Properties

Label 576.2.bb.c.241.1
Level $576$
Weight $2$
Character 576.241
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 241.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.241
Dual form 576.2.bb.c.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 1.50000i) q^{3} +(1.00000 - 3.73205i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 - 1.50000i) q^{3} +(1.00000 - 3.73205i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-2.86603 + 0.767949i) q^{11} +(6.09808 + 1.63397i) q^{13} +(-4.73205 - 4.73205i) q^{15} -2.26795 q^{17} +(0.633975 - 0.633975i) q^{19} +(-1.09808 + 0.633975i) q^{21} +(-1.09808 + 0.633975i) q^{23} +(-8.59808 - 4.96410i) q^{25} -5.19615 q^{27} +(0.633975 + 2.36603i) q^{29} +(3.73205 + 6.46410i) q^{31} +(-1.33013 + 4.96410i) q^{33} +(-2.00000 + 2.00000i) q^{35} +(1.26795 + 1.26795i) q^{37} +(7.73205 - 7.73205i) q^{39} +(2.59808 - 1.50000i) q^{41} +(1.23205 - 0.330127i) q^{43} +(-11.1962 + 3.00000i) q^{45} +(4.83013 - 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(-1.96410 + 3.40192i) q^{51} +(-0.535898 - 0.535898i) q^{53} +11.4641i q^{55} +(-0.401924 - 1.50000i) q^{57} +(1.33013 - 4.96410i) q^{59} +(0.803848 + 3.00000i) q^{61} +2.19615i q^{63} +(12.1962 - 21.1244i) q^{65} +(5.23205 + 1.40192i) q^{67} +2.19615i q^{69} -10.9282i q^{71} +9.73205i q^{73} +(-14.8923 + 8.59808i) q^{75} +(2.09808 + 0.562178i) q^{77} +(6.00000 - 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-0.366025 - 1.36603i) q^{83} +(-2.26795 + 8.46410i) q^{85} +(4.09808 + 1.09808i) q^{87} +2.00000i q^{89} +(-3.26795 - 3.26795i) q^{91} +12.9282 q^{93} +(-1.73205 - 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +(6.29423 + 6.29423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{5} - 6q^{7} - 6q^{9} + O(q^{10}) \) \( 4q + 4q^{5} - 6q^{7} - 6q^{9} - 8q^{11} + 14q^{13} - 12q^{15} - 16q^{17} + 6q^{19} + 6q^{21} + 6q^{23} - 24q^{25} + 6q^{29} + 8q^{31} + 12q^{33} - 8q^{35} + 12q^{37} + 24q^{39} - 2q^{43} - 24q^{45} + 2q^{47} - 6q^{49} + 6q^{51} - 16q^{53} - 12q^{57} - 12q^{59} + 24q^{61} + 28q^{65} + 14q^{67} - 18q^{75} - 2q^{77} + 24q^{79} - 18q^{81} + 2q^{83} - 16q^{85} + 6q^{87} - 20q^{91} + 24q^{93} - 20q^{97} - 6q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 0.866025 1.50000i 0.500000 0.866025i
\(4\) 0 0
\(5\) 1.00000 3.73205i 0.447214 1.66902i −0.262811 0.964847i \(-0.584650\pi\)
0.710025 0.704177i \(-0.248684\pi\)
\(6\) 0 0
\(7\) −0.633975 0.366025i −0.239620 0.138345i 0.375382 0.926870i \(-0.377511\pi\)
−0.615002 + 0.788526i \(0.710845\pi\)
\(8\) 0 0
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) 0 0
\(11\) −2.86603 + 0.767949i −0.864139 + 0.231545i −0.663552 0.748130i \(-0.730952\pi\)
−0.200587 + 0.979676i \(0.564285\pi\)
\(12\) 0 0
\(13\) 6.09808 + 1.63397i 1.69130 + 0.453183i 0.970725 0.240192i \(-0.0772105\pi\)
0.720577 + 0.693375i \(0.243877\pi\)
\(14\) 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
\(21\) −1.09808 + 0.633975i −0.239620 + 0.138345i
\(22\) 0 0
\(23\) −1.09808 + 0.633975i −0.228965 + 0.132193i −0.610094 0.792329i \(-0.708868\pi\)
0.381130 + 0.924522i \(0.375535\pi\)
\(24\) 0 0
\(25\) −8.59808 4.96410i −1.71962 0.992820i
\(26\) 0 0
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) 0.633975 + 2.36603i 0.117726 + 0.439360i 0.999476 0.0323566i \(-0.0103012\pi\)
−0.881750 + 0.471717i \(0.843635\pi\)
\(30\) 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 0.803608 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 \(-0.591400\pi\)
0.688963 + 0.724797i \(0.258066\pi\)
\(42\) 0 0
\(43\) 1.23205 0.330127i 0.187886 0.0503439i −0.163649 0.986519i \(-0.552326\pi\)
0.351535 + 0.936175i \(0.385660\pi\)
\(44\) 0 0
\(45\) −11.1962 + 3.00000i −1.66902 + 0.447214i
\(46\) 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
\(51\) −1.96410 + 3.40192i −0.275029 + 0.476365i
\(52\) 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
\(59\) 1.33013 4.96410i 0.173168 0.646271i −0.823689 0.567042i \(-0.808088\pi\)
0.996856 0.0792287i \(-0.0252457\pi\)
\(60\) 0 0
\(61\) 0.803848 + 3.00000i 0.102922 + 0.384111i 0.998101 0.0615961i \(-0.0196191\pi\)
−0.895179 + 0.445707i \(0.852952\pi\)
\(62\) 0 0
\(63\) 2.19615i 0.276689i
\(64\) 0 0
\(65\) 12.1962 21.1244i 1.51275 2.62015i
\(66\) 0 0
\(67\) 5.23205 + 1.40192i 0.639197 + 0.171272i 0.563840 0.825884i \(-0.309324\pi\)
0.0753572 + 0.997157i \(0.475990\pi\)
\(68\) 0 0
\(69\) 2.19615i 0.264386i
\(70\) 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
\(75\) −14.8923 + 8.59808i −1.71962 + 0.992820i
\(76\) 0 0
\(77\) 2.09808 + 0.562178i 0.239098 + 0.0640661i
\(78\) 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
\(83\) −0.366025 1.36603i −0.0401765 0.149941i 0.942924 0.333009i \(-0.108064\pi\)
−0.983100 + 0.183068i \(0.941397\pi\)
\(84\) 0 0
\(85\) −2.26795 + 8.46410i −0.245994 + 0.918061i
\(86\) 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
\(93\) 12.9282 1.34059
\(94\) 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
\(101\) 7.46410 2.00000i 0.742706 0.199007i 0.132426 0.991193i \(-0.457723\pi\)
0.610280 + 0.792186i \(0.291057\pi\)
\(102\) 0 0
\(103\) −7.90192 + 4.56218i −0.778600 + 0.449525i −0.835934 0.548830i \(-0.815073\pi\)
0.0573341 + 0.998355i \(0.481740\pi\)
\(104\) 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 0.982698 + 0.185216i \(0.0592984\pi\)
−0.330947 + 0.943649i \(0.607368\pi\)
\(114\) 0 0
\(115\) 1.26795 + 4.73205i 0.118237 + 0.441266i
\(116\) 0 0
\(117\) −4.90192 18.2942i −0.453183 1.69130i
\(118\) 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
\(123\) 5.19615i 0.468521i
\(124\) 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
\(131\) 3.09808 + 0.830127i 0.270680 + 0.0725285i 0.391606 0.920133i \(-0.371920\pi\)
−0.120926 + 0.992662i \(0.538586\pi\)
\(132\) 0 0
\(133\) −0.633975 + 0.169873i −0.0549726 + 0.0147299i
\(134\) 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 \(-0.581629\pi\)
−0.964527 + 0.263986i \(0.914963\pi\)
\(138\) 0 0
\(139\) −2.42820 + 9.06218i −0.205958 + 0.768644i 0.783198 + 0.621772i \(0.213587\pi\)
−0.989156 + 0.146872i \(0.953080\pi\)
\(140\) 0 0
\(141\) −8.36603 14.4904i −0.704546 1.22031i
\(142\) 0 0
\(143\) −18.7321 −1.56645
\(144\) 0 0
\(145\) 9.46410 0.785951
\(146\) 0 0
\(147\) −11.1962 −0.923443
\(148\) 0 0
\(149\) −0.830127 + 3.09808i −0.0680067 + 0.253804i −0.991557 0.129674i \(-0.958607\pi\)
0.923550 + 0.383478i \(0.125274\pi\)
\(150\) 0 0
\(151\) −2.36603 1.36603i −0.192544 0.111166i 0.400629 0.916240i \(-0.368792\pi\)
−0.593173 + 0.805075i \(0.702125\pi\)
\(152\) 0 0
\(153\) 3.40192 + 5.89230i 0.275029 + 0.476365i
\(154\) 0 0
\(155\) 27.8564 7.46410i 2.23748 0.599531i
\(156\) 0 0
\(157\) 4.73205 + 1.26795i 0.377659 + 0.101193i 0.442655 0.896692i \(-0.354037\pi\)
−0.0649959 + 0.997886i \(0.520703\pi\)
\(158\) 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
\(165\) 17.1962 + 9.92820i 1.33872 + 0.772910i
\(166\) 0 0
\(167\) 0.464102 0.267949i 0.0359133 0.0207345i −0.481936 0.876206i \(-0.660066\pi\)
0.517849 + 0.855472i \(0.326733\pi\)
\(168\) 0 0
\(169\) 23.2583 + 13.4282i 1.78910 + 1.03294i
\(170\) 0 0
\(171\) −2.59808 0.696152i −0.198680 0.0532361i
\(172\) 0 0
\(173\) 3.36603 + 12.5622i 0.255914 + 0.955085i 0.967580 + 0.252566i \(0.0812745\pi\)
−0.711665 + 0.702519i \(0.752059\pi\)
\(174\) 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
\(187\) 6.50000 1.74167i 0.475327 0.127364i
\(188\) 0 0
\(189\) 3.29423 + 1.90192i 0.239620 + 0.138345i
\(190\) 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
\(195\) −21.1244 36.5885i −1.51275 2.62015i
\(196\) 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
\(203\) 0.464102 1.73205i 0.0325735 0.121566i
\(204\) 0 0
\(205\) −3.00000 11.1962i −0.209529 0.781973i
\(206\) 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
\(211\) −4.09808 1.09808i −0.282123 0.0755947i 0.114983 0.993367i \(-0.463319\pi\)
−0.397106 + 0.917773i \(0.629985\pi\)
\(212\) 0 0
\(213\) −16.3923 9.46410i −1.12318 0.648470i
\(214\) 0 0
\(215\) 4.92820i 0.336101i
\(216\) 0 0
\(217\) 5.46410i 0.370927i
\(218\) 0 0
\(219\) 14.5981 + 8.42820i 0.986447 + 0.569525i
\(220\) 0 0
\(221\) −13.8301 3.70577i −0.930315 0.249277i
\(222\) 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
\(227\) −3.86603 14.4282i −0.256597 0.957633i −0.967195 0.254035i \(-0.918242\pi\)
0.710598 0.703598i \(-0.248425\pi\)
\(228\) 0 0
\(229\) −1.83013 + 6.83013i −0.120938 + 0.451347i −0.999662 0.0259823i \(-0.991729\pi\)
0.878724 + 0.477330i \(0.158395\pi\)
\(230\) 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
\(237\) −10.3923 18.0000i −0.675053 1.16923i
\(238\) 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
\(243\) 7.79423 + 13.5000i 0.500000 + 0.866025i
\(244\) 0 0
\(245\) −24.1244 + 6.46410i −1.54125 + 0.412976i
\(246\) 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 0.694219 0.719763i \(-0.255750\pi\)
−0.970443 + 0.241330i \(0.922416\pi\)
\(258\) 0 0
\(259\) −0.339746 1.26795i −0.0211108 0.0787865i
\(260\) 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 \(-0.648607\pi\)
−0.998391 + 0.0567045i \(0.981941\pi\)
\(264\) 0 0
\(265\) −2.53590 + 1.46410i −0.155779 + 0.0899390i
\(266\) 0 0
\(267\) 3.00000 + 1.73205i 0.183597 + 0.106000i
\(268\) 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
\(275\) 28.4545 + 7.62436i 1.71587 + 0.459766i
\(276\) 0 0
\(277\) 15.7583 4.22243i 0.946826 0.253701i 0.247811 0.968808i \(-0.420289\pi\)
0.699015 + 0.715107i \(0.253622\pi\)
\(278\) 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 \(-0.236922\pi\)
−0.218926 + 0.975741i \(0.570255\pi\)
\(282\) 0 0
\(283\) 7.43782 27.7583i 0.442133 1.65006i −0.281265 0.959630i \(-0.590754\pi\)
0.723398 0.690431i \(-0.242579\pi\)
\(284\) 0 0
\(285\) −6.00000 −0.355409
\(286\) 0 0
\(287\) −2.19615 −0.129635
\(288\) 0 0
\(289\) −11.8564 −0.697436
\(290\) 0 0
\(291\) 7.16025 + 12.4019i 0.419742 + 0.727014i
\(292\) 0 0
\(293\) −3.63397 + 13.5622i −0.212299 + 0.792311i 0.774801 + 0.632205i \(0.217850\pi\)
−0.987100 + 0.160106i \(0.948817\pi\)
\(294\) 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
\(299\) −7.73205 + 2.07180i −0.447156 + 0.119815i
\(300\) 0 0
\(301\) −0.901924 0.241670i −0.0519860 0.0139296i
\(302\) 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
\(309\) 15.8038i 0.899049i
\(310\) 0 0
\(311\) 13.9019 8.02628i 0.788306 0.455129i −0.0510600 0.998696i \(-0.516260\pi\)
0.839366 + 0.543567i \(0.182927\pi\)
\(312\) 0 0
\(313\) −24.6506 14.2321i −1.39334 0.804443i −0.399653 0.916666i \(-0.630869\pi\)
−0.993683 + 0.112223i \(0.964203\pi\)
\(314\) 0 0
\(315\) 8.19615 + 2.19615i 0.461801 + 0.123739i
\(316\) 0 0
\(317\) −8.43782 31.4904i −0.473915 1.76868i −0.625492 0.780231i \(-0.715102\pi\)
0.151577 0.988445i \(-0.451565\pi\)
\(318\) 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
\(331\) 19.0263 5.09808i 1.04578 0.280216i 0.305273 0.952265i \(-0.401252\pi\)
0.740506 + 0.672049i \(0.234586\pi\)
\(332\) 0 0
\(333\) 1.39230 5.19615i 0.0762978 0.284747i
\(334\) 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
\(339\) 24.0000 1.30350
\(340\) 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
\(347\) −6.62436 + 24.7224i −0.355614 + 1.32717i 0.524096 + 0.851659i \(0.324403\pi\)
−0.879710 + 0.475510i \(0.842263\pi\)
\(348\) 0 0
\(349\) 2.07180 + 7.73205i 0.110901 + 0.413887i 0.998948 0.0458657i \(-0.0146046\pi\)
−0.888047 + 0.459753i \(0.847938\pi\)
\(350\) 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
\(355\) −40.7846 10.9282i −2.16462 0.580009i
\(356\) 0 0
\(357\) 2.49038 1.43782i 0.131805 0.0760976i
\(358\) 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
\(363\) 3.80385i 0.199650i
\(364\) 0 0
\(365\) 36.3205 + 9.73205i 1.90110 + 0.509399i
\(366\) 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
\(371\) 0.143594 + 0.535898i 0.00745501 + 0.0278225i
\(372\) 0 0
\(373\) 1.50962 5.63397i 0.0781651 0.291716i −0.915767 0.401709i \(-0.868416\pi\)
0.993932 + 0.109993i \(0.0350829\pi\)
\(374\) 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
\(381\) 5.36603 9.29423i 0.274910 0.476158i
\(382\) 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
\(389\) 10.2942 2.75833i 0.521938 0.139853i 0.0117752 0.999931i \(-0.496252\pi\)
0.510163 + 0.860078i \(0.329585\pi\)
\(390\) 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 0.972210 + 0.234111i \(0.0752179\pi\)
−0.283359 + 0.959014i \(0.591449\pi\)
\(402\) 0 0
\(403\) 12.1962 + 45.5167i 0.607534 + 2.26735i
\(404\) 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 \(-0.398602\pi\)
0.979051 + 0.203614i \(0.0652688\pi\)
\(410\) 0 0
\(411\) −24.6962 + 14.2583i −1.21817 + 0.703312i
\(412\) 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
\(419\) −31.2224 8.36603i −1.52532 0.408707i −0.603828 0.797115i \(-0.706359\pi\)
−0.921488 + 0.388408i \(0.873025\pi\)
\(420\) 0 0
\(421\) −2.19615 + 0.588457i −0.107034 + 0.0286797i −0.311938 0.950102i \(-0.600978\pi\)
0.204905 + 0.978782i \(0.434312\pi\)
\(422\) 0 0
\(423\) −28.9808 −1.40909
\(424\) 0 0
\(425\) 19.5000 + 11.2583i 0.945889 + 0.546109i
\(426\) 0 0
\(427\) 0.588457 2.19615i 0.0284774 0.106279i
\(428\) 0 0
\(429\) −16.2224 + 28.0981i −0.783226 + 1.35659i
\(430\) 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
\(435\) 8.19615 14.1962i 0.392975 0.680653i
\(436\) 0 0
\(437\) −0.294229 + 1.09808i −0.0140749 + 0.0525281i
\(438\) 0 0
\(439\) −4.85641 2.80385i −0.231784 0.133820i 0.379611 0.925146i \(-0.376058\pi\)
−0.611395 + 0.791326i \(0.709391\pi\)
\(440\) 0 0
\(441\) −9.69615 + 16.7942i −0.461722 + 0.799725i
\(442\) 0 0
\(443\) −19.6244 + 5.25833i −0.932381 + 0.249831i −0.692870 0.721063i \(-0.743654\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(444\) 0 0
\(445\) 7.46410 + 2.00000i 0.353832 + 0.0948091i
\(446\) 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
\(453\) −4.09808 + 2.36603i −0.192544 + 0.111166i
\(454\) 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 \(-0.517610\pi\)
−0.892348 + 0.451347i \(0.850944\pi\)
\(458\) 0 0
\(459\) 11.7846 0.550058
\(460\) 0 0
\(461\) −0.686533 2.56218i −0.0319751 0.119333i 0.948094 0.317991i \(-0.103008\pi\)
−0.980069 + 0.198659i \(0.936342\pi\)
\(462\) 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 −0.800872 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
\(475\) −8.59808 + 2.30385i −0.394507 + 0.105708i
\(476\) 0 0
\(477\) −0.588457 + 2.19615i −0.0269436 + 0.100555i
\(478\) 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
\(483\) 0.803848 1.39230i 0.0365763 0.0633521i
\(484\) 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
\(491\) −6.89230 + 25.7224i −0.311045 + 1.16084i 0.616570 + 0.787300i \(0.288522\pi\)
−0.927615 + 0.373537i \(0.878145\pi\)
\(492\) 0 0
\(493\) −1.43782 5.36603i −0.0647563 0.241674i
\(494\) 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
\(499\) −6.33013 1.69615i −0.283375 0.0759302i 0.114332 0.993443i \(-0.463527\pi\)
−0.397707 + 0.917512i \(0.630194\pi\)
\(500\) 0 0
\(501\) 0.928203i 0.0414691i
\(502\) 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
\(507\) 40.2846 23.2583i 1.78910 1.03294i
\(508\) 0 0
\(509\) 16.9282 + 4.53590i 0.750329 + 0.201050i 0.613664 0.789567i \(-0.289695\pi\)
0.136665 + 0.990617i \(0.456362\pi\)
\(510\) 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
\(515\) 9.12436 + 34.0526i 0.402067 + 1.50054i
\(516\) 0 0
\(517\) −7.41858 + 27.6865i −0.326269 + 1.21765i
\(518\) 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
\(525\) 12.5885 0.549405
\(526\) 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
\(531\) −14.8923 + 3.99038i −0.646271 + 0.173168i
\(532\) 0 0
\(533\) 18.2942 4.90192i 0.792411 0.212326i
\(534\) 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
\(547\) −8.37564 31.2583i −0.358117 1.33651i −0.876517 0.481371i \(-0.840139\pi\)
0.518400 0.855138i \(-0.326528\pi\)
\(548\) 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
\(555\) 12.0000i 0.509372i
\(556\) 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
\(563\) 3.76795 + 1.00962i 0.158800 + 0.0425504i 0.337343 0.941382i \(-0.390472\pi\)
−0.178543 + 0.983932i \(0.557138\pi\)
\(564\) 0 0
\(565\) 51.7128 13.8564i 2.17557 0.582943i
\(566\) 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 \(-0.526841\pi\)
−0.905060 + 0.425284i \(0.860174\pi\)
\(570\) 0 0
\(571\) −5.33013 + 19.8923i −0.223059 + 0.832467i 0.760114 + 0.649790i \(0.225143\pi\)
−0.983173 + 0.182677i \(0.941524\pi\)
\(572\) 0 0
\(573\) 12.1699 + 21.0788i 0.508404 + 0.880581i
\(574\) 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
\(579\) −31.6410 −1.31496
\(580\) 0 0
\(581\) −0.267949 + 1.00000i −0.0111164 + 0.0414870i
\(582\) 0 0
\(583\) 1.94744 + 1.12436i 0.0806548 + 0.0465661i
\(584\) 0 0
\(585\) −73.1769 −3.02549
\(586\) 0 0
\(587\) −3.76795 + 1.00962i −0.155520 + 0.0416714i −0.335739 0.941955i \(-0.608986\pi\)
0.180219 + 0.983626i \(0.442319\pi\)
\(588\) 0 0
\(589\) 6.46410 + 1.73205i 0.266349 + 0.0713679i
\(590\) 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
\(597\) 1.31347 + 0.758330i 0.0537566 + 0.0310364i
\(598\) 0 0
\(599\) 23.3205 13.4641i 0.952850 0.550128i 0.0588850 0.998265i \(-0.481245\pi\)
0.893965 + 0.448136i \(0.147912\pi\)
\(600\) 0 0
\(601\) 17.5526 + 10.1340i 0.715984 + 0.413373i 0.813273 0.581883i \(-0.197684\pi\)
−0.0972889 + 0.995256i \(0.531017\pi\)
\(602\) 0 0
\(603\) −4.20577 15.6962i −0.171272 0.639197i
\(604\) 0 0
\(605\) 2.19615 + 8.19615i 0.0892863 + 0.333221i
\(606\) 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 0.739840 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 \(-0.695646\pi\)
0.419193 + 0.907897i \(0.362313\pi\)
\(618\) 0 0
\(619\) −38.8205 + 10.4019i −1.56033 + 0.418089i −0.932767 0.360479i \(-0.882613\pi\)
−0.627561 + 0.778568i \(0.715947\pi\)
\(620\) 0 0
\(621\) 5.70577 3.29423i 0.228965 0.132193i
\(622\) 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
\(627\) 2.30385 + 3.99038i 0.0920068 + 0.159360i
\(628\) 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
\(635\) 6.19615 23.1244i 0.245887 0.917662i
\(636\) 0 0
\(637\) −10.5622 39.4186i −0.418489 1.56182i
\(638\) 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
\(643\) 45.6506 + 12.2321i 1.80029 + 0.482385i 0.994023 0.109173i \(-0.0348202\pi\)
0.806263 + 0.591558i \(0.201487\pi\)
\(644\) 0 0
\(645\) −7.39230 4.26795i −0.291072 0.168050i
\(646\) 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
\(651\) −8.19615 4.73205i −0.321233 0.185464i
\(652\) 0 0
\(653\) 5.63397 + 1.50962i 0.220474 + 0.0590760i 0.367365 0.930077i \(-0.380260\pi\)
−0.146891 + 0.989153i \(0.546927\pi\)
\(654\) 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
\(659\) −4.02628 15.0263i −0.156842 0.585341i −0.998941 0.0460178i \(-0.985347\pi\)
0.842099 0.539323i \(-0.181320\pi\)
\(660\) 0 0
\(661\) 2.19615 8.19615i 0.0854204 0.318793i −0.909973 0.414667i \(-0.863898\pi\)
0.995393 + 0.0958740i \(0.0305646\pi\)
\(662\) 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
\(669\) 19.0981 + 33.0788i 0.738374 + 1.27890i
\(670\) 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
\(675\) 44.6769 + 25.7942i 1.71962 + 0.992820i
\(676\) 0 0
\(677\) 4.73205 1.26795i 0.181867 0.0487312i −0.166736 0.986002i \(-0.553323\pi\)
0.348603 + 0.937270i \(0.386656\pi\)
\(678\) 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
\(691\) 6.29423 + 23.4904i 0.239444 + 0.893616i 0.976095 + 0.217344i \(0.0697392\pi\)
−0.736651 + 0.676273i \(0.763594\pi\)
\(692\) 0 0
\(693\) −1.68653 6.29423i −0.0640661 0.239098i
\(694\) 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
\(699\) −10.7942 6.23205i −0.408275 0.235718i
\(700\) 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
\(707\) −5.46410 1.46410i −0.205499 0.0550632i
\(708\) 0 0
\(709\) −20.1962 + 5.41154i −0.758482 + 0.203235i −0.617277 0.786746i \(-0.711764\pi\)
−0.141205 + 0.989980i \(0.545098\pi\)
\(710\) 0 0
\(711\) −36.0000 −1.35011
\(712\) 0 0
\(713\) −8.19615 4.73205i −0.306948 0.177217i
\(714\) 0 0
\(715\) −18.7321 + 69.9090i −0.700539 + 2.61445i
\(716\) 0 0
\(717\) 45.3731 1.69449
\(718\) 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
\(723\) 11.0885 + 19.2058i 0.412384 + 0.714270i
\(724\) 0 0
\(725\) 6.29423 23.4904i 0.233762 0.872411i
\(726\) 0 0
\(727\) −31.8109 18.3660i −1.17980 0.681158i −0.223832 0.974628i \(-0.571857\pi\)
−0.955968 + 0.293470i \(0.905190\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −2.79423 + 0.748711i −0.103348 + 0.0276921i
\(732\) 0 0
\(733\) −29.9545 8.02628i −1.10639 0.296457i −0.341028 0.940053i \(-0.610775\pi\)
−0.765366 + 0.643596i \(0.777442\pi\)
\(734\) 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
\(741\) 9.80385i 0.360153i
\(742\) 0 0
\(743\) −2.24167 + 1.29423i −0.0822389 + 0.0474806i −0.540556 0.841308i \(-0.681786\pi\)
0.458317 + 0.888789i \(0.348453\pi\)
\(744\) 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
\(749\) −3.61474 13.4904i −0.132080 0.492928i
\(750\) 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 0.588103 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 \(-0.860844\pi\)
−0.0863200 + 0.996267i \(0.527511\pi\)
\(762\) 0 0
\(763\) −7.26795 + 1.94744i −0.263117 + 0.0705021i
\(764\) 0 0
\(765\) 25.3923 6.80385i 0.918061 0.245994i
\(766\) 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
\(771\) −15.3397 −0.552447
\(772\) 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
\(779\) 0.696152 2.59808i 0.0249422 0.0930857i
\(780\) 0 0
\(781\) 8.39230 + 31.3205i 0.300300 + 1.12074i
\(782\) 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
\(787\) −49.8109 13.3468i −1.77557 0.475762i −0.785803 0.618477i \(-0.787750\pi\)
−0.989764 + 0.142716i \(0.954417\pi\)
\(788\) 0 0
\(789\) −40.6865 + 23.4904i −1.44848 + 0.836280i
\(790\) 0 0
\(791\) 10.1436i 0.360665i
\(792\) 0 0
\(793\) 19.6077i 0.696290i