0.266349i
\(590\) 0 0
\(591\) −8.66025 + 2.32051i −0.356235 + 0.0954529i
\(592\) 0 0
\(593\) 10.5359 0.432657 0.216329 0.976321i \(-0.430592\pi\)
0.216329 + 0.976321i \(0.430592\pi\)
\(594\) 0 0
\(595\) 4.53590 + 4.53590i 0.185954 + 0.185954i
\(596\) 0 0
\(597\) 0.758330 1.31347i 0.0310364 0.0537566i
\(598\) 0 0
\(599\) −23.3205 + 13.4641i −0.952850 + 0.550128i −0.893965 0.448136i \(-0.852088\pi\)
−0.0588850 + 0.998265i \(0.518755\pi\)
\(600\) 0 0
\(601\) −17.5526 10.1340i −0.715984 0.413373i 0.0972889 0.995256i \(-0.468983\pi\)
−0.813273 + 0.581883i \(0.802316\pi\)
\(602\) 0 0
\(603\) −15.6962 + 4.20577i −0.639197 + 0.171272i
\(604\) 0 0
\(605\) −8.19615 + 2.19615i −0.333221 + 0.0892863i
\(606\) 0 0
\(607\) −22.5885 39.1244i −0.916837 1.58801i −0.804189 0.594374i \(-0.797400\pi\)
−0.112648 0.993635i \(-0.535933\pi\)
\(608\) 0 0
\(609\) −2.19615 2.19615i −0.0889926 0.0889926i
\(610\) 0 0
\(611\) 43.1244 + 43.1244i 1.74462 + 1.74462i
\(612\) 0 0
\(613\) 1.66025 1.66025i 0.0670570 0.0670570i −0.672783 0.739840i \(-0.734901\pi\)
0.739840 + 0.672783i \(0.234901\pi\)
\(614\) 0 0
\(615\) 19.3923 + 5.19615i 0.781973 + 0.209529i
\(616\) 0 0
\(617\) 3.91154 2.25833i 0.157473 0.0909170i −0.419193 0.907897i \(-0.637687\pi\)
0.576666 + 0.816980i \(0.304354\pi\)
\(618\) 0 0
\(619\) 10.4019 + 38.8205i 0.418089 + 1.56033i 0.778568 + 0.627561i \(0.215947\pi\)
−0.360479 + 0.932767i \(0.617387\pi\)
\(620\) 0 0
\(621\) 3.29423 + 5.70577i 0.132193 + 0.228965i
\(622\) 0 0
\(623\) 0.732051 1.26795i 0.0293290 0.0507993i
\(624\) 0 0
\(625\) 11.9641 + 20.7224i 0.478564 + 0.828897i
\(626\) 0 0
\(627\) −3.99038 + 2.30385i −0.159360 + 0.0920068i
\(628\) 0 0
\(629\) −2.87564 + 2.87564i −0.114659 + 0.114659i
\(630\) 0 0
\(631\) 38.3923i 1.52837i −0.644995 0.764187i \(-0.723141\pi\)
0.644995 0.764187i \(-0.276859\pi\)
\(632\) 0 0
\(633\) 5.19615 5.19615i 0.206529 0.206529i
\(634\) 0 0
\(635\) −23.1244 6.19615i −0.917662 0.245887i
\(636\) 0 0
\(637\) 39.4186 10.5622i 1.56182 0.418489i
\(638\) 0 0
\(639\) −28.3923 + 16.3923i −1.12318 + 0.648470i
\(640\) 0 0
\(641\) −4.20577 + 7.28461i −0.166118 + 0.287725i −0.937052 0.349191i \(-0.886457\pi\)
0.770934 + 0.636915i \(0.219790\pi\)
\(642\) 0 0
\(643\) −12.2321 + 45.6506i −0.482385 + 1.80029i 0.109173 + 0.994023i \(0.465180\pi\)
−0.591558 + 0.806263i \(0.701487\pi\)
\(644\) 0 0
\(645\) −4.26795 + 7.39230i −0.168050 + 0.291072i
\(646\) 0 0
\(647\) 13.2679i 0.521617i −0.965391 0.260808i \(-0.916011\pi\)
0.965391 0.260808i \(-0.0839891\pi\)
\(648\) 0 0
\(649\) 15.2487i 0.598564i
\(650\) 0 0
\(651\) −4.73205 + 8.19615i −0.185464 + 0.321233i
\(652\) 0 0
\(653\) −1.50962 + 5.63397i −0.0590760 + 0.220474i −0.989153 0.146891i \(-0.953073\pi\)
0.930077 + 0.367365i \(0.119740\pi\)
\(654\) 0 0
\(655\) 6.19615 10.7321i 0.242104 0.419336i
\(656\) 0 0
\(657\) 25.2846 14.5981i 0.986447 0.569525i
\(658\) 0 0
\(659\) 15.0263 4.02628i 0.585341 0.156842i 0.0460178 0.998941i \(-0.485347\pi\)
0.539323 + 0.842099i \(0.318680\pi\)
\(660\) 0 0
\(661\) −8.19615 2.19615i −0.318793 0.0854204i 0.0958740 0.995393i \(-0.469435\pi\)
−0.414667 + 0.909973i \(0.636102\pi\)
\(662\) 0 0
\(663\) 17.5359 17.5359i 0.681038 0.681038i
\(664\) 0 0
\(665\) 2.53590i 0.0983379i
\(666\) 0 0
\(667\) −2.19615 + 2.19615i −0.0850354 + 0.0850354i
\(668\) 0 0
\(669\) −33.0788 + 19.0981i −1.27890 + 0.738374i
\(670\) 0 0
\(671\) −4.60770 7.98076i −0.177878 0.308094i
\(672\) 0 0
\(673\) 8.80385 15.2487i 0.339363 0.587795i −0.644950 0.764225i \(-0.723122\pi\)
0.984313 + 0.176430i \(0.0564550\pi\)
\(674\) 0 0
\(675\) −25.7942 + 44.6769i −0.992820 + 1.71962i
\(676\) 0 0
\(677\) −1.26795 4.73205i −0.0487312 0.181867i 0.937270 0.348603i \(-0.113344\pi\)
−0.986002 + 0.166736i \(0.946677\pi\)
\(678\) 0 0
\(679\) −5.24167 + 3.02628i −0.201157 + 0.116138i
\(680\) 0 0
\(681\) 24.9904 + 6.69615i 0.957633 + 0.256597i
\(682\) 0 0
\(683\) 4.70577 4.70577i 0.180061 0.180061i −0.611321 0.791383i \(-0.709362\pi\)
0.791383 + 0.611321i \(0.209362\pi\)
\(684\) 0 0
\(685\) −44.9808 44.9808i −1.71863 1.71863i
\(686\) 0 0
\(687\) 8.66025 + 8.66025i 0.330409 + 0.330409i
\(688\) 0 0
\(689\) −2.39230 4.14359i −0.0911396 0.157858i
\(690\) 0 0
\(691\) −23.4904 + 6.29423i −0.893616 + 0.239444i −0.676273 0.736651i \(-0.736406\pi\)
−0.217344 + 0.976095i \(0.569739\pi\)
\(692\) 0 0
\(693\) −6.29423 + 1.68653i −0.239098 + 0.0640661i
\(694\) 0 0
\(695\) −31.3923 18.1244i −1.19078 0.687496i
\(696\) 0 0
\(697\) 5.89230 3.40192i 0.223187 0.128857i
\(698\) 0 0
\(699\) −6.23205 + 10.7942i −0.235718 + 0.408275i
\(700\) 0 0
\(701\) 10.6603 + 10.6603i 0.402632 + 0.402632i 0.879160 0.476527i \(-0.158105\pi\)
−0.476527 + 0.879160i \(0.658105\pi\)
\(702\) 0 0
\(703\) 1.60770 0.0606354
\(704\) 0 0
\(705\) −62.4449 + 16.7321i −2.35181 + 0.630165i
\(706\) 0 0
\(707\) 1.46410 5.46410i 0.0550632 0.205499i
\(708\) 0 0
\(709\) 5.41154 + 20.1962i 0.203235 + 0.758482i 0.989980 + 0.141205i \(0.0450977\pi\)
−0.786746 + 0.617277i \(0.788236\pi\)
\(710\) 0 0
\(711\) 36.0000 1.35011
\(712\) 0 0
\(713\) 8.19615 + 4.73205i 0.306948 + 0.177217i
\(714\) 0 0
\(715\) 69.9090 + 18.7321i 2.61445 + 0.700539i
\(716\) 0 0
\(717\) 45.3731i 1.69449i
\(718\) 0 0
\(719\) 16.3923 0.611330 0.305665 0.952139i \(-0.401121\pi\)
0.305665 + 0.952139i \(0.401121\pi\)
\(720\) 0 0
\(721\) 6.67949 0.248757
\(722\) 0 0
\(723\) −19.2058 + 11.0885i −0.714270 + 0.412384i
\(724\) 0 0
\(725\) −23.4904 6.29423i −0.872411 0.233762i
\(726\) 0 0
\(727\) 31.8109 + 18.3660i 1.17980 + 0.681158i 0.955968 0.293470i \(-0.0948099\pi\)
0.223832 + 0.974628i \(0.428143\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 0.748711 + 2.79423i 0.0276921 + 0.103348i
\(732\) 0 0
\(733\) 8.02628 29.9545i 0.296457 1.10639i −0.643596 0.765366i \(-0.722558\pi\)
0.940053 0.341028i \(-0.110775\pi\)
\(734\) 0 0
\(735\) −11.1962 + 41.7846i −0.412976 + 1.54125i
\(736\) 0 0
\(737\) −16.0718 −0.592012
\(738\) 0 0
\(739\) −21.2224 21.2224i −0.780680 0.780680i 0.199266 0.979945i \(-0.436144\pi\)
−0.979945 + 0.199266i \(0.936144\pi\)
\(740\) 0 0
\(741\) −9.80385 −0.360153
\(742\) 0 0
\(743\) 2.24167 1.29423i 0.0822389 0.0474806i −0.458317 0.888789i \(-0.651547\pi\)
0.540556 + 0.841308i \(0.318214\pi\)
\(744\) 0 0
\(745\) −10.7321 6.19615i −0.393192 0.227009i
\(746\) 0 0
\(747\) 3.00000 + 3.00000i 0.109764 + 0.109764i
\(748\) 0 0
\(749\) 13.4904 3.61474i 0.492928 0.132080i
\(750\) 0 0
\(751\) −18.8564 32.6603i −0.688080 1.19179i −0.972458 0.233077i \(-0.925120\pi\)
0.284378 0.958712i \(-0.408213\pi\)
\(752\) 0 0
\(753\) −6.69615 + 1.79423i −0.244021 + 0.0653853i
\(754\) 0 0
\(755\) −7.46410 7.46410i −0.271646 0.271646i
\(756\) 0 0
\(757\) −6.07180 + 6.07180i −0.220683 + 0.220683i −0.808786 0.588103i \(-0.799875\pi\)
0.588103 + 0.808786i \(0.299875\pi\)
\(758\) 0 0
\(759\) 1.68653 + 6.29423i 0.0612173 + 0.228466i
\(760\) 0 0
\(761\) 27.3731 15.8038i 0.992273 0.572889i 0.0863200 0.996267i \(-0.472489\pi\)
0.905953 + 0.423378i \(0.139156\pi\)
\(762\) 0 0
\(763\) 1.94744 + 7.26795i 0.0705021 + 0.263117i
\(764\) 0 0
\(765\) 6.80385 + 25.3923i 0.245994 + 0.918061i
\(766\) 0 0
\(767\) 16.2224 28.0981i 0.585758 1.01456i
\(768\) 0 0
\(769\) 10.1244 + 17.5359i 0.365094 + 0.632361i 0.988791 0.149305i \(-0.0477036\pi\)
−0.623698 + 0.781666i \(0.714370\pi\)
\(770\) 0 0
\(771\) 15.3397i 0.552447i
\(772\) 0 0
\(773\) 4.41154 4.41154i 0.158672 0.158672i −0.623306 0.781978i \(-0.714211\pi\)
0.781978 + 0.623306i \(0.214211\pi\)
\(774\) 0 0
\(775\) 74.1051i 2.66193i
\(776\) 0 0
\(777\) 2.19615 + 0.588457i 0.0787865 + 0.0211108i
\(778\) 0 0
\(779\) −2.59808 0.696152i −0.0930857 0.0249422i
\(780\) 0 0
\(781\) −31.3205 + 8.39230i −1.12074 + 0.300300i
\(782\) 0 0
\(783\) −3.29423 12.2942i −0.117726 0.439360i
\(784\) 0 0
\(785\) 9.46410 16.3923i 0.337788 0.585066i
\(786\) 0 0
\(787\) 13.3468 49.8109i 0.475762 1.77557i −0.142716 0.989764i \(-0.545583\pi\)
0.618477 0.785803i \(-0.287750\pi\)
\(788\) 0 0
\(789\) 23.4904 + 40.6865i 0.836280 + 1.44848i
\(790\) 0 0
\(791\) 10.1436i 0.360665i
\(792\) 0 0
\(793\) 19.6077i − </