Properties

Label 260.2.bk.a.193.1
Level $260$
Weight $2$
Character 260.193
Analytic conductor $2.076$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bk (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 193.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.193
Dual form 260.2.bk.a.97.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 1.86603i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 1.86603i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +(-0.633975 - 0.366025i) q^{9} +(-2.86603 - 0.767949i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(2.86603 - 3.23205i) q^{15} +(3.23205 - 0.866025i) q^{17} +(-1.13397 - 4.23205i) q^{19} +(6.09808 - 6.09808i) q^{21} +(-6.96410 - 1.86603i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-3.09808 + 3.09808i) q^{27} +(-1.50000 + 0.866025i) q^{29} +(5.19615 + 5.19615i) q^{31} +(2.86603 - 4.96410i) q^{33} +(5.50000 + 8.33013i) q^{35} +(-7.33013 + 4.23205i) q^{37} +(-4.59808 - 5.23205i) q^{39} +(0.669873 - 2.50000i) q^{41} +(0.964102 + 3.59808i) q^{43} +(0.901924 + 1.36603i) q^{45} -2.92820i q^{47} +(6.46410 + 11.1962i) q^{49} +6.46410i q^{51} +(-4.46410 - 4.46410i) q^{53} +(4.96410 + 4.40192i) q^{55} +8.46410 q^{57} +(-6.33013 + 1.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(1.63397 + 2.83013i) q^{63} +(7.00000 - 4.00000i) q^{65} +(7.86603 + 13.6244i) q^{67} +(6.96410 - 12.0622i) q^{69} +(-4.59808 + 1.23205i) q^{71} -1.07180 q^{73} +(-8.96410 + 3.59808i) q^{75} +(9.36603 + 9.36603i) q^{77} -7.46410i q^{79} +(-5.33013 - 9.23205i) q^{81} -10.9282i q^{83} +(-7.33013 - 1.50000i) q^{85} +(-0.866025 - 3.23205i) q^{87} +(0.794229 - 2.96410i) q^{89} +(14.4282 - 7.13397i) q^{91} +(-12.2942 + 7.09808i) q^{93} +(-1.96410 + 9.59808i) q^{95} +(2.13397 - 3.69615i) q^{97} +(1.53590 + 1.53590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9} - 8 q^{11} - 8 q^{13} + 8 q^{15} + 6 q^{17} - 8 q^{19} + 14 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} - 6 q^{29} + 8 q^{33} + 22 q^{35} - 12 q^{37} - 8 q^{39} + 20 q^{41} - 10 q^{43} + 14 q^{45} + 12 q^{49} - 4 q^{53} + 6 q^{55} + 20 q^{57} - 8 q^{59} + 18 q^{61} + 10 q^{63} + 28 q^{65} + 28 q^{67} + 14 q^{69} - 8 q^{71} - 32 q^{73} - 22 q^{75} + 34 q^{77} - 4 q^{81} - 12 q^{85} - 28 q^{89} + 30 q^{91} - 18 q^{93} + 6 q^{95} + 12 q^{97} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −0.500000 + 1.86603i −0.288675 + 1.07735i 0.657437 + 0.753510i \(0.271641\pi\)
−0.946112 + 0.323840i \(0.895026\pi\)
\(4\) 0 0
\(5\) −2.00000 1.00000i −0.894427 0.447214i
\(6\) 0 0
\(7\) −3.86603 2.23205i −1.46122 0.843636i −0.462152 0.886801i \(-0.652923\pi\)
−0.999068 + 0.0431647i \(0.986256\pi\)
\(8\) 0 0
\(9\) −0.633975 0.366025i −0.211325 0.122008i
\(10\) 0 0
\(11\) −2.86603 0.767949i −0.864139 0.231545i −0.200587 0.979676i \(-0.564285\pi\)
−0.663552 + 0.748130i \(0.730952\pi\)
\(12\) 0 0
\(13\) −2.00000 + 3.00000i −0.554700 + 0.832050i
\(14\) 0 0
\(15\) 2.86603 3.23205i 0.740005 0.834512i
\(16\) 0 0
\(17\) 3.23205 0.866025i 0.783887 0.210042i 0.155390 0.987853i \(-0.450337\pi\)
0.628498 + 0.777811i \(0.283670\pi\)
\(18\) 0 0
\(19\) −1.13397 4.23205i −0.260152 0.970899i −0.965152 0.261692i \(-0.915720\pi\)
0.705000 0.709207i \(-0.250947\pi\)
\(20\) 0 0
\(21\) 6.09808 6.09808i 1.33071 1.33071i
\(22\) 0 0
\(23\) −6.96410 1.86603i −1.45212 0.389093i −0.555357 0.831612i \(-0.687418\pi\)
−0.896759 + 0.442519i \(0.854085\pi\)
\(24\) 0 0
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 0 0
\(27\) −3.09808 + 3.09808i −0.596225 + 0.596225i
\(28\) 0 0
\(29\) −1.50000 + 0.866025i −0.278543 + 0.160817i −0.632764 0.774345i \(-0.718080\pi\)
0.354221 + 0.935162i \(0.384746\pi\)
\(30\) 0 0
\(31\) 5.19615 + 5.19615i 0.933257 + 0.933257i 0.997908 0.0646514i \(-0.0205935\pi\)
−0.0646514 + 0.997908i \(0.520594\pi\)
\(32\) 0 0
\(33\) 2.86603 4.96410i 0.498911 0.864139i
\(34\) 0 0
\(35\) 5.50000 + 8.33013i 0.929670 + 1.40805i
\(36\) 0 0
\(37\) −7.33013 + 4.23205i −1.20507 + 0.695745i −0.961677 0.274184i \(-0.911592\pi\)
−0.243388 + 0.969929i \(0.578259\pi\)
\(38\) 0 0
\(39\) −4.59808 5.23205i −0.736281 0.837799i
\(40\) 0 0
\(41\) 0.669873 2.50000i 0.104617 0.390434i −0.893685 0.448695i \(-0.851889\pi\)
0.998301 + 0.0582609i \(0.0185555\pi\)
\(42\) 0 0
\(43\) 0.964102 + 3.59808i 0.147024 + 0.548701i 0.999657 + 0.0261910i \(0.00833780\pi\)
−0.852633 + 0.522511i \(0.824996\pi\)
\(44\) 0 0
\(45\) 0.901924 + 1.36603i 0.134451 + 0.203635i
\(46\) 0 0
\(47\) 2.92820i 0.427122i −0.976930 0.213561i \(-0.931494\pi\)
0.976930 0.213561i \(-0.0685063\pi\)
\(48\) 0 0
\(49\) 6.46410 + 11.1962i 0.923443 + 1.59945i
\(50\) 0 0
\(51\) 6.46410i 0.905155i
\(52\) 0 0
\(53\) −4.46410 4.46410i −0.613192 0.613192i 0.330585 0.943776i \(-0.392754\pi\)
−0.943776 + 0.330585i \(0.892754\pi\)
\(54\) 0 0
\(55\) 4.96410 + 4.40192i 0.669359 + 0.593555i
\(56\) 0 0
\(57\) 8.46410 1.12110
\(58\) 0 0
\(59\) −6.33013 + 1.69615i −0.824112 + 0.220820i −0.646144 0.763216i \(-0.723619\pi\)
−0.177969 + 0.984036i \(0.556953\pi\)
\(60\) 0 0
\(61\) 4.50000 7.79423i 0.576166 0.997949i −0.419748 0.907641i \(-0.637882\pi\)
0.995914 0.0903080i \(-0.0287851\pi\)
\(62\) 0 0
\(63\) 1.63397 + 2.83013i 0.205861 + 0.356562i
\(64\) 0 0
\(65\) 7.00000 4.00000i 0.868243 0.496139i
\(66\) 0 0
\(67\) 7.86603 + 13.6244i 0.960988 + 1.66448i 0.720028 + 0.693945i \(0.244129\pi\)
0.240960 + 0.970535i \(0.422538\pi\)
\(68\) 0 0
\(69\) 6.96410 12.0622i 0.838379 1.45212i
\(70\) 0 0
\(71\) −4.59808 + 1.23205i −0.545691 + 0.146218i −0.521125 0.853481i \(-0.674487\pi\)
−0.0245667 + 0.999698i \(0.507821\pi\)
\(72\) 0 0
\(73\) −1.07180 −0.125444 −0.0627222 0.998031i \(-0.519978\pi\)
−0.0627222 + 0.998031i \(0.519978\pi\)
\(74\) 0 0
\(75\) −8.96410 + 3.59808i −1.03509 + 0.415470i
\(76\) 0 0
\(77\) 9.36603 + 9.36603i 1.06736 + 1.06736i
\(78\) 0 0
\(79\) 7.46410i 0.839777i −0.907576 0.419889i \(-0.862069\pi\)
0.907576 0.419889i \(-0.137931\pi\)
\(80\) 0 0
\(81\) −5.33013 9.23205i −0.592236 1.02578i
\(82\) 0 0
\(83\) 10.9282i 1.19953i −0.800178 0.599763i \(-0.795261\pi\)
0.800178 0.599763i \(-0.204739\pi\)
\(84\) 0 0
\(85\) −7.33013 1.50000i −0.795064 0.162698i
\(86\) 0 0
\(87\) −0.866025 3.23205i −0.0928477 0.346512i
\(88\) 0 0
\(89\) 0.794229 2.96410i 0.0841881 0.314194i −0.910971 0.412470i \(-0.864666\pi\)
0.995159 + 0.0982760i \(0.0313328\pi\)
\(90\) 0 0
\(91\) 14.4282 7.13397i 1.51249 0.747844i
\(92\) 0 0
\(93\) −12.2942 + 7.09808i −1.27485 + 0.736036i
\(94\) 0 0
\(95\) −1.96410 + 9.59808i −0.201513 + 0.984742i
\(96\) 0 0
\(97\) 2.13397 3.69615i 0.216672 0.375287i −0.737116 0.675766i \(-0.763813\pi\)
0.953789 + 0.300478i \(0.0971464\pi\)
\(98\) 0 0
\(99\) 1.53590 + 1.53590i 0.154364 + 0.154364i
\(100\) 0 0
\(101\) 5.89230 3.40192i 0.586306 0.338504i −0.177329 0.984152i \(-0.556746\pi\)
0.763636 + 0.645647i \(0.223412\pi\)
\(102\) 0 0
\(103\) −0.803848 + 0.803848i −0.0792055 + 0.0792055i −0.745600 0.666394i \(-0.767837\pi\)
0.666394 + 0.745600i \(0.267837\pi\)
\(104\) 0 0
\(105\) −18.2942 + 6.09808i −1.78533 + 0.595111i
\(106\) 0 0
\(107\) 4.96410 + 1.33013i 0.479898 + 0.128588i 0.490655 0.871354i \(-0.336758\pi\)
−0.0107572 + 0.999942i \(0.503424\pi\)
\(108\) 0 0
\(109\) −10.4641 + 10.4641i −1.00228 + 1.00228i −0.00228176 + 0.999997i \(0.500726\pi\)
−0.999997 + 0.00228176i \(0.999274\pi\)
\(110\) 0 0
\(111\) −4.23205 15.7942i −0.401688 1.49912i
\(112\) 0 0
\(113\) 4.23205 1.13397i 0.398118 0.106675i −0.0542046 0.998530i \(-0.517262\pi\)
0.452322 + 0.891854i \(0.350596\pi\)
\(114\) 0 0
\(115\) 12.0622 + 10.6962i 1.12480 + 0.997421i
\(116\) 0 0
\(117\) 2.36603 1.16987i 0.218739 0.108155i
\(118\) 0 0
\(119\) −14.4282 3.86603i −1.32263 0.354398i
\(120\) 0 0
\(121\) −1.90192 1.09808i −0.172902 0.0998251i
\(122\) 0 0
\(123\) 4.33013 + 2.50000i 0.390434 + 0.225417i
\(124\) 0 0
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 0.892305 3.33013i 0.0791793 0.295501i −0.914969 0.403524i \(-0.867785\pi\)
0.994148 + 0.108023i \(0.0344519\pi\)
\(128\) 0 0
\(129\) −7.19615 −0.633586
\(130\) 0 0
\(131\) −21.8564 −1.90960 −0.954802 0.297244i \(-0.903933\pi\)
−0.954802 + 0.297244i \(0.903933\pi\)
\(132\) 0 0
\(133\) −5.06218 + 18.8923i −0.438946 + 1.63817i
\(134\) 0 0
\(135\) 9.29423 3.09808i 0.799920 0.266640i
\(136\) 0 0
\(137\) −17.5981 10.1603i −1.50351 0.868049i −0.999992 0.00406165i \(-0.998707\pi\)
−0.503513 0.863987i \(-0.667960\pi\)
\(138\) 0 0
\(139\) −4.50000 2.59808i −0.381685 0.220366i 0.296866 0.954919i \(-0.404058\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 5.46410 + 1.46410i 0.460160 + 0.123300i
\(142\) 0 0
\(143\) 8.03590 7.06218i 0.671996 0.590569i
\(144\) 0 0
\(145\) 3.86603 0.232051i 0.321056 0.0192708i
\(146\) 0 0
\(147\) −24.1244 + 6.46410i −1.98974 + 0.533150i
\(148\) 0 0
\(149\) 5.33013 + 19.8923i 0.436661 + 1.62964i 0.737060 + 0.675827i \(0.236214\pi\)
−0.300399 + 0.953814i \(0.597120\pi\)
\(150\) 0 0
\(151\) −3.73205 + 3.73205i −0.303710 + 0.303710i −0.842463 0.538753i \(-0.818895\pi\)
0.538753 + 0.842463i \(0.318895\pi\)
\(152\) 0 0
\(153\) −2.36603 0.633975i −0.191282 0.0512538i
\(154\) 0 0
\(155\) −5.19615 15.5885i −0.417365 1.25210i
\(156\) 0 0
\(157\) −0.464102 + 0.464102i −0.0370393 + 0.0370393i −0.725384 0.688345i \(-0.758338\pi\)
0.688345 + 0.725384i \(0.258338\pi\)
\(158\) 0 0
\(159\) 10.5622 6.09808i 0.837635 0.483609i
\(160\) 0 0
\(161\) 22.7583 + 22.7583i 1.79361 + 1.79361i
\(162\) 0 0
\(163\) 3.59808 6.23205i 0.281823 0.488132i −0.690011 0.723799i \(-0.742394\pi\)
0.971834 + 0.235667i \(0.0757275\pi\)
\(164\) 0 0
\(165\) −10.6962 + 7.06218i −0.832694 + 0.549790i
\(166\) 0 0
\(167\) 9.99038 5.76795i 0.773079 0.446337i −0.0608930 0.998144i \(-0.519395\pi\)
0.833972 + 0.551807i \(0.186061\pi\)
\(168\) 0 0
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) 0 0
\(171\) −0.830127 + 3.09808i −0.0634814 + 0.236916i
\(172\) 0 0
\(173\) −6.23205 23.2583i −0.473814 1.76830i −0.625871 0.779926i \(-0.715256\pi\)
0.152057 0.988372i \(-0.451410\pi\)
\(174\) 0 0
\(175\) −2.66987 22.1603i −0.201823 1.67516i
\(176\) 0 0
\(177\) 12.6603i 0.951603i
\(178\) 0 0
\(179\) 0.0358984 + 0.0621778i 0.00268317 + 0.00464739i 0.867364 0.497675i \(-0.165813\pi\)
−0.864681 + 0.502322i \(0.832479\pi\)
\(180\) 0 0
\(181\) 9.07180i 0.674301i 0.941451 + 0.337151i \(0.109463\pi\)
−0.941451 + 0.337151i \(0.890537\pi\)
\(182\) 0 0
\(183\) 12.2942 + 12.2942i 0.908816 + 0.908816i
\(184\) 0 0
\(185\) 18.8923 1.13397i 1.38899 0.0833715i
\(186\) 0 0
\(187\) −9.92820 −0.726022
\(188\) 0 0
\(189\) 18.8923 5.06218i 1.37421 0.368219i
\(190\) 0 0
\(191\) 7.50000 12.9904i 0.542681 0.939951i −0.456068 0.889945i \(-0.650743\pi\)
0.998749 0.0500060i \(-0.0159241\pi\)
\(192\) 0 0
\(193\) −2.79423 4.83975i −0.201133 0.348373i 0.747761 0.663968i \(-0.231129\pi\)
−0.948894 + 0.315596i \(0.897796\pi\)
\(194\) 0 0
\(195\) 3.96410 + 15.0622i 0.283875 + 1.07862i
\(196\) 0 0
\(197\) 3.86603 + 6.69615i 0.275443 + 0.477081i 0.970247 0.242118i \(-0.0778422\pi\)
−0.694804 + 0.719199i \(0.744509\pi\)
\(198\) 0 0
\(199\) −4.42820 + 7.66987i −0.313907 + 0.543703i −0.979205 0.202875i \(-0.934971\pi\)
0.665298 + 0.746578i \(0.268305\pi\)
\(200\) 0 0
\(201\) −29.3564 + 7.86603i −2.07064 + 0.554827i
\(202\) 0 0
\(203\) 7.73205 0.542684
\(204\) 0 0
\(205\) −3.83975 + 4.33013i −0.268179 + 0.302429i
\(206\) 0 0
\(207\) 3.73205 + 3.73205i 0.259395 + 0.259395i
\(208\) 0 0
\(209\) 13.0000i 0.899229i
\(210\) 0 0
\(211\) 3.96410 + 6.86603i 0.272900 + 0.472677i 0.969603 0.244683i \(-0.0786838\pi\)
−0.696703 + 0.717360i \(0.745351\pi\)
\(212\) 0 0
\(213\) 9.19615i 0.630110i
\(214\) 0 0
\(215\) 1.66987 8.16025i 0.113884 0.556525i
\(216\) 0 0
\(217\) −8.49038 31.6865i −0.576365 2.15102i
\(218\) 0 0
\(219\) 0.535898 2.00000i 0.0362127 0.135147i
\(220\) 0 0
\(221\) −3.86603 + 11.4282i −0.260057 + 0.768744i
\(222\) 0 0
\(223\) 7.33013 4.23205i 0.490862 0.283399i −0.234070 0.972220i \(-0.575205\pi\)
0.724932 + 0.688821i \(0.241871\pi\)
\(224\) 0 0
\(225\) −0.437822 3.63397i −0.0291881 0.242265i
\(226\) 0 0
\(227\) −3.59808 + 6.23205i −0.238813 + 0.413636i −0.960374 0.278715i \(-0.910092\pi\)
0.721561 + 0.692351i \(0.243425\pi\)
\(228\) 0 0
\(229\) 13.9282 + 13.9282i 0.920402 + 0.920402i 0.997058 0.0766560i \(-0.0244243\pi\)
−0.0766560 + 0.997058i \(0.524424\pi\)
\(230\) 0 0
\(231\) −22.1603 + 12.7942i −1.45804 + 0.841798i
\(232\) 0 0
\(233\) −14.8564 + 14.8564i −0.973276 + 0.973276i −0.999652 0.0263765i \(-0.991603\pi\)
0.0263765 + 0.999652i \(0.491603\pi\)
\(234\) 0 0
\(235\) −2.92820 + 5.85641i −0.191015 + 0.382030i
\(236\) 0 0
\(237\) 13.9282 + 3.73205i 0.904734 + 0.242423i
\(238\) 0 0
\(239\) −0.660254 + 0.660254i −0.0427083 + 0.0427083i −0.728138 0.685430i \(-0.759614\pi\)
0.685430 + 0.728138i \(0.259614\pi\)
\(240\) 0 0
\(241\) 2.66987 + 9.96410i 0.171982 + 0.641844i 0.997046 + 0.0768056i \(0.0244721\pi\)
−0.825064 + 0.565039i \(0.808861\pi\)
\(242\) 0 0
\(243\) 7.19615 1.92820i 0.461633 0.123694i
\(244\) 0 0
\(245\) −1.73205 28.8564i −0.110657 1.84357i
\(246\) 0 0
\(247\) 14.9641 + 5.06218i 0.952143 + 0.322099i
\(248\) 0 0
\(249\) 20.3923 + 5.46410i 1.29231 + 0.346273i
\(250\) 0 0
\(251\) 12.3564 + 7.13397i 0.779929 + 0.450292i 0.836405 0.548111i \(-0.184653\pi\)
−0.0564758 + 0.998404i \(0.517986\pi\)
\(252\) 0 0
\(253\) 18.5263 + 10.6962i 1.16474 + 0.672461i
\(254\) 0 0
\(255\) 6.46410 12.9282i 0.404798 0.809595i
\(256\) 0 0
\(257\) −2.62436 + 9.79423i −0.163703 + 0.610947i 0.834499 + 0.551009i \(0.185757\pi\)
−0.998202 + 0.0599382i \(0.980910\pi\)
\(258\) 0 0
\(259\) 37.7846 2.34782
\(260\) 0 0
\(261\) 1.26795 0.0784841
\(262\) 0 0
\(263\) −6.89230 + 25.7224i −0.424998 + 1.58611i 0.338930 + 0.940812i \(0.389935\pi\)
−0.763928 + 0.645302i \(0.776732\pi\)
\(264\) 0 0
\(265\) 4.46410 + 13.3923i 0.274228 + 0.822683i
\(266\) 0 0
\(267\) 5.13397 + 2.96410i 0.314194 + 0.181400i
\(268\) 0 0
\(269\) −18.8205 10.8660i −1.14751 0.662513i −0.199228 0.979953i \(-0.563844\pi\)
−0.948278 + 0.317440i \(0.897177\pi\)
\(270\) 0 0
\(271\) −4.33013 1.16025i −0.263036 0.0704804i 0.124890 0.992171i \(-0.460142\pi\)
−0.387927 + 0.921690i \(0.626809\pi\)
\(272\) 0 0
\(273\) 6.09808 + 30.4904i 0.369072 + 1.84536i
\(274\) 0 0
\(275\) −5.52628 13.7679i −0.333247 0.830239i
\(276\) 0 0
\(277\) −6.23205 + 1.66987i −0.374448 + 0.100333i −0.441134 0.897441i \(-0.645424\pi\)
0.0666868 + 0.997774i \(0.478757\pi\)
\(278\) 0 0
\(279\) −1.39230 5.19615i −0.0833551 0.311086i
\(280\) 0 0
\(281\) −9.53590 + 9.53590i −0.568864 + 0.568864i −0.931810 0.362946i \(-0.881771\pi\)
0.362946 + 0.931810i \(0.381771\pi\)
\(282\) 0 0
\(283\) 1.03590 + 0.277568i 0.0615778 + 0.0164997i 0.289476 0.957185i \(-0.406519\pi\)
−0.227899 + 0.973685i \(0.573185\pi\)
\(284\) 0 0
\(285\) −16.9282 8.46410i −1.00274 0.501370i
\(286\) 0 0
\(287\) −8.16987 + 8.16987i −0.482252 + 0.482252i
\(288\) 0 0
\(289\) −5.02628 + 2.90192i −0.295663 + 0.170701i
\(290\) 0 0
\(291\) 5.83013 + 5.83013i 0.341768 + 0.341768i
\(292\) 0 0
\(293\) 12.2583 21.2321i 0.716139 1.24039i −0.246379 0.969174i \(-0.579241\pi\)
0.962518 0.271216i \(-0.0874258\pi\)
\(294\) 0 0
\(295\) 14.3564 + 2.93782i 0.835862 + 0.171047i
\(296\) 0 0
\(297\) 11.2583 6.50000i 0.653275 0.377168i
\(298\) 0 0
\(299\) 19.5263 17.1603i 1.12923 0.992403i
\(300\) 0 0
\(301\) 4.30385 16.0622i 0.248070 0.925809i
\(302\) 0 0
\(303\) 3.40192 + 12.6962i 0.195435 + 0.729375i
\(304\) 0 0
\(305\) −16.7942 + 11.0885i −0.961635 + 0.634923i
\(306\) 0 0
\(307\) 4.00000i 0.228292i −0.993464 0.114146i \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364132\pi\)
\(308\) 0 0
\(309\) −1.09808 1.90192i −0.0624674 0.108197i
\(310\) 0 0
\(311\) 3.46410i 0.196431i 0.995165 + 0.0982156i \(0.0313135\pi\)
−0.995165 + 0.0982156i \(0.968687\pi\)
\(312\) 0 0
\(313\) −12.4641 12.4641i −0.704513 0.704513i 0.260863 0.965376i \(-0.415993\pi\)
−0.965376 + 0.260863i \(0.915993\pi\)
\(314\) 0 0
\(315\) −0.437822 7.29423i −0.0246685 0.410983i
\(316\) 0 0
\(317\) −5.07180 −0.284860 −0.142430 0.989805i \(-0.545492\pi\)
−0.142430 + 0.989805i \(0.545492\pi\)
\(318\) 0 0
\(319\) 4.96410 1.33013i 0.277936 0.0744728i
\(320\) 0 0
\(321\) −4.96410 + 8.59808i −0.277069 + 0.479898i
\(322\) 0 0
\(323\) −7.33013 12.6962i −0.407859 0.706433i
\(324\) 0 0
\(325\) −18.0000 + 1.00000i −0.998460 + 0.0554700i
\(326\) 0 0
\(327\) −14.2942 24.7583i −0.790473 1.36914i
\(328\) 0 0
\(329\) −6.53590 + 11.3205i −0.360336 + 0.624120i
\(330\) 0 0
\(331\) −28.4545 + 7.62436i −1.56400 + 0.419072i −0.933927 0.357464i \(-0.883642\pi\)
−0.630073 + 0.776536i \(0.716975\pi\)
\(332\) 0 0
\(333\) 6.19615 0.339547
\(334\) 0 0
\(335\) −2.10770 35.1147i −0.115156 1.91852i
\(336\) 0 0
\(337\) −2.07180 2.07180i −0.112858 0.112858i 0.648423 0.761281i \(-0.275429\pi\)
−0.761281 + 0.648423i \(0.775429\pi\)
\(338\) 0 0
\(339\) 8.46410i 0.459707i
\(340\) 0 0
\(341\) −10.9019 18.8827i −0.590372 1.02255i
\(342\) 0 0
\(343\) 26.4641i 1.42893i
\(344\) 0 0
\(345\) −25.9904 + 17.1603i −1.39928 + 0.923877i
\(346\) 0 0
\(347\) 3.42820 + 12.7942i 0.184036 + 0.686830i 0.994835 + 0.101506i \(0.0323661\pi\)
−0.810799 + 0.585324i \(0.800967\pi\)
\(348\) 0 0
\(349\) −6.13397 + 22.8923i −0.328344 + 1.22540i 0.582563 + 0.812786i \(0.302050\pi\)
−0.910907 + 0.412611i \(0.864617\pi\)
\(350\) 0 0
\(351\) −3.09808 15.4904i −0.165363 0.826815i
\(352\) 0 0
\(353\) −3.06218 + 1.76795i −0.162983 + 0.0940984i −0.579273 0.815134i \(-0.696664\pi\)
0.416290 + 0.909232i \(0.363330\pi\)
\(354\) 0 0
\(355\) 10.4282 + 2.13397i 0.553472 + 0.113260i
\(356\) 0 0
\(357\) 14.4282 24.9904i 0.763621 1.32263i
\(358\) 0 0
\(359\) 2.80385 + 2.80385i 0.147981 + 0.147981i 0.777216 0.629234i \(-0.216631\pi\)
−0.629234 + 0.777216i \(0.716631\pi\)
\(360\) 0 0
\(361\) −0.169873 + 0.0980762i −0.00894068 + 0.00516191i
\(362\) 0 0
\(363\) 3.00000 3.00000i 0.157459 0.157459i
\(364\) 0 0
\(365\) 2.14359 + 1.07180i 0.112201 + 0.0561004i
\(366\) 0 0
\(367\) 2.96410 + 0.794229i 0.154725 + 0.0414584i 0.335350 0.942094i \(-0.391145\pi\)
−0.180625 + 0.983552i \(0.557812\pi\)
\(368\) 0 0
\(369\) −1.33975 + 1.33975i −0.0697444 + 0.0697444i
\(370\) 0 0
\(371\) 7.29423 + 27.2224i 0.378697 + 1.41332i
\(372\) 0 0
\(373\) 15.6962 4.20577i 0.812716 0.217767i 0.171557 0.985174i \(-0.445120\pi\)
0.641159 + 0.767408i \(0.278454\pi\)
\(374\) 0 0
\(375\) 21.5263 + 1.76795i 1.11161 + 0.0912965i
\(376\) 0 0
\(377\) 0.401924 6.23205i 0.0207001 0.320967i
\(378\) 0 0
\(379\) −2.59808 0.696152i −0.133454 0.0357589i 0.191474 0.981498i \(-0.438673\pi\)
−0.324928 + 0.945739i \(0.605340\pi\)
\(380\) 0 0
\(381\) 5.76795 + 3.33013i 0.295501 + 0.170608i
\(382\) 0 0
\(383\) 28.1147 + 16.2321i 1.43660 + 0.829419i 0.997611 0.0690756i \(-0.0220050\pi\)
0.438985 + 0.898495i \(0.355338\pi\)
\(384\) 0 0
\(385\) −9.36603 28.0981i −0.477337 1.43201i
\(386\) 0 0
\(387\) 0.705771 2.63397i 0.0358764 0.133892i
\(388\) 0 0
\(389\) −28.9282 −1.46672 −0.733359 0.679842i \(-0.762049\pi\)
−0.733359 + 0.679842i \(0.762049\pi\)
\(390\) 0 0
\(391\) −24.1244 −1.22002
\(392\) 0 0
\(393\) 10.9282 40.7846i 0.551255 2.05731i
\(394\) 0 0
\(395\) −7.46410 + 14.9282i −0.375560 + 0.751119i
\(396\) 0 0
\(397\) −8.13397 4.69615i −0.408232 0.235693i 0.281798 0.959474i \(-0.409069\pi\)
−0.690030 + 0.723781i \(0.742403\pi\)
\(398\) 0 0
\(399\) −32.7224 18.8923i −1.63817 0.945798i
\(400\) 0 0
\(401\) 11.3301 + 3.03590i 0.565800 + 0.151606i 0.530369 0.847767i \(-0.322053\pi\)
0.0354301 + 0.999372i \(0.488720\pi\)
\(402\) 0 0
\(403\) −25.9808 + 5.19615i −1.29419 + 0.258839i
\(404\) 0 0
\(405\) 1.42820 + 23.7942i 0.0709680 + 1.18234i
\(406\) 0 0
\(407\) 24.2583 6.50000i 1.20244 0.322193i
\(408\) 0 0
\(409\) −0.526279 1.96410i −0.0260228 0.0971186i 0.951693 0.307051i \(-0.0993422\pi\)
−0.977716 + 0.209932i \(0.932676\pi\)
\(410\) 0 0
\(411\) 27.7583 27.7583i 1.36922 1.36922i
\(412\) 0 0
\(413\) 28.2583 + 7.57180i 1.39050 + 0.372584i
\(414\) 0 0
\(415\) −10.9282 + 21.8564i −0.536444 + 1.07289i
\(416\) 0 0
\(417\) 7.09808 7.09808i 0.347594 0.347594i
\(418\) 0 0
\(419\) −31.5000 + 18.1865i −1.53888 + 0.888470i −0.539971 + 0.841684i \(0.681565\pi\)
−0.998905 + 0.0467865i \(0.985102\pi\)
\(420\) 0 0
\(421\) −20.8564 20.8564i −1.01648 1.01648i −0.999862 0.0166171i \(-0.994710\pi\)
−0.0166171 0.999862i \(-0.505290\pi\)
\(422\) 0 0
\(423\) −1.07180 + 1.85641i −0.0521125 + 0.0902616i
\(424\) 0 0
\(425\) 13.1603 + 10.3301i 0.638366 + 0.501085i
\(426\) 0 0
\(427\) −34.7942 + 20.0885i −1.68381 + 0.972149i
\(428\) 0 0
\(429\) 9.16025 + 18.5263i 0.442261 + 0.894457i
\(430\) 0 0
\(431\) −0.741670 + 2.76795i −0.0357250 + 0.133327i −0.981485 0.191538i \(-0.938652\pi\)
0.945760 + 0.324866i \(0.105319\pi\)
\(432\) 0 0
\(433\) −5.55256 20.7224i −0.266839 0.995857i −0.961115 0.276148i \(-0.910942\pi\)
0.694276 0.719709i \(-0.255725\pi\)
\(434\) 0 0
\(435\) −1.50000 + 7.33013i −0.0719195 + 0.351453i
\(436\) 0 0
\(437\) 31.5885i 1.51108i
\(438\) 0 0
\(439\) 6.96410 + 12.0622i 0.332378 + 0.575696i 0.982978 0.183725i \(-0.0588156\pi\)
−0.650599 + 0.759421i \(0.725482\pi\)
\(440\) 0 0
\(441\) 9.46410i 0.450672i
\(442\) 0 0
\(443\) 15.5885 + 15.5885i 0.740630 + 0.740630i 0.972699 0.232069i \(-0.0745496\pi\)
−0.232069 + 0.972699i \(0.574550\pi\)
\(444\) 0 0
\(445\) −4.55256 + 5.13397i −0.215812 + 0.243374i
\(446\) 0 0
\(447\) −39.7846 −1.88175
\(448\) 0 0
\(449\) −20.7942 + 5.57180i −0.981340 + 0.262949i −0.713609 0.700544i \(-0.752941\pi\)
−0.267731 + 0.963494i \(0.586274\pi\)
\(450\) 0 0
\(451\) −3.83975 + 6.65064i −0.180807 + 0.313166i
\(452\) 0 0
\(453\) −5.09808 8.83013i −0.239529 0.414876i
\(454\) 0 0
\(455\) −35.9904 0.160254i −1.68726 0.00751283i
\(456\) 0 0
\(457\) 8.79423 + 15.2321i 0.411377 + 0.712525i 0.995041 0.0994701i \(-0.0317148\pi\)
−0.583664 + 0.811995i \(0.698381\pi\)
\(458\) 0 0
\(459\) −7.33013 + 12.6962i −0.342141 + 0.592606i
\(460\) 0 0
\(461\) 37.1865 9.96410i 1.73195 0.464074i 0.751319 0.659940i \(-0.229418\pi\)
0.980631 + 0.195865i \(0.0627515\pi\)
\(462\) 0 0
\(463\) −42.3923 −1.97014 −0.985069 0.172161i \(-0.944925\pi\)
−0.985069 + 0.172161i \(0.944925\pi\)
\(464\) 0 0
\(465\) 31.6865 1.90192i 1.46943 0.0881996i
\(466\) 0 0
\(467\) −0.660254 0.660254i −0.0305529 0.0305529i 0.691665 0.722218i \(-0.256877\pi\)
−0.722218 + 0.691665i \(0.756877\pi\)
\(468\) 0 0
\(469\) 70.2295i 3.24290i
\(470\) 0 0
\(471\) −0.633975 1.09808i −0.0292120 0.0505967i
\(472\) 0 0
\(473\) 11.0526i 0.508197i
\(474\) 0 0
\(475\) 13.5263 17.2321i 0.620628 0.790661i
\(476\) 0 0
\(477\) 1.19615 + 4.46410i 0.0547681 + 0.204397i
\(478\) 0 0
\(479\) −4.86603 + 18.1603i −0.222334 + 0.829763i 0.761121 + 0.648610i \(0.224650\pi\)
−0.983455 + 0.181153i \(0.942017\pi\)
\(480\) 0 0
\(481\) 1.96410 30.4545i 0.0895553 1.38860i
\(482\) 0 0
\(483\) −53.8468 + 31.0885i −2.45011 + 1.41457i
\(484\) 0 0
\(485\) −7.96410 + 5.25833i −0.361631 + 0.238768i
\(486\) 0 0
\(487\) 14.7942 25.6244i 0.670390 1.16115i −0.307403 0.951579i \(-0.599460\pi\)
0.977793 0.209571i \(-0.0672067\pi\)
\(488\) 0 0
\(489\) 9.83013 + 9.83013i 0.444534 + 0.444534i
\(490\) 0 0
\(491\) −14.8923 + 8.59808i −0.672080 + 0.388026i −0.796864 0.604158i \(-0.793510\pi\)
0.124784 + 0.992184i \(0.460176\pi\)
\(492\) 0 0
\(493\) −4.09808 + 4.09808i −0.184568 + 0.184568i
\(494\) 0 0
\(495\) −1.53590 4.60770i −0.0690335 0.207100i
\(496\) 0 0
\(497\) 20.5263 + 5.50000i 0.920729 + 0.246709i
\(498\) 0 0
\(499\) 23.7321 23.7321i 1.06239 1.06239i 0.0644731 0.997919i \(-0.479463\pi\)
0.997919 0.0644731i \(-0.0205367\pi\)
\(500\) 0 0
\(501\) 5.76795 + 21.5263i 0.257693 + 0.961723i
\(502\) 0 0
\(503\) 24.3564 6.52628i 1.08600 0.290992i 0.328947 0.944348i \(-0.393306\pi\)
0.757051 + 0.653356i \(0.226639\pi\)
\(504\) 0 0
\(505\) −15.1865 + 0.911543i −0.675792 + 0.0405631i
\(506\) 0 0
\(507\) 24.8923 3.33013i 1.10551 0.147896i
\(508\) 0 0
\(509\) 25.4545 + 6.82051i 1.12825 + 0.302314i 0.774218 0.632919i \(-0.218144\pi\)
0.354032 + 0.935233i \(0.384810\pi\)
\(510\) 0 0
\(511\) 4.14359 + 2.39230i 0.183302 + 0.105829i
\(512\) 0 0
\(513\) 16.6244 + 9.59808i 0.733983 + 0.423765i
\(514\) 0 0
\(515\) 2.41154 0.803848i 0.106265 0.0354218i
\(516\) 0 0
\(517\) −2.24871 + 8.39230i −0.0988982 + 0.369093i
\(518\) 0 0
\(519\) 46.5167 2.04185
\(520\) 0 0
\(521\) 19.8564 0.869925 0.434962 0.900449i \(-0.356762\pi\)
0.434962 + 0.900449i \(0.356762\pi\)
\(522\) 0 0
\(523\) 4.03590 15.0622i 0.176478 0.658623i −0.819818 0.572625i \(-0.805925\pi\)
0.996295 0.0859985i \(-0.0274080\pi\)
\(524\) 0 0
\(525\) 42.6865 + 6.09808i 1.86299 + 0.266142i
\(526\) 0 0
\(527\) 21.2942 + 12.2942i 0.927591 + 0.535545i
\(528\) 0 0
\(529\) 25.0981 + 14.4904i 1.09122 + 0.630017i
\(530\) 0 0
\(531\) 4.63397 + 1.24167i 0.201097 + 0.0538839i
\(532\) 0 0
\(533\) 6.16025 + 7.00962i 0.266830 + 0.303620i
\(534\) 0 0
\(535\) −8.59808 7.62436i −0.371727 0.329630i
\(536\) 0 0
\(537\) −0.133975 + 0.0358984i −0.00578143 + 0.00154913i
\(538\) 0 0
\(539\) −9.92820 37.0526i −0.427638 1.59597i
\(540\) 0 0
\(541\) −19.7846 + 19.7846i −0.850607 + 0.850607i −0.990208 0.139601i \(-0.955418\pi\)
0.139601 + 0.990208i \(0.455418\pi\)
\(542\) 0 0
\(543\) −16.9282 4.53590i −0.726459 0.194654i
\(544\) 0 0
\(545\) 31.3923 10.4641i 1.34470 0.448233i
\(546\) 0 0
\(547\) 24.1244 24.1244i 1.03148 1.03148i 0.0319949 0.999488i \(-0.489814\pi\)
0.999488 0.0319949i \(-0.0101860\pi\)
\(548\) 0 0
\(549\) −5.70577 + 3.29423i −0.243516 + 0.140594i
\(550\) 0 0
\(551\) 5.36603 + 5.36603i 0.228600 + 0.228600i
\(552\) 0 0
\(553\) −16.6603 + 28.8564i −0.708466 + 1.22710i
\(554\) 0 0
\(555\) −7.33013 + 35.8205i −0.311147 + 1.52050i
\(556\) 0 0
\(557\) 4.66987 2.69615i 0.197869 0.114240i −0.397792 0.917476i \(-0.630223\pi\)
0.595661 + 0.803236i \(0.296890\pi\)
\(558\) 0 0
\(559\) −12.7224 4.30385i −0.538102 0.182033i
\(560\) 0 0
\(561\) 4.96410 18.5263i 0.209585 0.782180i
\(562\) 0 0
\(563\) −4.10770 15.3301i −0.173119 0.646088i −0.996864 0.0791284i \(-0.974786\pi\)
0.823746 0.566959i \(-0.191880\pi\)
\(564\) 0 0
\(565\) −9.59808 1.96410i −0.403794 0.0826304i
\(566\) 0 0
\(567\) 47.5885i 1.99853i
\(568\) 0 0
\(569\) −15.8205 27.4019i −0.663230 1.14875i −0.979762 0.200166i \(-0.935852\pi\)
0.316532 0.948582i \(-0.397482\pi\)
\(570\) 0 0
\(571\) 42.3923i 1.77406i −0.461709 0.887031i \(-0.652764\pi\)
0.461709 0.887031i \(-0.347236\pi\)
\(572\) 0 0
\(573\) 20.4904 + 20.4904i 0.855998 + 0.855998i
\(574\) 0 0
\(575\) −13.4282 33.4545i −0.559995 1.39515i
\(576\) 0 0
\(577\) −20.7846 −0.865275 −0.432637 0.901568i \(-0.642417\pi\)
−0.432637 + 0.901568i \(0.642417\pi\)
\(578\) 0 0
\(579\) 10.4282 2.79423i 0.433381 0.116124i
\(580\) 0 0
\(581\) −24.3923 + 42.2487i −1.01196 + 1.75277i
\(582\) 0 0
\(583\) 9.36603 + 16.2224i 0.387901 + 0.671864i
\(584\) 0 0
\(585\) −5.90192 0.0262794i −0.244015 0.00108652i
\(586\) 0 0
\(587\) 5.72243 + 9.91154i 0.236190 + 0.409093i 0.959618 0.281307i \(-0.0907679\pi\)
−0.723428 + 0.690400i \(0.757435\pi\)
\(588\) 0 0
\(589\) 16.0981 27.8827i 0.663310 1.14889i
\(590\) 0 0
\(591\) −14.4282 + 3.86603i −0.593497 + 0.159027i
\(592\) 0 0
\(593\) −17.0718 −0.701055 −0.350527 0.936553i \(-0.613998\pi\)
−0.350527 + 0.936553i \(0.613998\pi\)
\(594\) 0 0
\(595\) 24.9904 + 22.1603i 1.02451 + 0.908482i
\(596\) 0 0
\(597\) −12.0981 12.0981i −0.495141 0.495141i
\(598\) 0 0
\(599\) 12.2487i 0.500469i 0.968185 + 0.250234i \(0.0805077\pi\)
−0.968185 + 0.250234i \(0.919492\pi\)
\(600\) 0 0
\(601\) −6.42820 11.1340i −0.262212 0.454164i 0.704618 0.709587i \(-0.251119\pi\)
−0.966829 + 0.255423i \(0.917785\pi\)
\(602\) 0 0
\(603\) 11.5167i 0.468995i
\(604\) 0 0
\(605\) 2.70577 + 4.09808i 0.110005 + 0.166610i
\(606\) 0 0
\(607\) 9.96410 + 37.1865i 0.404430 + 1.50935i 0.805104 + 0.593134i \(0.202110\pi\)
−0.400673 + 0.916221i \(0.631224\pi\)
\(608\) 0 0
\(609\) −3.86603 + 14.4282i −0.156659 + 0.584660i
\(610\) 0 0
\(611\) 8.78461 + 5.85641i 0.355387 + 0.236925i
\(612\) 0 0
\(613\) 15.1865 8.76795i 0.613378 0.354134i −0.160908 0.986969i \(-0.551442\pi\)
0.774286 + 0.632835i \(0.218109\pi\)
\(614\) 0 0
\(615\) −6.16025 9.33013i −0.248405 0.376227i
\(616\) 0 0
\(617\) −6.79423 + 11.7679i −0.273525 + 0.473760i −0.969762 0.244053i \(-0.921523\pi\)
0.696237 + 0.717812i \(0.254856\pi\)
\(618\) 0 0
\(619\) −2.66025 2.66025i −0.106925 0.106925i 0.651620 0.758545i \(-0.274089\pi\)
−0.758545 + 0.651620i \(0.774089\pi\)
\(620\) 0 0
\(621\) 27.3564 15.7942i 1.09777 0.633801i
\(622\) 0 0
\(623\) −9.68653 + 9.68653i −0.388083 + 0.388083i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) −24.2583 6.50000i −0.968784 0.259585i
\(628\) 0 0
\(629\) −20.0263 + 20.0263i −0.798500 + 0.798500i
\(630\) 0 0
\(631\) −1.65064 6.16025i −0.0657107 0.245236i 0.925256 0.379343i \(-0.123850\pi\)
−0.990967 + 0.134107i \(0.957183\pi\)
\(632\) 0 0
\(633\) −14.7942 + 3.96410i −0.588018 + 0.157559i
\(634\) 0 0
\(635\) −5.11474 + 5.76795i −0.202972 + 0.228894i
\(636\) 0 0
\(637\) −46.5167 3.00000i −1.84306 0.118864i
\(638\) 0 0
\(639\) 3.36603 + 0.901924i 0.133158 + 0.0356796i
\(640\) 0 0
\(641\) 33.3564 + 19.2583i 1.31750 + 0.760658i 0.983326 0.181853i \(-0.0582096\pi\)
0.334173 + 0.942512i \(0.391543\pi\)
\(642\) 0 0
\(643\) −22.6699 13.0885i −0.894013 0.516158i −0.0187597 0.999824i \(-0.505972\pi\)
−0.875253 + 0.483666i \(0.839305\pi\)
\(644\) 0 0
\(645\) 14.3923 + 7.19615i 0.566696 + 0.283348i
\(646\) 0 0
\(647\) 2.50000 9.33013i 0.0982851 0.366805i −0.899212 0.437513i \(-0.855859\pi\)
0.997497 + 0.0707082i \(0.0225259\pi\)
\(648\) 0 0
\(649\) 19.4449 0.763278
\(650\) 0 0
\(651\) 63.3731 2.48379
\(652\) 0 0
\(653\) −10.9449 + 40.8468i −0.428306 + 1.59846i 0.328291 + 0.944577i \(0.393527\pi\)
−0.756597 + 0.653882i \(0.773139\pi\)
\(654\) 0 0
\(655\) 43.7128 + 21.8564i 1.70800 + 0.854000i
\(656\) 0 0
\(657\) 0.679492 + 0.392305i 0.0265095 + 0.0153053i
\(658\) 0 0
\(659\) −21.5718 12.4545i −0.840318 0.485158i 0.0170544 0.999855i \(-0.494571\pi\)
−0.857372 + 0.514697i \(0.827904\pi\)
\(660\) 0 0
\(661\) 14.7942 + 3.96410i 0.575429 + 0.154186i 0.534785 0.844988i \(-0.320393\pi\)
0.0406436 + 0.999174i \(0.487059\pi\)
\(662\) 0 0
\(663\) −19.3923 12.9282i −0.753135 0.502090i
\(664\) 0 0
\(665\) 29.0167 32.7224i 1.12522 1.26892i
\(666\) 0 0
\(667\) 12.0622 3.23205i 0.467049 0.125146i
\(668\) 0 0
\(669\) 4.23205 + 15.7942i 0.163621 + 0.610640i
\(670\) 0 0
\(671\) −18.8827 + 18.8827i −0.728958 + 0.728958i
\(672\) 0 0
\(673\) −14.6244 3.91858i −0.563727 0.151050i −0.0343092 0.999411i \(-0.510923\pi\)
−0.529418 + 0.848361i \(0.677590\pi\)
\(674\) 0 0
\(675\) −21.6865 3.09808i −0.834715 0.119245i
\(676\) 0 0
\(677\) 34.1769 34.1769i 1.31353 1.31353i 0.394727 0.918798i \(-0.370839\pi\)
0.918798 0.394727i \(-0.129161\pi\)
\(678\) 0 0
\(679\) −16.5000 + 9.52628i −0.633212 + 0.365585i
\(680\) 0 0
\(681\) −9.83013 9.83013i −0.376691 0.376691i
\(682\) 0 0
\(683\) −1.33013 + 2.30385i −0.0508959 + 0.0881543i −0.890351 0.455275i \(-0.849541\pi\)
0.839455 + 0.543429i \(0.182874\pi\)
\(684\) 0 0
\(685\) 25.0359 + 37.9186i 0.956573 + 1.44879i
\(686\) 0 0
\(687\) −32.9545 + 19.0263i −1.25729 + 0.725898i
\(688\) 0 0
\(689\) 22.3205 4.46410i 0.850344 0.170069i
\(690\) 0 0
\(691\) 5.65064 21.0885i 0.214960 0.802243i −0.771220 0.636568i \(-0.780353\pi\)
0.986181 0.165674i \(-0.0529800\pi\)
\(692\) 0 0
\(693\) −2.50962 9.36603i −0.0953325 0.355786i
\(694\) 0 0
\(695\) 6.40192 + 9.69615i 0.242839 + 0.367796i
\(696\) 0 0
\(697\) 8.66025i 0.328031i
\(698\) 0 0
\(699\) −20.2942 35.1506i −0.767598 1.32952i
\(700\) 0 0
\(701\) 34.9282i 1.31922i −0.751608 0.659610i \(-0.770721\pi\)
0.751608 0.659610i \(-0.229279\pi\)
\(702\) 0 0
\(703\) 26.2224 + 26.2224i 0.988998 + 0.988998i
\(704\) 0 0
\(705\) −9.46410 8.39230i −0.356439 0.316072i
\(706\) 0 0
\(707\) −30.3731 −1.14230
\(708\) 0 0
\(709\) −33.7224 + 9.03590i −1.26647 + 0.339350i −0.828678 0.559725i \(-0.810907\pi\)
−0.437794 + 0.899075i \(0.644240\pi\)
\(710\) 0 0
\(711\) −2.73205 + 4.73205i −0.102460 + 0.177466i
\(712\) 0 0
\(713\) −26.4904 45.8827i −0.992073 1.71832i
\(714\) 0 0
\(715\) −23.1340 + 6.08846i −0.865162 + 0.227695i
\(716\) 0 0
\(717\) −0.901924 1.56218i −0.0336830 0.0583406i
\(718\) 0 0
\(719\) −14.0359 + 24.3109i −0.523451 + 0.906643i 0.476177 + 0.879350i \(0.342022\pi\)
−0.999627 + 0.0272936i \(0.991311\pi\)
\(720\) 0 0
\(721\) 4.90192 1.31347i 0.182557 0.0489160i
\(722\) 0 0
\(723\) −19.9282 −0.741138
\(724\) 0 0
\(725\) −7.96410 3.40192i −0.295779 0.126344i
\(726\) 0 0
\(727\) −2.41154 2.41154i −0.0894392 0.0894392i 0.660972 0.750411i \(-0.270144\pi\)
−0.750411 + 0.660972i \(0.770144\pi\)
\(728\) 0 0
\(729\) 17.5885i 0.651424i
\(730\) 0 0
\(731\) 6.23205 + 10.7942i 0.230501 + 0.399239i
\(732\) 0 0
\(733\) 14.7846i 0.546082i −0.962002 0.273041i \(-0.911971\pi\)
0.962002 0.273041i \(-0.0880295\pi\)
\(734\) 0 0
\(735\) 54.7128 + 11.1962i 2.01811 + 0.412976i
\(736\) 0 0
\(737\) −12.0814 45.0885i −0.445025 1.66085i
\(738\) 0 0
\(739\) 1.91858 7.16025i 0.0705763 0.263394i −0.921618 0.388099i \(-0.873132\pi\)
0.992194 + 0.124705i \(0.0397985\pi\)
\(740\) 0 0
\(741\) −16.9282 + 25.3923i −0.621873 + 0.932810i
\(742\) 0 0
\(743\) −10.6699 + 6.16025i −0.391440 + 0.225998i −0.682784 0.730621i \(-0.739231\pi\)
0.291344 + 0.956618i \(0.405898\pi\)
\(744\) 0 0
\(745\) 9.23205 45.1147i 0.338236 1.65288i
\(746\) 0 0
\(747\) −4.00000 + 6.92820i −0.146352 + 0.253490i
\(748\) 0 0
\(749\) −16.2224 16.2224i −0.592755 0.592755i
\(750\) 0 0
\(751\) 45.3564 26.1865i 1.65508 0.955560i 0.680141 0.733081i \(-0.261918\pi\)
0.974937 0.222479i \(-0.0714149\pi\)
\(752\) 0 0
\(753\) −19.4904 + 19.4904i −0.710269 + 0.710269i
\(754\) 0 0
\(755\) 11.1962 3.73205i 0.407470 0.135823i
\(756\) 0 0
\(757\) −22.1603 5.93782i −0.805428 0.215814i −0.167462 0.985878i \(-0.553557\pi\)
−0.637966 + 0.770065i \(0.720224\pi\)
\(758\) 0 0
\(759\) −29.2224 + 29.2224i −1.06071 + 1.06071i
\(760\) 0 0
\(761\) −9.33013 34.8205i −0.338217 1.26224i −0.900339 0.435188i \(-0.856682\pi\)
0.562123 0.827054i \(-0.309985\pi\)
\(762\) 0 0
\(763\) 63.8109 17.0981i 2.31011 0.618992i
\(764\) 0 0
\(765\) 4.09808 + 3.63397i 0.148166 + 0.131387i
\(766\) 0 0
\(767\) 7.57180 22.3827i 0.273402 0.808192i
\(768\) 0 0
\(769\) 24.5263 + 6.57180i 0.884440 + 0.236985i 0.672322 0.740259i \(-0.265297\pi\)
0.212118 + 0.977244i \(0.431964\pi\)
\(770\) 0 0
\(771\) −16.9641 9.79423i −0.610947 0.352731i
\(772\) 0 0
\(773\) −47.0429 27.1603i −1.69202 0.976886i −0.952888 0.303323i \(-0.901904\pi\)
−0.739129 0.673564i \(-0.764763\pi\)
\(774\) 0 0
\(775\) −5.19615 + 36.3731i −0.186651 + 1.30656i
\(776\) 0 0
\(777\) −18.8923 + 70.5070i −0.677758 + 2.52943i
\(778\) 0 0
\(779\) −11.3397 −0.406289
\(780\) 0 0
\(781\) 14.1244 0.505409
\(782\) 0 0
\(783\) 1.96410 7.33013i 0.0701913 0.261957i
\(784\) 0 0
\(785\) 1.39230 0.464102i 0.0496935 0.0165645i
\(786\) 0 0
\(787\) −4.54552 2.62436i −0.162030 0.0935482i 0.416792 0.909002i \(-0.363154\pi\)
−0.578822 + 0.815454i \(0.696488\pi\)
\(788\) 0 0
\(789\) −44.5526 25.7224i −1.58611 0.915743i
\(790\) 0 0