Properties

Label 576.2.bb.d.49.1
Level $576$
Weight $2$
Character 576.49
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 49.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.d.529.1

$q$-expansion

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

Character values

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

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

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 −0.964847 0.262811i \(-0.915350\pi\)
−0.704177 + 0.710025i \(0.748684\pi\)
\(6\) 0 0
\(7\) 0.633975 0.366025i 0.239620 0.138345i −0.375382 0.926870i \(-0.622489\pi\)
0.615002 + 0.788526i \(0.289155\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) 0.767949 2.86603i 0.231545 0.864139i −0.748130 0.663552i \(-0.769048\pi\)
0.979676 0.200587i \(-0.0642851\pi\)
\(12\) 0 0
\(13\) −1.63397 6.09808i −0.453183 1.69130i −0.693375 0.720577i \(-0.743877\pi\)
0.240192 0.970725i \(-0.422790\pi\)
\(14\) 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 −0.630635 0.776079i \(-0.717206\pi\)
0.776079 + 0.630635i \(0.217206\pi\)
\(20\) 0 0
\(21\) 0.633975 1.09808i 0.138345 0.239620i
\(22\) 0 0
\(23\) 1.09808 + 0.633975i 0.228965 + 0.132193i 0.610094 0.792329i \(-0.291132\pi\)
−0.381130 + 0.924522i \(0.624465\pi\)
\(24\) 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 0.0323566 0.999476i \(-0.489699\pi\)
−0.471717 + 0.881750i \(0.656365\pi\)
\(30\) 0 0
\(31\) 3.73205 6.46410i 0.670296 1.16099i −0.307524 0.951540i \(-0.599500\pi\)
0.977820 0.209447i \(-0.0671662\pi\)
\(32\) 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 0.803608 0.595159i \(-0.202911\pi\)
−0.595159 + 0.803608i \(0.702911\pi\)
\(38\) 0 0
\(39\) −7.73205 7.73205i −1.23812 1.23812i
\(40\) 0 0
\(41\) −2.59808 1.50000i −0.405751 0.234261i 0.283211 0.959058i \(-0.408600\pi\)
−0.688963 + 0.724797i \(0.741934\pi\)
\(42\) 0 0
\(43\) −0.330127 + 1.23205i −0.0503439 + 0.187886i −0.986519 0.163649i \(-0.947674\pi\)
0.936175 + 0.351535i \(0.114340\pi\)
\(44\) 0 0
\(45\) −3.00000 + 11.1962i −0.447214 + 1.66902i
\(46\) 0 0
\(47\) 4.83013 + 8.36603i 0.704546 + 1.22031i 0.966855 + 0.255326i \(0.0821828\pi\)
−0.262309 + 0.964984i \(0.584484\pi\)
\(48\) 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 0.669343 0.742954i \(-0.266576\pi\)
−0.742954 + 0.669343i \(0.766576\pi\)
\(54\) 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 −0.567042 0.823689i \(-0.691912\pi\)
−0.0792287 + 0.996856i \(0.525246\pi\)
\(60\) 0 0
\(61\) −3.00000 0.803848i −0.384111 0.102922i 0.0615961 0.998101i \(-0.480381\pi\)
−0.445707 + 0.895179i \(0.647048\pi\)
\(62\) 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 −0.997157 0.0753572i \(-0.975990\pi\)
0.825884 0.563840i \(-0.190676\pi\)
\(68\) 0 0
\(69\) 2.19615 0.264386
\(70\) 0 0
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) 0 0
\(73\) 9.73205i 1.13905i 0.821974 + 0.569525i \(0.192873\pi\)
−0.821974 + 0.569525i \(0.807127\pi\)
\(74\) 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 0.976453 + 0.215728i \(0.0692125\pi\)
−0.301401 + 0.953498i \(0.597454\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 1.36603 + 0.366025i 0.149941 + 0.0401765i 0.333009 0.942924i \(-0.391936\pi\)
−0.183068 + 0.983100i \(0.558603\pi\)
\(84\) 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 \(0.0338043\pi\)
−0.994366 + 0.106000i \(0.966196\pi\)
\(90\) 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 0.576172 0.817329i \(-0.304546\pi\)
−0.995913 + 0.0903150i \(0.971213\pi\)
\(98\) 0 0
\(99\) −6.29423 6.29423i −0.632594 0.632594i
\(100\) 0 0
\(101\) −2.00000 + 7.46410i −0.199007 + 0.742706i 0.792186 + 0.610280i \(0.208943\pi\)
−0.991193 + 0.132426i \(0.957723\pi\)
\(102\) 0 0
\(103\) 7.90192 + 4.56218i 0.778600 + 0.449525i 0.835934 0.548830i \(-0.184927\pi\)
−0.0573341 + 0.998355i \(0.518260\pi\)
\(104\) 0 0
\(105\) −1.26795 + 4.73205i −0.123739 + 0.461801i
\(106\) 0 0
\(107\) 13.4904 + 13.4904i 1.30416 + 1.30416i 0.925558 + 0.378607i \(0.123597\pi\)
0.378607 + 0.925558i \(0.376403\pi\)
\(108\) 0 0
\(109\) 7.26795 7.26795i 0.696143 0.696143i −0.267433 0.963576i \(-0.586175\pi\)
0.963576 + 0.267433i \(0.0861754\pi\)
\(110\) 0 0
\(111\) 3.00000 + 0.803848i 0.284747 + 0.0762978i
\(112\) 0 0
\(113\) 6.92820 12.0000i 0.651751 1.12887i −0.330947 0.943649i \(-0.607368\pi\)
0.982698 0.185216i \(-0.0592984\pi\)
\(114\) 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 0.920133 0.391606i \(-0.128080\pi\)
−0.992662 + 0.120926i \(0.961414\pi\)
\(132\) 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 0.253645 0.967297i \(-0.418371\pi\)
0.964527 + 0.263986i \(0.0850372\pi\)
\(138\) 0 0
\(139\) 9.06218 2.42820i 0.768644 0.205958i 0.146872 0.989156i \(-0.453080\pi\)
0.621772 + 0.783198i \(0.286413\pi\)
\(140\) 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 −0.129674 0.991557i \(-0.541393\pi\)
0.383478 + 0.923550i \(0.374726\pi\)
\(150\) 0 0
\(151\) 2.36603 1.36603i 0.192544 0.111166i −0.400629 0.916240i \(-0.631208\pi\)
0.593173 + 0.805075i \(0.297875\pi\)
\(152\) 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 0.896692 0.442655i \(-0.145963\pi\)
−0.997886 + 0.0649959i \(0.979297\pi\)
\(158\) 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 −0.377661 0.925944i \(-0.623272\pi\)
0.925944 + 0.377661i \(0.123272\pi\)
\(164\) 0 0
\(165\) 9.92820 + 17.1962i 0.772910 + 1.33872i
\(166\) 0 0
\(167\) −0.464102 0.267949i −0.0359133 0.0207345i 0.481936 0.876206i \(-0.339934\pi\)
−0.517849 + 0.855472i \(0.673267\pi\)
\(168\) 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 −0.252566 0.967580i \(-0.581275\pi\)
−0.702519 + 0.711665i \(0.747941\pi\)
\(174\) 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 −0.994670 0.103114i \(-0.967119\pi\)
0.103114 + 0.994670i \(0.467119\pi\)
\(180\) 0 0
\(181\) 13.3923 + 13.3923i 0.995442 + 0.995442i 0.999990 0.00454748i \(-0.00144751\pi\)
−0.00454748 + 0.999990i \(0.501448\pi\)
\(182\) 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 −0.999953 0.00973114i \(-0.996902\pi\)
0.491549 0.870850i \(-0.336431\pi\)
\(192\) 0 0
\(193\) −9.13397 + 15.8205i −0.657478 + 1.13879i 0.323789 + 0.946129i \(0.395043\pi\)
−0.981266 + 0.192656i \(0.938290\pi\)
\(194\) 0 0
\(195\) 36.5885 + 21.1244i 2.62015 + 1.51275i
\(196\) 0 0
\(197\) −3.66025 3.66025i −0.260782 0.260782i 0.564590 0.825372i \(-0.309034\pi\)
−0.825372 + 0.564590i \(0.809034\pi\)
\(198\) 0 0
\(199\) 0.875644i 0.0620728i 0.999518 + 0.0310364i \(0.00988078\pi\)
−0.999518 + 0.0310364i \(0.990119\pi\)
\(200\) 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 0.993367 0.114983i \(-0.0366812\pi\)
−0.917773 + 0.397106i \(0.870015\pi\)
\(212\) 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 −0.953227 0.302255i \(-0.902260\pi\)
0.214853 0.976646i \(-0.431073\pi\)
\(224\) 0 0
\(225\) 29.7846i 1.98564i
\(226\) 0 0
\(227\) 14.4282 + 3.86603i 0.957633 + 0.256597i 0.703598 0.710598i \(-0.251575\pi\)
0.254035 + 0.967195i \(0.418242\pi\)
\(228\) 0 0
\(229\) 6.83013 1.83013i 0.451347 0.120938i −0.0259823 0.999662i \(-0.508271\pi\)
0.477330 + 0.878724i \(0.341605\pi\)
\(230\) 0 0
\(231\) −2.66025 2.66025i −0.175032 0.175032i
\(232\) 0 0
\(233\) 7.19615i 0.471436i −0.971822 0.235718i \(-0.924256\pi\)
0.971822 0.235718i \(-0.0757441\pi\)
\(234\) 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 −0.0364139 0.999337i \(-0.511593\pi\)
0.883658 0.468133i \(-0.155073\pi\)
\(240\) 0 0
\(241\) −6.40192 11.0885i −0.412384 0.714270i 0.582766 0.812640i \(-0.301971\pi\)
−0.995150 + 0.0983699i \(0.968637\pi\)
\(242\) 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 0.612125 0.790761i \(-0.290315\pi\)
−0.790761 + 0.612125i \(0.790315\pi\)
\(252\) 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 −0.970443 0.241330i \(-0.922416\pi\)
0.694219 + 0.719763i \(0.255750\pi\)
\(258\) 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 0.450088 0.892984i \(-0.351393\pi\)
0.998391 + 0.0567045i \(0.0180593\pi\)
\(264\) 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 −0.547976 0.836494i \(-0.684601\pi\)
0.836494 + 0.547976i \(0.184601\pi\)
\(270\) 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 0.715107 + 0.699015i \(0.246378\pi\)
−0.968808 + 0.247811i \(0.920289\pi\)
\(278\) 0 0
\(279\) −11.1962 19.3923i −0.670296 1.16099i
\(280\) 0 0
\(281\) −8.66025 + 5.00000i −0.516627 + 0.298275i −0.735554 0.677466i \(-0.763078\pi\)
0.218926 + 0.975741i \(0.429745\pi\)
\(282\) 0 0
\(283\) −27.7583 + 7.43782i −1.65006 + 0.442133i −0.959630 0.281265i \(-0.909246\pi\)
−0.690431 + 0.723398i \(0.742579\pi\)
\(284\) 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 0.160106 0.987100i \(-0.448817\pi\)
0.632205 + 0.774801i \(0.282150\pi\)
\(294\) 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 −0.0819670 0.996635i \(-0.526120\pi\)
0.996635 + 0.0819670i \(0.0261202\pi\)
\(308\) 0 0
\(309\) 15.8038 0.899049
\(310\) 0 0
\(311\) −13.9019 8.02628i −0.788306 0.455129i 0.0510600 0.998696i \(-0.483740\pi\)
−0.839366 + 0.543567i \(0.817073\pi\)
\(312\) 0 0
\(313\) 24.6506 14.2321i 1.39334 0.804443i 0.399653 0.916666i \(-0.369131\pi\)
0.993683 + 0.112223i \(0.0357972\pi\)
\(314\) 0 0
\(315\) 2.19615 + 8.19615i 0.123739 + 0.461801i
\(316\) 0 0
\(317\) 31.4904 + 8.43782i 1.76868 + 0.473915i 0.988445 0.151577i \(-0.0484351\pi\)
0.780231 + 0.625492i \(0.215102\pi\)
\(318\) 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 0.672049 + 0.740506i \(0.265414\pi\)
−0.952265 + 0.305273i \(0.901252\pi\)
\(332\) 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 0.335829 + 0.941923i \(0.390984\pi\)
−0.983644 + 0.180126i \(0.942350\pi\)
\(338\) 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 0.475510 0.879710i \(-0.342263\pi\)
0.851659 + 0.524096i \(0.175597\pi\)
\(348\) 0 0
\(349\) −7.73205 2.07180i −0.413887 0.110901i 0.0458657 0.998948i \(-0.485395\pi\)
−0.459753 + 0.888047i \(0.652062\pi\)
\(350\) 0 0
\(351\) −31.6865 + 8.49038i −1.69130 + 0.453183i
\(352\) 0 0
\(353\) −10.1603 17.5981i −0.540776 0.936651i −0.998860 0.0477421i \(-0.984797\pi\)
0.458084 0.888909i \(-0.348536\pi\)
\(354\) 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 \(0.127098\pi\)
−0.921337 + 0.388764i \(0.872902\pi\)
\(360\) 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 0.999448 + 0.0332125i \(0.0105738\pi\)
−0.470961 + 0.882154i \(0.656093\pi\)
\(368\) 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 −0.401709 0.915767i \(-0.631584\pi\)
0.109993 + 0.993932i \(0.464917\pi\)
\(374\) 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 0.999359 0.0358080i \(-0.0114005\pi\)
−0.0358080 + 0.999359i \(0.511400\pi\)
\(380\) 0 0
\(381\) 9.29423 5.36603i 0.476158 0.274910i
\(382\) 0 0
\(383\) 3.26795 5.66025i 0.166984 0.289225i −0.770374 0.637593i \(-0.779930\pi\)
0.937358 + 0.348367i \(0.113264\pi\)
\(384\) 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 0.860078 + 0.510163i \(0.170415\pi\)
−0.999931 + 0.0117752i \(0.996252\pi\)
\(390\) 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 −0.950310 0.311306i \(-0.899233\pi\)
0.311306 + 0.950310i \(0.399233\pi\)
\(398\) 0 0
\(399\) −0.294229 1.09808i −0.0147299 0.0549726i
\(400\) 0 0
\(401\) 13.7942 23.8923i 0.688851 1.19312i −0.283359 0.959014i \(-0.591449\pi\)
0.972210 0.234111i \(-0.0752179\pi\)
\(402\) 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 −0.313191 0.949690i \(-0.601398\pi\)
−0.979051 + 0.203614i \(0.934731\pi\)
\(410\) 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 0.797115 + 0.603828i \(0.206359\pi\)
−0.388408 + 0.921488i \(0.626975\pi\)
\(420\) 0 0
\(421\) 0.588457 2.19615i 0.0286797 0.107034i −0.950102 0.311938i \(-0.899022\pi\)
0.978782 + 0.204905i \(0.0656884\pi\)
\(422\) 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 −0.379611 0.925146i \(-0.623942\pi\)
0.611395 + 0.791326i \(0.290609\pi\)
\(440\) 0 0
\(441\) 9.69615 + 16.7942i 0.461722 + 0.799725i
\(442\) 0 0
\(443\) 5.25833 19.6244i 0.249831 0.932381i −0.721063 0.692870i \(-0.756346\pi\)
0.970894 0.239511i \(-0.0769873\pi\)
\(444\) 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 0.0552962 0.998470i \(-0.482390\pi\)
0.892348 + 0.451347i \(0.149056\pi\)
\(458\) 0 0
\(459\) 11.7846i 0.550058i
\(460\) 0 0
\(461\) 2.56218 + 0.686533i 0.119333 + 0.0319751i 0.317991 0.948094i \(-0.396992\pi\)
−0.198659 + 0.980069i \(0.563658\pi\)
\(462\) 0 0
\(463\) 9.19615 15.9282i 0.427381 0.740246i −0.569258 0.822159i \(-0.692769\pi\)
0.996640 + 0.0819125i \(0.0261028\pi\)
\(464\) 0 0
\(465\) 12.9282 + 48.2487i 0.599531 + 2.23748i
\(466\) 0 0
\(467\) −4.36603 + 4.36603i −0.202036 + 0.202036i −0.800872 0.598836i \(-0.795630\pi\)
0.598836 + 0.800872i \(0.295630\pi\)
\(468\) 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 −0.994722 0.102610i \(-0.967281\pi\)
0.408498 0.912759i \(-0.366053\pi\)
\(480\) 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 \(0.119601\pi\)
−0.930237 + 0.366959i \(0.880399\pi\)
\(488\) 0 0
\(489\) 4.43782 16.5622i 0.200685 0.748968i
\(490\) 0 0
\(491\) 25.7224 6.89230i 1.16084 0.311045i 0.373537 0.927615i \(-0.378145\pi\)
0.787300 + 0.616570i \(0.211478\pi\)
\(492\) 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 0.993443 0.114332i \(-0.0364727\pi\)
−0.917512 + 0.397707i \(0.869806\pi\)
\(500\) 0 0
\(501\) −0.928203 −0.0414691
\(502\) 0 0
\(503\) 27.7128i 1.23565i 0.786314 + 0.617827i \(0.211987\pi\)
−0.786314 + 0.617827i \(0.788013\pi\)
\(504\) 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 −0.990617 0.136665i \(-0.956362\pi\)
0.789567 0.613664i \(-0.210305\pi\)
\(510\) 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 \(-0.908083\pi\)
0.958596 0.284770i \(-0.0919173\pi\)
\(522\) 0 0
\(523\) 14.4641 + 14.4641i 0.632471 + 0.632471i 0.948687 0.316216i \(-0.102412\pi\)
−0.316216 + 0.948687i \(0.602412\pi\)
\(524\) 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 −0.860994 0.508614i \(-0.830158\pi\)
0.508614 + 0.860994i \(0.330158\pi\)
\(542\) 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 0.855138 0.518400i \(-0.173472\pi\)
0.481371 + 0.876517i \(0.340139\pi\)
\(548\) 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 −0.0700519 + 0.997543i \(0.522316\pi\)
−0.997543 + 0.0700519i \(0.977684\pi\)
\(558\) 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 0.941382 0.337343i \(-0.109528\pi\)
−0.983932 + 0.178543i \(0.942862\pi\)
\(564\) 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 0.0842230 0.996447i \(-0.473159\pi\)
0.905060 + 0.425284i \(0.139826\pi\)
\(570\) 0 0
\(571\) 19.8923 5.33013i 0.832467 0.223059i 0.182677 0.983173i \(-0.441524\pi\)
0.649790 + 0.760114i \(0.274857\pi\)
\(572\) 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 −0.941955 0.335739i \(-0.891014\pi\)
0.983626 + 0.180219i \(0.0576807\pi\)
\(588\) 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 −0.0588850 0.998265i \(-0.518755\pi\)
−0.893965 + 0.448136i \(0.852088\pi\)
\(600\) 0 0
\(601\) −17.5526 + 10.1340i −0.715984 + 0.413373i −0.813273 0.581883i \(-0.802316\pi\)
0.0972889 + 0.995256i \(0.468983\pi\)
\(602\) 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 −0.112648 + 0.993635i \(0.535933\pi\)
−0.804189 + 0.594374i \(0.797400\pi\)
\(608\) 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 0.739840 0.672783i \(-0.234901\pi\)
−0.672783 + 0.739840i \(0.734901\pi\)
\(614\) 0 0
\(615\) 19.3923 5.19615i 0.781973 0.209529i
\(616\) 0 0
\(617\) 3.91154 + 2.25833i 0.157473 + 0.0909170i 0.576666 0.816980i \(-0.304354\pi\)
−0.419193 + 0.907897i \(0.637687\pi\)
\(618\) 0 0
\(619\) 10.4019 38.8205i 0.418089 1.56033i −0.360479 0.932767i \(-0.617387\pi\)
0.778568 0.627561i \(-0.215947\pi\)
\(620\) 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 \(0.276859\pi\)
−0.644995 + 0.764187i \(0.723141\pi\)
\(632\) 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 0.770934 0.636915i \(-0.219790\pi\)
−0.937052 + 0.349191i \(0.886457\pi\)
\(642\) 0 0
\(643\) −12.2321 45.6506i −0.482385 1.80029i −0.591558 0.806263i \(-0.701487\pi\)
0.109173 0.994023i \(-0.465180\pi\)
\(644\) 0 0
\(645\) −4.26795 7.39230i −0.168050 0.291072i
\(646\) 0 0
\(647\) 13.2679i 0.521617i 0.965391 + 0.260808i \(0.0839891\pi\)
−0.965391 + 0.260808i \(0.916011\pi\)
\(648\) 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 0.930077 0.367365i \(-0.119740\pi\)
−0.989153 + 0.146891i \(0.953073\pi\)
\(654\) 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 0.539323 0.842099i \(-0.318680\pi\)
0.0460178 + 0.998941i \(0.485347\pi\)
\(660\) 0 0
\(661\) −8.19615 + 2.19615i −0.318793 + 0.0854204i −0.414667 0.909973i \(-0.636102\pi\)
0.0958740 + 0.995393i \(0.469435\pi\)
\(662\) 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 0.984313 0.176430i \(-0.0564550\pi\)
−0.644950 + 0.764225i \(0.723122\pi\)
\(674\) 0 0
\(675\) −25.7942 44.6769i −0.992820 1.71962i
\(676\) 0 0
\(677\) −1.26795 + 4.73205i −0.0487312 + 0.181867i −0.986002 0.166736i \(-0.946677\pi\)
0.937270 + 0.348603i \(0.113344\pi\)
\(678\) 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 0.791383 0.611321i \(-0.209362\pi\)
−0.611321 + 0.791383i \(0.709362\pi\)
\(684\) 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 −0.217344 0.976095i \(-0.569739\pi\)
−0.676273 + 0.736651i \(0.736406\pi\)
\(692\) 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 −0.476527 0.879160i \(-0.658105\pi\)
0.879160 + 0.476527i \(0.158105\pi\)
\(702\) 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 −0.786746 0.617277i \(-0.788236\pi\)
0.989980 0.141205i \(-0.0450977\pi\)
\(710\) 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 0.223832 0.974628i \(-0.428143\pi\)
0.955968 + 0.293470i \(0.0948099\pi\)
\(728\) 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 0.940053 + 0.341028i \(0.110775\pi\)
−0.643596 + 0.765366i \(0.722558\pi\)
\(734\) 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 −0.979945 0.199266i \(-0.936144\pi\)
0.199266 + 0.979945i \(0.436144\pi\)
\(740\) 0 0
\(741\) −9.80385 −0.360153
\(742\) 0 0
\(743\) 2.24167 + 1.29423i 0.0822389 + 0.0474806i 0.540556 0.841308i \(-0.318214\pi\)
−0.458317 + 0.888789i \(0.651547\pi\)
\(744\) 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 0.284378 + 0.958712i \(0.408213\pi\)
−0.972458 + 0.233077i \(0.925120\pi\)
\(752\) 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 0.588103 0.808786i \(-0.299875\pi\)
−0.808786 + 0.588103i \(0.799875\pi\)
\(758\) 0 0
\(759\) 1.68653 6.29423i 0.0612173 0.228466i
\(760\) 0 0
\(761\) 27.3731 + 15.8038i 0.992273 + 0.572889i 0.905953 0.423378i \(-0.139156\pi\)
0.0863200 + 0.996267i \(0.472489\pi\)
\(762\) 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 −0.623698 0.781666i \(-0.714370\pi\)
0.988791 + 0.149305i \(0.0477036\pi\)
\(770\) 0 0
\(771\) 15.3397i 0.552447i
\(772\) 0 0
\(773\) 4.41154 + 4.41154i 0.158672 + 0.158672i 0.781978 0.623306i \(-0.214211\pi\)
−0.623306 + 0.781978i \(0.714211\pi\)
\(774\) 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 0.618477 + 0.785803i \(0.287750\pi\)
−0.142716 + 0.989764i \(0.545583\pi\)
\(788\) 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 0.696290i