Properties

Label 260.2.bf.b.37.1
Level $260$
Weight $2$
Character 260.37
Analytic conductor $2.076$
Analytic rank $0$
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.bf (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
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 37.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 260.37
Dual form 260.2.bf.b.253.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.23205 - 3.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +O(q^{10})\) \(q+(1.86603 + 0.500000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(2.23205 - 3.86603i) q^{7} +(0.633975 + 0.366025i) q^{9} +(-2.86603 - 0.767949i) q^{11} +(3.00000 + 2.00000i) q^{13} +(-0.866025 - 4.23205i) q^{15} +(0.866025 + 3.23205i) q^{17} +(1.13397 + 4.23205i) q^{19} +(6.09808 - 6.09808i) q^{21} +(-1.86603 + 6.96410i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(-3.09808 - 3.09808i) q^{27} +(1.50000 - 0.866025i) q^{29} +(5.19615 + 5.19615i) q^{31} +(-4.96410 - 2.86603i) q^{33} +(-9.96410 - 0.598076i) q^{35} +(-4.23205 - 7.33013i) q^{37} +(4.59808 + 5.23205i) q^{39} +(0.669873 - 2.50000i) q^{41} +(3.59808 - 0.964102i) q^{43} +(0.0980762 - 1.63397i) q^{45} +2.92820 q^{47} +(-6.46410 - 11.1962i) q^{49} +6.46410i q^{51} +(-4.46410 + 4.46410i) q^{53} +(1.33013 + 6.50000i) q^{55} +8.46410i q^{57} +(6.33013 - 1.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(2.83013 - 1.63397i) q^{63} +(1.00000 - 8.00000i) q^{65} +(-13.6244 + 7.86603i) q^{67} +(-6.96410 + 12.0622i) q^{69} +(-4.59808 + 1.23205i) q^{71} +1.07180i q^{73} +(-7.59808 + 5.96410i) q^{75} +(-9.36603 + 9.36603i) q^{77} +7.46410i q^{79} +(-5.33013 - 9.23205i) q^{81} -10.9282 q^{83} +(5.59808 - 4.96410i) q^{85} +(3.23205 - 0.866025i) q^{87} +(-0.794229 + 2.96410i) q^{89} +(14.4282 - 7.13397i) q^{91} +(7.09808 + 12.2942i) q^{93} +(7.33013 - 6.50000i) q^{95} +(3.69615 + 2.13397i) q^{97} +(-1.53590 - 1.53590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9} - 8 q^{11} + 12 q^{13} + 8 q^{19} + 14 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} + 6 q^{29} - 6 q^{33} - 26 q^{35} - 10 q^{37} + 8 q^{39} + 20 q^{41} + 4 q^{43} - 10 q^{45} - 16 q^{47} - 12 q^{49} - 4 q^{53} - 12 q^{55} + 8 q^{59} + 18 q^{61} - 6 q^{63} + 4 q^{65} - 6 q^{67} - 14 q^{69} - 8 q^{71} - 20 q^{75} - 34 q^{77} - 4 q^{81} - 16 q^{83} + 12 q^{85} + 6 q^{87} + 28 q^{89} + 30 q^{91} + 18 q^{93} + 12 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) 1.86603 + 0.500000i 1.07735 + 0.288675i 0.753510 0.657437i \(-0.228359\pi\)
0.323840 + 0.946112i \(0.395026\pi\)
\(4\) 0 0
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 0 0
\(7\) 2.23205 3.86603i 0.843636 1.46122i −0.0431647 0.999068i \(-0.513744\pi\)
0.886801 0.462152i \(-0.152923\pi\)
\(8\) 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
\(13\) 3.00000 + 2.00000i 0.832050 + 0.554700i
\(14\) 0 0
\(15\) −0.866025 4.23205i −0.223607 1.09271i
\(16\) 0 0
\(17\) 0.866025 + 3.23205i 0.210042 + 0.783887i 0.987853 + 0.155390i \(0.0496633\pi\)
−0.777811 + 0.628498i \(0.783670\pi\)
\(18\) 0 0
\(19\) 1.13397 + 4.23205i 0.260152 + 0.970899i 0.965152 + 0.261692i \(0.0842803\pi\)
−0.705000 + 0.709207i \(0.749053\pi\)
\(20\) 0 0
\(21\) 6.09808 6.09808i 1.33071 1.33071i
\(22\) 0 0
\(23\) −1.86603 + 6.96410i −0.389093 + 1.45212i 0.442519 + 0.896759i \(0.354085\pi\)
−0.831612 + 0.555357i \(0.812582\pi\)
\(24\) 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 −0.354221 0.935162i \(-0.615254\pi\)
0.632764 + 0.774345i \(0.281920\pi\)
\(30\) 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
\(33\) −4.96410 2.86603i −0.864139 0.498911i
\(34\) 0 0
\(35\) −9.96410 0.598076i −1.68424 0.101093i
\(36\) 0 0
\(37\) −4.23205 7.33013i −0.695745 1.20507i −0.969929 0.243388i \(-0.921741\pi\)
0.274184 0.961677i \(-0.411592\pi\)
\(38\) 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
\(43\) 3.59808 0.964102i 0.548701 0.147024i 0.0261910 0.999657i \(-0.491662\pi\)
0.522511 + 0.852633i \(0.324996\pi\)
\(44\) 0 0
\(45\) 0.0980762 1.63397i 0.0146203 0.243579i
\(46\) 0 0
\(47\) 2.92820 0.427122 0.213561 0.976930i \(-0.431494\pi\)
0.213561 + 0.976930i \(0.431494\pi\)
\(48\) 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 −0.943776 0.330585i \(-0.892754\pi\)
0.330585 + 0.943776i \(0.392754\pi\)
\(54\) 0 0
\(55\) 1.33013 + 6.50000i 0.179354 + 0.876460i
\(56\) 0 0
\(57\) 8.46410i 1.12110i
\(58\) 0 0
\(59\) 6.33013 1.69615i 0.824112 0.220820i 0.177969 0.984036i \(-0.443047\pi\)
0.646144 + 0.763216i \(0.276381\pi\)
\(60\) 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
\(63\) 2.83013 1.63397i 0.356562 0.205861i
\(64\) 0 0
\(65\) 1.00000 8.00000i 0.124035 0.992278i
\(66\) 0 0
\(67\) −13.6244 + 7.86603i −1.66448 + 0.960988i −0.693945 + 0.720028i \(0.744129\pi\)
−0.970535 + 0.240960i \(0.922538\pi\)
\(68\) 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
\(73\) 1.07180i 0.125444i 0.998031 + 0.0627222i \(0.0199782\pi\)
−0.998031 + 0.0627222i \(0.980022\pi\)
\(74\) 0 0
\(75\) −7.59808 + 5.96410i −0.877350 + 0.688675i
\(76\) 0 0
\(77\) −9.36603 + 9.36603i −1.06736 + 1.06736i
\(78\) 0 0
\(79\) 7.46410i 0.839777i 0.907576 + 0.419889i \(0.137931\pi\)
−0.907576 + 0.419889i \(0.862069\pi\)
\(80\) 0 0
\(81\) −5.33013 9.23205i −0.592236 1.02578i
\(82\) 0 0
\(83\) −10.9282 −1.19953 −0.599763 0.800178i \(-0.704739\pi\)
−0.599763 + 0.800178i \(0.704739\pi\)
\(84\) 0 0
\(85\) 5.59808 4.96410i 0.607197 0.538432i
\(86\) 0 0
\(87\) 3.23205 0.866025i 0.346512 0.0928477i
\(88\) 0 0
\(89\) −0.794229 + 2.96410i −0.0841881 + 0.314194i −0.995159 0.0982760i \(-0.968667\pi\)
0.910971 + 0.412470i \(0.135334\pi\)
\(90\) 0 0
\(91\) 14.4282 7.13397i 1.51249 0.747844i
\(92\) 0 0
\(93\) 7.09808 + 12.2942i 0.736036 + 1.27485i
\(94\) 0 0
\(95\) 7.33013 6.50000i 0.752055 0.666886i
\(96\) 0 0
\(97\) 3.69615 + 2.13397i 0.375287 + 0.216672i 0.675766 0.737116i \(-0.263813\pi\)
−0.300478 + 0.953789i \(0.597146\pi\)
\(98\) 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 \(-0.232163\pi\)
−0.666394 + 0.745600i \(0.732163\pi\)
\(104\) 0 0
\(105\) −18.2942 6.09808i −1.78533 0.595111i
\(106\) 0 0
\(107\) −1.33013 + 4.96410i −0.128588 + 0.479898i −0.999942 0.0107572i \(-0.996576\pi\)
0.871354 + 0.490655i \(0.163242\pi\)
\(108\) 0 0
\(109\) 10.4641 10.4641i 1.00228 1.00228i 0.00228176 0.999997i \(-0.499274\pi\)
0.999997 0.00228176i \(-0.000726308\pi\)
\(110\) 0 0
\(111\) −4.23205 15.7942i −0.401688 1.49912i
\(112\) 0 0
\(113\) −1.13397 4.23205i −0.106675 0.398118i 0.891854 0.452322i \(-0.149404\pi\)
−0.998530 + 0.0542046i \(0.982738\pi\)
\(114\) 0 0
\(115\) 15.7942 3.23205i 1.47282 0.301390i
\(116\) 0 0
\(117\) 1.16987 + 2.36603i 0.108155 + 0.218739i
\(118\) 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
\(123\) 2.50000 4.33013i 0.225417 0.390434i
\(124\) 0 0
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) 3.33013 + 0.892305i 0.295501 + 0.0791793i 0.403524 0.914969i \(-0.367785\pi\)
−0.108023 + 0.994148i \(0.534452\pi\)
\(128\) 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
\(133\) 18.8923 + 5.06218i 1.63817 + 0.438946i
\(134\) 0 0
\(135\) −3.09808 + 9.29423i −0.266640 + 0.799920i
\(136\) 0 0
\(137\) 10.1603 17.5981i 0.868049 1.50351i 0.00406165 0.999992i \(-0.498707\pi\)
0.863987 0.503513i \(-0.167960\pi\)
\(138\) 0 0
\(139\) 4.50000 + 2.59808i 0.381685 + 0.220366i 0.678551 0.734553i \(-0.262608\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 0 0
\(141\) 5.46410 + 1.46410i 0.460160 + 0.123300i
\(142\) 0 0
\(143\) −7.06218 8.03590i −0.590569 0.671996i
\(144\) 0 0
\(145\) −3.23205 2.13397i −0.268407 0.177217i
\(146\) 0 0
\(147\) −6.46410 24.1244i −0.533150 1.98974i
\(148\) 0 0
\(149\) −5.33013 19.8923i −0.436661 1.62964i −0.737060 0.675827i \(-0.763786\pi\)
0.300399 0.953814i \(-0.402880\pi\)
\(150\) 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
\(153\) −0.633975 + 2.36603i −0.0512538 + 0.191282i
\(154\) 0 0
\(155\) 5.19615 15.5885i 0.417365 1.25210i
\(156\) 0 0
\(157\) −0.464102 0.464102i −0.0370393 0.0370393i 0.688345 0.725384i \(-0.258338\pi\)
−0.725384 + 0.688345i \(0.758338\pi\)
\(158\) 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
\(163\) −6.23205 3.59808i −0.488132 0.281823i 0.235667 0.971834i \(-0.424272\pi\)
−0.723799 + 0.690011i \(0.757606\pi\)
\(164\) 0 0
\(165\) −0.767949 + 12.7942i −0.0597848 + 0.996029i
\(166\) 0 0
\(167\) 5.76795 + 9.99038i 0.446337 + 0.773079i 0.998144 0.0608930i \(-0.0193948\pi\)
−0.551807 + 0.833972i \(0.686061\pi\)
\(168\) 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
\(173\) −23.2583 + 6.23205i −1.76830 + 0.473814i −0.988372 0.152057i \(-0.951410\pi\)
−0.779926 + 0.625871i \(0.784744\pi\)
\(174\) 0 0
\(175\) 8.76795 + 20.5263i 0.662795 + 1.55164i
\(176\) 0 0
\(177\) 12.6603 0.951603
\(178\) 0 0
\(179\) −0.0358984 0.0621778i −0.00268317 0.00464739i 0.864681 0.502322i \(-0.167521\pi\)
−0.867364 + 0.497675i \(0.834187\pi\)
\(180\) 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
\(185\) −10.4282 + 15.7942i −0.766697 + 1.16121i
\(186\) 0 0
\(187\) 9.92820i 0.726022i
\(188\) 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
\(193\) −4.83975 + 2.79423i −0.348373 + 0.201133i −0.663968 0.747761i \(-0.731129\pi\)
0.315596 + 0.948894i \(0.397796\pi\)
\(194\) 0 0
\(195\) 5.86603 14.4282i 0.420075 1.03323i
\(196\) 0 0
\(197\) −6.69615 + 3.86603i −0.477081 + 0.275443i −0.719199 0.694804i \(-0.755491\pi\)
0.242118 + 0.970247i \(0.422158\pi\)
\(198\) 0 0
\(199\) 4.42820 7.66987i 0.313907 0.543703i −0.665298 0.746578i \(-0.731695\pi\)
0.979205 + 0.202875i \(0.0650286\pi\)
\(200\) 0 0
\(201\) −29.3564 + 7.86603i −2.07064 + 0.554827i
\(202\) 0 0
\(203\) 7.73205i 0.542684i
\(204\) 0 0
\(205\) −5.66987 + 1.16025i −0.396001 + 0.0810357i
\(206\) 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
\(213\) −9.19615 −0.630110
\(214\) 0 0
\(215\) −5.52628 6.23205i −0.376889 0.425022i
\(216\) 0 0
\(217\) 31.6865 8.49038i 2.15102 0.576365i
\(218\) 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
\(223\) −4.23205 7.33013i −0.283399 0.490862i 0.688821 0.724932i \(-0.258129\pi\)
−0.972220 + 0.234070i \(0.924795\pi\)
\(224\) 0 0
\(225\) −3.36603 + 1.43782i −0.224402 + 0.0958548i
\(226\) 0 0
\(227\) −6.23205 3.59808i −0.413636 0.238813i 0.278715 0.960374i \(-0.410092\pi\)
−0.692351 + 0.721561i \(0.743425\pi\)
\(228\) 0 0
\(229\) −13.9282 13.9282i −0.920402 0.920402i 0.0766560 0.997058i \(-0.475576\pi\)
−0.997058 + 0.0766560i \(0.975576\pi\)
\(230\) 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 \(-0.00839688\pi\)
−0.0263765 + 0.999652i \(0.508397\pi\)
\(234\) 0 0
\(235\) −2.92820 5.85641i −0.191015 0.382030i
\(236\) 0 0
\(237\) −3.73205 + 13.9282i −0.242423 + 0.904734i
\(238\) 0 0
\(239\) 0.660254 0.660254i 0.0427083 0.0427083i −0.685430 0.728138i \(-0.740386\pi\)
0.728138 + 0.685430i \(0.240386\pi\)
\(240\) 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
\(243\) −1.92820 7.19615i −0.123694 0.461633i
\(244\) 0 0
\(245\) −15.9282 + 24.1244i −1.01762 + 1.54125i
\(246\) 0 0
\(247\) −5.06218 + 14.9641i −0.322099 + 0.952143i
\(248\) 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
\(253\) 10.6962 18.5263i 0.672461 1.16474i
\(254\) 0 0
\(255\) 12.9282 6.46410i 0.809595 0.404798i
\(256\) 0 0
\(257\) −9.79423 2.62436i −0.610947 0.163703i −0.0599382 0.998202i \(-0.519090\pi\)
−0.551009 + 0.834499i \(0.685757\pi\)
\(258\) 0 0
\(259\) −37.7846 −2.34782
\(260\) 0 0
\(261\) 1.26795 0.0784841
\(262\) 0 0
\(263\) 25.7224 + 6.89230i 1.58611 + 0.424998i 0.940812 0.338930i \(-0.110065\pi\)
0.645302 + 0.763928i \(0.276732\pi\)
\(264\) 0 0
\(265\) 13.3923 + 4.46410i 0.822683 + 0.274228i
\(266\) 0 0
\(267\) −2.96410 + 5.13397i −0.181400 + 0.314194i
\(268\) 0 0
\(269\) 18.8205 + 10.8660i 1.14751 + 0.662513i 0.948278 0.317440i \(-0.102823\pi\)
0.199228 + 0.979953i \(0.436156\pi\)
\(270\) 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
\(273\) 30.4904 6.09808i 1.84536 0.369072i
\(274\) 0 0
\(275\) 11.6699 9.16025i 0.703720 0.552384i
\(276\) 0 0
\(277\) −1.66987 6.23205i −0.100333 0.374448i 0.897441 0.441134i \(-0.145424\pi\)
−0.997774 + 0.0666868i \(0.978757\pi\)
\(278\) 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
\(283\) 0.277568 1.03590i 0.0164997 0.0615778i −0.957185 0.289476i \(-0.906519\pi\)
0.973685 + 0.227899i \(0.0731855\pi\)
\(284\) 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
\(293\) −21.2321 12.2583i −1.24039 0.716139i −0.271216 0.962518i \(-0.587426\pi\)
−0.969174 + 0.246379i \(0.920759\pi\)
\(294\) 0 0
\(295\) −9.72243 10.9641i −0.566062 0.638355i
\(296\) 0 0
\(297\) 6.50000 + 11.2583i 0.377168 + 0.653275i
\(298\) 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
\(303\) 12.6962 3.40192i 0.729375 0.195435i
\(304\) 0 0
\(305\) −20.0885 1.20577i −1.15026 0.0690423i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 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 −0.965376 0.260863i \(-0.915993\pi\)
0.260863 + 0.965376i \(0.415993\pi\)
\(314\) 0 0
\(315\) −6.09808 4.02628i −0.343588 0.226855i
\(316\) 0 0
\(317\) 5.07180i 0.284860i −0.989805 0.142430i \(-0.954508\pi\)
0.989805 0.142430i \(-0.0454917\pi\)
\(318\) 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
\(323\) −12.6962 + 7.33013i −0.706433 + 0.407859i
\(324\) 0 0
\(325\) −17.0000 + 6.00000i −0.942990 + 0.332820i
\(326\) 0 0
\(327\) 24.7583 14.2942i 1.36914 0.790473i
\(328\) 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
\(333\) 6.19615i 0.339547i
\(334\) 0 0
\(335\) 29.3564 + 19.3827i 1.60391 + 1.05899i
\(336\) 0 0
\(337\) 2.07180 2.07180i 0.112858 0.112858i −0.648423 0.761281i \(-0.724571\pi\)
0.761281 + 0.648423i \(0.224571\pi\)
\(338\) 0 0
\(339\) 8.46410i 0.459707i
\(340\) 0 0
\(341\) −10.9019 18.8827i −0.590372 1.02255i
\(342\) 0 0
\(343\) −26.4641 −1.42893
\(344\) 0 0
\(345\) 31.0885 + 1.86603i 1.67375 + 0.100463i
\(346\) 0 0
\(347\) −12.7942 + 3.42820i −0.686830 + 0.184036i −0.585324 0.810799i \(-0.699033\pi\)
−0.101506 + 0.994835i \(0.532366\pi\)
\(348\) 0 0
\(349\) 6.13397 22.8923i 0.328344 1.22540i −0.582563 0.812786i \(-0.697950\pi\)
0.910907 0.412611i \(-0.135383\pi\)
\(350\) 0 0
\(351\) −3.09808 15.4904i −0.165363 0.826815i
\(352\) 0 0
\(353\) 1.76795 + 3.06218i 0.0940984 + 0.162983i 0.909232 0.416290i \(-0.136670\pi\)
−0.815134 + 0.579273i \(0.803336\pi\)
\(354\) 0 0
\(355\) 7.06218 + 7.96410i 0.374821 + 0.422691i
\(356\) 0 0
\(357\) 24.9904 + 14.4282i 1.32263 + 0.763621i
\(358\) 0 0
\(359\) −2.80385 2.80385i −0.147981 0.147981i 0.629234 0.777216i \(-0.283369\pi\)
−0.777216 + 0.629234i \(0.783369\pi\)
\(360\) 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
\(367\) −0.794229 + 2.96410i −0.0414584 + 0.154725i −0.983552 0.180625i \(-0.942188\pi\)
0.942094 + 0.335350i \(0.108855\pi\)
\(368\) 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
\(373\) −4.20577 15.6962i −0.217767 0.812716i −0.985174 0.171557i \(-0.945120\pi\)
0.767408 0.641159i \(-0.221546\pi\)
\(374\) 0 0
\(375\) 19.5263 + 9.23205i 1.00833 + 0.476741i
\(376\) 0 0
\(377\) 6.23205 + 0.401924i 0.320967 + 0.0207001i
\(378\) 0 0
\(379\) 2.59808 + 0.696152i 0.133454 + 0.0357589i 0.324928 0.945739i \(-0.394660\pi\)
−0.191474 + 0.981498i \(0.561327\pi\)
\(380\) 0 0
\(381\) 5.76795 + 3.33013i 0.295501 + 0.170608i
\(382\) 0 0
\(383\) 16.2321 28.1147i 0.829419 1.43660i −0.0690756 0.997611i \(-0.522005\pi\)
0.898495 0.438985i \(-0.144662\pi\)
\(384\) 0 0
\(385\) 28.0981 + 9.36603i 1.43201 + 0.477337i
\(386\) 0 0
\(387\) 2.63397 + 0.705771i 0.133892 + 0.0358764i
\(388\) 0 0
\(389\) 28.9282 1.46672 0.733359 0.679842i \(-0.237951\pi\)
0.733359 + 0.679842i \(0.237951\pi\)
\(390\) 0 0
\(391\) −24.1244 −1.22002
\(392\) 0 0
\(393\) −40.7846 10.9282i −2.05731 0.551255i
\(394\) 0 0
\(395\) 14.9282 7.46410i 0.751119 0.375560i
\(396\) 0 0
\(397\) 4.69615 8.13397i 0.235693 0.408232i −0.723781 0.690030i \(-0.757597\pi\)
0.959474 + 0.281798i \(0.0909306\pi\)
\(398\) 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
\(403\) 5.19615 + 25.9808i 0.258839 + 1.29419i
\(404\) 0 0
\(405\) −13.1340 + 19.8923i −0.652632 + 0.988457i
\(406\) 0 0
\(407\) 6.50000 + 24.2583i 0.322193 + 1.20244i
\(408\) 0 0
\(409\) 0.526279 + 1.96410i 0.0260228 + 0.0971186i 0.977716 0.209932i \(-0.0673244\pi\)
−0.951693 + 0.307051i \(0.900658\pi\)
\(410\) 0 0
\(411\) 27.7583 27.7583i 1.36922 1.36922i
\(412\) 0 0
\(413\) 7.57180 28.2583i 0.372584 1.39050i
\(414\) 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 \(-0.318435\pi\)
0.998905 0.0467865i \(-0.0148981\pi\)
\(420\) 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
\(423\) 1.85641 + 1.07180i 0.0902616 + 0.0521125i
\(424\) 0 0
\(425\) −15.5263 6.23205i −0.753135 0.302299i
\(426\) 0 0
\(427\) −20.0885 34.7942i −0.972149 1.68381i
\(428\) 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
\(433\) −20.7224 + 5.55256i −0.995857 + 0.266839i −0.719709 0.694276i \(-0.755725\pi\)
−0.276148 + 0.961115i \(0.589058\pi\)
\(434\) 0 0
\(435\) −4.96410 5.59808i −0.238010 0.268407i
\(436\) 0 0
\(437\) −31.5885 −1.51108
\(438\) 0 0
\(439\) −6.96410 12.0622i −0.332378 0.575696i 0.650599 0.759421i \(-0.274518\pi\)
−0.982978 + 0.183725i \(0.941184\pi\)
\(440\) 0 0
\(441\) 9.46410i 0.450672i
\(442\) 0 0
\(443\) 15.5885 15.5885i 0.740630 0.740630i −0.232069 0.972699i \(-0.574550\pi\)
0.972699 + 0.232069i \(0.0745496\pi\)
\(444\) 0 0
\(445\) 6.72243 1.37564i 0.318674 0.0652118i
\(446\) 0 0
\(447\) 39.7846i 1.88175i
\(448\) 0 0
\(449\) 20.7942 5.57180i 0.981340 0.262949i 0.267731 0.963494i \(-0.413726\pi\)
0.713609 + 0.700544i \(0.247059\pi\)
\(450\) 0 0
\(451\) −3.83975 + 6.65064i −0.180807 + 0.313166i
\(452\) 0 0
\(453\) −8.83013 + 5.09808i −0.414876 + 0.239529i
\(454\) 0 0
\(455\) −28.6962 21.7224i −1.34530 1.01836i
\(456\) 0 0
\(457\) −15.2321 + 8.79423i −0.712525 + 0.411377i −0.811995 0.583664i \(-0.801619\pi\)
0.0994701 + 0.995041i \(0.468285\pi\)
\(458\) 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
\(463\) 42.3923i 1.97014i 0.172161 + 0.985069i \(0.444925\pi\)
−0.172161 + 0.985069i \(0.555075\pi\)
\(464\) 0 0
\(465\) 17.4904 26.4904i 0.811097 1.22846i
\(466\) 0 0
\(467\) 0.660254 0.660254i 0.0305529 0.0305529i −0.691665 0.722218i \(-0.743123\pi\)
0.722218 + 0.691665i \(0.243123\pi\)
\(468\) 0 0
\(469\) 70.2295i 3.24290i
\(470\) 0 0
\(471\) −0.633975 1.09808i −0.0292120 0.0505967i
\(472\) 0 0
\(473\) −11.0526 −0.508197
\(474\) 0 0
\(475\) −20.3301 8.16025i −0.932810 0.374418i
\(476\) 0 0
\(477\) −4.46410 + 1.19615i −0.204397 + 0.0547681i
\(478\) 0 0
\(479\) 4.86603 18.1603i 0.222334 0.829763i −0.761121 0.648610i \(-0.775350\pi\)
0.983455 0.181153i \(-0.0579829\pi\)
\(480\) 0 0
\(481\) 1.96410 30.4545i 0.0895553 1.38860i
\(482\) 0 0
\(483\) 31.0885 + 53.8468i 1.41457 + 2.45011i
\(484\) 0 0
\(485\) 0.571797 9.52628i 0.0259640 0.432566i
\(486\) 0 0
\(487\) 25.6244 + 14.7942i 1.16115 + 0.670390i 0.951579 0.307403i \(-0.0994599\pi\)
0.209571 + 0.977793i \(0.432793\pi\)
\(488\) 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
\(497\) −5.50000 + 20.5263i −0.246709 + 0.920729i
\(498\) 0 0
\(499\) −23.7321 + 23.7321i −1.06239 + 1.06239i −0.0644731 + 0.997919i \(0.520537\pi\)
−0.997919 + 0.0644731i \(0.979463\pi\)
\(500\) 0 0
\(501\) 5.76795 + 21.5263i 0.257693 + 0.961723i
\(502\) 0 0
\(503\) −6.52628 24.3564i −0.290992 1.08600i −0.944348 0.328947i \(-0.893306\pi\)
0.653356 0.757051i \(-0.273361\pi\)
\(504\) 0 0
\(505\) −12.6962 8.38269i −0.564971 0.373025i
\(506\) 0 0
\(507\) 3.33013 + 24.8923i 0.147896 + 1.10551i
\(508\) 0 0
\(509\) −25.4545 6.82051i −1.12825 0.302314i −0.354032 0.935233i \(-0.615190\pi\)
−0.774218 + 0.632919i \(0.781856\pi\)
\(510\) 0 0
\(511\) 4.14359 + 2.39230i 0.183302 + 0.105829i
\(512\) 0 0
\(513\) 9.59808 16.6244i 0.423765 0.733983i
\(514\) 0 0
\(515\) 0.803848 2.41154i 0.0354218 0.106265i
\(516\) 0 0
\(517\) −8.39230 2.24871i −0.369093 0.0988982i
\(518\) 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
\(523\) −15.0622 4.03590i −0.658623 0.176478i −0.0859985 0.996295i \(-0.527408\pi\)
−0.572625 + 0.819818i \(0.694075\pi\)
\(524\) 0 0
\(525\) 6.09808 + 42.6865i 0.266142 + 1.86299i
\(526\) 0 0
\(527\) −12.2942 + 21.2942i −0.535545 + 0.927591i
\(528\) 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
\(533\) 7.00962 6.16025i 0.303620 0.266830i
\(534\) 0 0
\(535\) 11.2583 2.30385i 0.486740 0.0996040i
\(536\) 0 0
\(537\) −0.0358984 0.133975i −0.00154913 0.00578143i
\(538\) 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
\(543\) −4.53590 + 16.9282i −0.194654 + 0.726459i
\(544\) 0 0
\(545\) −31.3923 10.4641i −1.34470 0.448233i
\(546\) 0 0
\(547\) 24.1244 + 24.1244i 1.03148 + 1.03148i 0.999488 + 0.0319949i \(0.0101860\pi\)
0.0319949 + 0.999488i \(0.489814\pi\)
\(548\) 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
\(553\) 28.8564 + 16.6603i 1.22710 + 0.708466i
\(554\) 0 0
\(555\) −27.3564 + 24.2583i −1.16121 + 1.02971i
\(556\) 0 0
\(557\) 2.69615 + 4.66987i 0.114240 + 0.197869i 0.917476 0.397792i \(-0.130223\pi\)
−0.803236 + 0.595661i \(0.796890\pi\)
\(558\) 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
\(563\) −15.3301 + 4.10770i −0.646088 + 0.173119i −0.566959 0.823746i \(-0.691880\pi\)
−0.0791284 + 0.996864i \(0.525214\pi\)
\(564\) 0 0
\(565\) −7.33013 + 6.50000i −0.308381 + 0.273457i
\(566\) 0 0
\(567\) −47.5885 −1.99853
\(568\) 0 0
\(569\) 15.8205 + 27.4019i 0.663230 + 1.14875i 0.979762 + 0.200166i \(0.0641483\pi\)
−0.316532 + 0.948582i \(0.602518\pi\)
\(570\) 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
\(575\) −22.2583 28.3564i −0.928237 1.18254i
\(576\) 0 0
\(577\) 20.7846i 0.865275i −0.901568 0.432637i \(-0.857583\pi\)
0.901568 0.432637i \(-0.142417\pi\)
\(578\) 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
\(583\) 16.2224 9.36603i 0.671864 0.387901i
\(584\) 0 0
\(585\) 3.56218 4.70577i 0.147278 0.194560i
\(586\) 0 0
\(587\) −9.91154 + 5.72243i −0.409093 + 0.236190i −0.690400 0.723428i \(-0.742565\pi\)
0.281307 + 0.959618i \(0.409232\pi\)
\(588\) 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
\(593\) 17.0718i 0.701055i 0.936553 + 0.350527i \(0.113998\pi\)
−0.936553 + 0.350527i \(0.886002\pi\)
\(594\) 0 0
\(595\) −6.69615 32.7224i −0.274515 1.34149i
\(596\) 0 0
\(597\) 12.0981 12.0981i 0.495141 0.495141i
\(598\) 0 0
\(599\) 12.2487i 0.500469i −0.968185 0.250234i \(-0.919492\pi\)
0.968185 0.250234i \(-0.0805077\pi\)
\(600\) 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
\(603\) −11.5167 −0.468995
\(604\) 0 0
\(605\) −0.294229 + 4.90192i −0.0119621 + 0.199292i
\(606\) 0 0
\(607\) −37.1865 + 9.96410i −1.50935 + 0.404430i −0.916221 0.400673i \(-0.868776\pi\)
−0.593134 + 0.805104i \(0.702110\pi\)
\(608\) 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
\(613\) −8.76795 15.1865i −0.354134 0.613378i 0.632835 0.774286i \(-0.281891\pi\)
−0.986969 + 0.160908i \(0.948558\pi\)
\(614\) 0 0
\(615\) −11.1603 0.669873i −0.450025 0.0270119i
\(616\) 0 0
\(617\) −11.7679 6.79423i −0.473760 0.273525i 0.244053 0.969762i \(-0.421523\pi\)
−0.717812 + 0.696237i \(0.754856\pi\)
\(618\) 0 0
\(619\) 2.66025 + 2.66025i 0.106925 + 0.106925i 0.758545 0.651620i \(-0.225911\pi\)
−0.651620 + 0.758545i \(0.725911\pi\)
\(620\) 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
\(627\) 6.50000 24.2583i 0.259585 0.968784i
\(628\) 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
\(633\) 3.96410 + 14.7942i 0.157559 + 0.588018i
\(634\) 0 0
\(635\) −1.54552 7.55256i −0.0613320 0.299714i
\(636\) 0 0
\(637\) 3.00000 46.5167i 0.118864 1.84306i
\(638\) 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
\(643\) −13.0885 + 22.6699i −0.516158 + 0.894013i 0.483666 + 0.875253i \(0.339305\pi\)
−0.999824 + 0.0187597i \(0.994028\pi\)
\(644\) 0 0
\(645\) −7.19615 14.3923i −0.283348 0.566696i
\(646\) 0 0
\(647\) 9.33013 + 2.50000i 0.366805 + 0.0982851i 0.437513 0.899212i \(-0.355859\pi\)
−0.0707082 + 0.997497i \(0.522526\pi\)
\(648\) 0 0
\(649\) −19.4449 −0.763278
\(650\) 0 0
\(651\) 63.3731 2.48379
\(652\) 0 0
\(653\) 40.8468 + 10.9449i 1.59846 + 0.428306i 0.944577 0.328291i \(-0.106473\pi\)
0.653882 + 0.756597i \(0.273139\pi\)
\(654\) 0 0
\(655\) 21.8564 + 43.7128i 0.854000 + 1.70800i
\(656\) 0 0
\(657\) −0.392305 + 0.679492i −0.0153053 + 0.0265095i
\(658\) 0 0
\(659\) 21.5718 + 12.4545i 0.840318 + 0.485158i 0.857372 0.514697i \(-0.172096\pi\)
−0.0170544 + 0.999855i \(0.505429\pi\)
\(660\) 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
\(663\) −12.9282 + 19.3923i −0.502090 + 0.753135i
\(664\) 0 0
\(665\) −8.76795 42.8468i −0.340006 1.66153i
\(666\) 0 0
\(667\) 3.23205 + 12.0622i 0.125146 + 0.467049i
\(668\) 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
\(673\) −3.91858 + 14.6244i −0.151050 + 0.563727i 0.848361 + 0.529418i \(0.177590\pi\)
−0.999411 + 0.0343092i \(0.989077\pi\)
\(674\) 0 0
\(675\) 21.6865 3.09808i 0.834715 0.119245i
\(676\) 0 0
\(677\) 34.1769 + 34.1769i 1.31353 + 1.31353i 0.918798 + 0.394727i \(0.129161\pi\)
0.394727 + 0.918798i \(0.370839\pi\)
\(678\) 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
\(683\) 2.30385 + 1.33013i 0.0881543 + 0.0508959i 0.543429 0.839455i \(-0.317126\pi\)
−0.455275 + 0.890351i \(0.650459\pi\)
\(684\) 0 0
\(685\) −45.3564 2.72243i −1.73298 0.104019i
\(686\) 0 0
\(687\) −19.0263 32.9545i −0.725898 1.25729i
\(688\) 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
\(693\) −9.36603 + 2.50962i −0.355786 + 0.0953325i
\(694\) 0 0
\(695\) 0.696152 11.5981i 0.0264066 0.439940i
\(696\) 0 0
\(697\) 8.66025 0.328031
\(698\) 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
\(705\) −2.53590 12.3923i −0.0955075 0.466721i
\(706\) 0 0
\(707\) 30.3731i 1.14230i
\(708\) 0 0
\(709\) 33.7224 9.03590i 1.26647 0.339350i 0.437794 0.899075i \(-0.355760\pi\)
0.828678 + 0.559725i \(0.189093\pi\)
\(710\) 0 0
\(711\) −2.73205 + 4.73205i −0.102460 + 0.177466i
\(712\) 0 0
\(713\) −45.8827 + 26.4904i −1.71832 + 0.992073i
\(714\) 0 0
\(715\) −9.00962 + 22.1603i −0.336941 + 0.828747i
\(716\) 0 0
\(717\) 1.56218 0.901924i 0.0583406 0.0336830i
\(718\) 0 0
\(719\) 14.0359 24.3109i 0.523451 0.906643i −0.476177 0.879350i \(-0.657978\pi\)
0.999627 0.0272936i \(-0.00868890\pi\)
\(720\) 0 0
\(721\) 4.90192 1.31347i 0.182557 0.0489160i
\(722\) 0 0
\(723\) 19.9282i 0.741138i
\(724\) 0 0
\(725\) −1.03590 + 8.59808i −0.0384723 + 0.319325i
\(726\) 0 0
\(727\) 2.41154 2.41154i 0.0894392 0.0894392i −0.660972 0.750411i \(-0.729856\pi\)
0.750411 + 0.660972i \(0.229856\pi\)
\(728\) 0 0
\(729\) 17.5885i 0.651424i
\(730\) 0 0
\(731\) 6.23205 + 10.7942i 0.230501 + 0.399239i
\(732\) 0 0
\(733\) −14.7846 −0.546082 −0.273041 0.962002i \(-0.588029\pi\)
−0.273041 + 0.962002i \(0.588029\pi\)
\(734\) 0 0
\(735\) −41.7846 + 37.0526i −1.54125 + 1.36670i
\(736\) 0 0
\(737\) 45.0885 12.0814i 1.66085 0.445025i
\(738\) 0 0
\(739\) −1.91858 + 7.16025i −0.0705763 + 0.263394i −0.992194 0.124705i \(-0.960202\pi\)
0.921618 + 0.388099i \(0.126868\pi\)
\(740\) 0 0
\(741\) −16.9282 + 25.3923i −0.621873 + 0.932810i
\(742\) 0 0
\(743\) 6.16025 + 10.6699i 0.225998 + 0.391440i 0.956618 0.291344i \(-0.0941024\pi\)
−0.730621 + 0.682784i \(0.760769\pi\)
\(744\) 0 0
\(745\) −34.4545 + 30.5526i −1.26231 + 1.11936i
\(746\) 0 0
\(747\) −6.92820 4.00000i −0.253490 0.146352i
\(748\) 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
\(757\) 5.93782 22.1603i 0.215814 0.805428i −0.770065 0.637966i \(-0.779776\pi\)
0.985878 0.167462i \(-0.0535572\pi\)
\(758\) 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
\(763\) −17.0981 63.8109i −0.618992 2.31011i
\(764\) 0 0
\(765\) 5.36603 1.09808i 0.194009 0.0397010i
\(766\) 0 0
\(767\) 22.3827 + 7.57180i 0.808192 + 0.273402i
\(768\) 0 0
\(769\) −24.5263 6.57180i −0.884440 0.236985i −0.212118 0.977244i \(-0.568036\pi\)
−0.672322 + 0.740259i \(0.734703\pi\)
\(770\) 0 0
\(771\) −16.9641 9.79423i −0.610947 0.352731i
\(772\) 0 0
\(773\) −27.1603 + 47.0429i −0.976886 + 1.69202i −0.303323 + 0.952888i \(0.598096\pi\)
−0.673564 + 0.739129i \(0.735237\pi\)
\(774\) 0 0
\(775\) −36.3731 + 5.19615i −1.30656 + 0.186651i
\(776\) 0 0
\(777\) −70.5070 18.8923i −2.52943 0.677758i
\(778\) 0 0
\(779\) 11.3397 0.406289
\(780\) 0 0
\(781\) 14.1244 0.505409
\(782\) 0 0
\(783\) −7.33013 1.96410i −0.261957 0.0701913i
\(784\) 0 0
\(785\) −0.464102 + 1.39230i −0.0165645 + 0.0496935i
\(786\) 0 0
\(787\) 2.62436 4.54552i 0.0935482 0.162030i −0.815454 0.578822i \(-0.803512\pi\)
0.909002 + 0.416792i \(0.136846\pi\)
\(788\) 0 0
\(789\) 44.5526 + 25.7224i 1.58611 + 0.915743i
\(790\) 0 0
\(791\) −18.8923 5.06218i −0.671733 0.179990i
\(792\) 0