Properties

Label 1300.2.bs.b.193.1
Level $1300$
Weight $2$
Character 1300.193
Analytic conductor $10.381$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.bs (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.3805522628\)
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: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 193.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1300.193
Dual form 1300.2.bs.b.357.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(651\) \(677\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 \(-0.728359\pi\)
0.946112 0.323840i \(-0.104974\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.86603 + 2.23205i 1.46122 + 0.843636i 0.999068 0.0431647i \(-0.0137440\pi\)
0.462152 + 0.886801i \(0.347077\pi\)
\(8\) 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
\(15\) 0 0
\(16\) 0 0
\(17\) −3.23205 + 0.866025i −0.783887 + 0.210042i −0.628498 0.777811i \(-0.716330\pi\)
−0.155390 + 0.987853i \(0.549663\pi\)
\(18\) 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 0.896759 0.442519i \(-0.145915\pi\)
0.555357 + 0.831612i \(0.312582\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 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
\(35\) 0 0
\(36\) 0 0
\(37\) 7.33013 4.23205i 1.20507 0.695745i 0.243388 0.969929i \(-0.421741\pi\)
0.961677 + 0.274184i \(0.0884078\pi\)
\(38\) 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 \(-0.991662\pi\)
0.852633 0.522511i \(-0.175004\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.92820i 0.427122i 0.976930 + 0.213561i \(0.0685063\pi\)
−0.976930 + 0.213561i \(0.931494\pi\)
\(48\) 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 \(-0.107246\pi\)
−0.330585 + 0.943776i \(0.607246\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 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
\(65\) 0 0
\(66\) 0 0
\(67\) −7.86603 13.6244i −0.960988 1.66448i −0.720028 0.693945i \(-0.755871\pi\)
−0.240960 0.970535i \(-0.577462\pi\)
\(68\) 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 \(-0.480022\pi\)
0.0627222 + 0.998031i \(0.480022\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 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 \(0.204739\pi\)
−0.800178 + 0.599763i \(0.795261\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 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
\(95\) 0 0
\(96\) 0 0
\(97\) −2.13397 + 3.69615i −0.216672 + 0.375287i −0.953789 0.300478i \(-0.902854\pi\)
0.737116 + 0.675766i \(0.236187\pi\)
\(98\) 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 −0.666394 0.745600i \(-0.732163\pi\)
0.745600 + 0.666394i \(0.232163\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.96410 1.33013i −0.479898 0.128588i 0.0107572 0.999942i \(-0.496576\pi\)
−0.490655 + 0.871354i \(0.663242\pi\)
\(108\) 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 −0.452322 0.891854i \(-0.649404\pi\)
0.0542046 + 0.998530i \(0.482738\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 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
\(125\) 0 0
\(126\) 0 0
\(127\) −0.892305 + 3.33013i −0.0791793 + 0.295501i −0.994148 0.108023i \(-0.965548\pi\)
0.914969 + 0.403524i \(0.132215\pi\)
\(128\) 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
\(135\) 0 0
\(136\) 0 0
\(137\) 17.5981 + 10.1603i 1.50351 + 0.868049i 0.999992 + 0.00406165i \(0.00129287\pi\)
0.503513 + 0.863987i \(0.332040\pi\)
\(138\) 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
\(145\) 0 0
\(146\) 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
\(155\) 0 0
\(156\) 0 0
\(157\) 0.464102 0.464102i 0.0370393 0.0370393i −0.688345 0.725384i \(-0.741662\pi\)
0.725384 + 0.688345i \(0.241662\pi\)
\(158\) 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 −0.971834 0.235667i \(-0.924272\pi\)
0.690011 + 0.723799i \(0.257606\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.99038 + 5.76795i −0.773079 + 0.446337i −0.833972 0.551807i \(-0.813939\pi\)
0.0608930 + 0.998144i \(0.480605\pi\)
\(168\) 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 \(0.284744\pi\)
−0.152057 + 0.988372i \(0.548590\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 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
\(185\) 0 0
\(186\) 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 0.948894 0.315596i \(-0.102204\pi\)
−0.747761 + 0.663968i \(0.768871\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.86603 6.69615i −0.275443 0.477081i 0.694804 0.719199i \(-0.255491\pi\)
−0.970247 + 0.242118i \(0.922158\pi\)
\(198\) 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
\(205\) 0 0
\(206\) 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
\(215\) 0 0
\(216\) 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 −0.724932 0.688821i \(-0.758129\pi\)
0.234070 + 0.972220i \(0.424795\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.59808 6.23205i 0.238813 0.413636i −0.721561 0.692351i \(-0.756575\pi\)
0.960374 + 0.278715i \(0.0899085\pi\)
\(228\) 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 −0.0263765 0.999652i \(-0.508397\pi\)
0.999652 + 0.0263765i \(0.00839688\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 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
\(245\) 0 0
\(246\) 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
\(255\) 0 0
\(256\) 0 0
\(257\) 2.62436 9.79423i 0.163703 0.610947i −0.834499 0.551009i \(-0.814243\pi\)
0.998202 0.0599382i \(-0.0190904\pi\)
\(258\) 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 \(-0.610065\pi\)
0.763928 0.645302i \(-0.223268\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 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
\(275\) 0 0
\(276\) 0 0
\(277\) 6.23205 1.66987i 0.374448 0.100333i −0.0666868 0.997774i \(-0.521243\pi\)
0.441134 + 0.897441i \(0.354576\pi\)
\(278\) 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 0.227899 0.973685i \(-0.426815\pi\)
−0.289476 + 0.957185i \(0.593481\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 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 \(0.420759\pi\)
−0.962518 + 0.271216i \(0.912574\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 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
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 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 \(-0.0840071\pi\)
−0.260863 + 0.965376i \(0.584007\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.07180 0.284860 0.142430 0.989805i \(-0.454508\pi\)
0.142430 + 0.989805i \(0.454508\pi\)
\(318\) 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
\(325\) 0 0
\(326\) 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
\(335\) 0 0
\(336\) 0 0
\(337\) 2.07180 + 2.07180i 0.112858 + 0.112858i 0.761281 0.648423i \(-0.224571\pi\)
−0.648423 + 0.761281i \(0.724571\pi\)
\(338\) 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
\(345\) 0 0
\(346\) 0 0
\(347\) −3.42820 12.7942i −0.184036 0.686830i −0.994835 0.101506i \(-0.967634\pi\)
0.810799 0.585324i \(-0.199033\pi\)
\(348\) 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 −0.416290 0.909232i \(-0.636670\pi\)
0.579273 + 0.815134i \(0.303336\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 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
\(365\) 0 0
\(366\) 0 0
\(367\) −2.96410 0.794229i −0.154725 0.0414584i 0.180625 0.983552i \(-0.442188\pi\)
−0.335350 + 0.942094i \(0.608855\pi\)
\(368\) 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 −0.641159 0.767408i \(-0.721546\pi\)
−0.171557 + 0.985174i \(0.554880\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 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 −0.438985 0.898495i \(-0.644662\pi\)
−0.997611 + 0.0690756i \(0.977995\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 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
\(395\) 0 0
\(396\) 0 0
\(397\) 8.13397 + 4.69615i 0.408232 + 0.235693i 0.690030 0.723781i \(-0.257597\pi\)
−0.281798 + 0.959474i \(0.590931\pi\)
\(398\) 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
\(405\) 0 0
\(406\) 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
\(415\) 0 0
\(416\) 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
\(425\) 0 0
\(426\) 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 \(0.0890580\pi\)
−0.694276 + 0.719709i \(0.744275\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 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 0.232069 0.972699i \(-0.425450\pi\)
−0.972699 + 0.232069i \(0.925450\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 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
\(455\) 0 0
\(456\) 0 0
\(457\) −8.79423 15.2321i −0.411377 0.712525i 0.583664 0.811995i \(-0.301619\pi\)
−0.995041 + 0.0994701i \(0.968285\pi\)
\(458\) 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 \(-0.0550751\pi\)
0.985069 + 0.172161i \(0.0550751\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.660254 + 0.660254i 0.0305529 + 0.0305529i 0.722218 0.691665i \(-0.243123\pi\)
−0.691665 + 0.722218i \(0.743123\pi\)
\(468\) 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
\(475\) 0 0
\(476\) 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
\(485\) 0 0
\(486\) 0 0
\(487\) −14.7942 + 25.6244i −0.670390 + 1.16115i 0.307403 + 0.951579i \(0.400540\pi\)
−0.977793 + 0.209571i \(0.932793\pi\)
\(488\) 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
\(495\) 0 0
\(496\) 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 −0.757051 0.653356i \(-0.773361\pi\)
−0.328947 + 0.944348i \(0.606694\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 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
\(515\) 0 0
\(516\) 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 \(0.194075\pi\)
−0.996295 + 0.0859985i \(0.972592\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 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
\(535\) 0 0
\(536\) 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
\(545\) 0 0
\(546\) 0 0
\(547\) −24.1244 + 24.1244i −1.03148 + 1.03148i −0.0319949 + 0.999488i \(0.510186\pi\)
−0.999488 + 0.0319949i \(0.989814\pi\)
\(548\) 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
\(555\) 0 0
\(556\) 0 0
\(557\) −4.66987 + 2.69615i −0.197869 + 0.114240i −0.595661 0.803236i \(-0.703110\pi\)
0.397792 + 0.917476i \(0.369777\pi\)
\(558\) 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 \(0.0252137\pi\)
−0.823746 + 0.566959i \(0.808120\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 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
\(575\) 0 0
\(576\) 0 0
\(577\) 20.7846 0.865275 0.432637 0.901568i \(-0.357583\pi\)
0.432637 + 0.901568i \(0.357583\pi\)
\(578\) 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
\(585\) 0 0
\(586\) 0 0
\(587\) −5.72243 9.91154i −0.236190 0.409093i 0.723428 0.690400i \(-0.242565\pi\)
−0.959618 + 0.281307i \(0.909232\pi\)
\(588\) 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 \(-0.386002\pi\)
0.350527 + 0.936553i \(0.386002\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 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
\(605\) 0 0
\(606\) 0 0
\(607\) −9.96410 37.1865i −0.404430 1.50935i −0.805104 0.593134i \(-0.797890\pi\)
0.400673 0.916221i \(-0.368776\pi\)
\(608\) 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 −0.774286 0.632835i \(-0.781891\pi\)
0.160908 + 0.986969i \(0.448558\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.79423 11.7679i 0.273525 0.473760i −0.696237 0.717812i \(-0.745144\pi\)
0.969762 + 0.244053i \(0.0784769\pi\)
\(618\) 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
\(625\) 0 0
\(626\) 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
\(635\) 0 0
\(636\) 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 0.875253 0.483666i \(-0.160695\pi\)
0.0187597 + 0.999824i \(0.494028\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.50000 + 9.33013i −0.0982851 + 0.366805i −0.997497 0.0707082i \(-0.977474\pi\)
0.899212 + 0.437513i \(0.144141\pi\)
\(648\) 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 \(-0.606473\pi\)
0.756597 0.653882i \(-0.226861\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 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
\(665\) 0 0
\(666\) 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 0.529418 0.848361i \(-0.322410\pi\)
0.0343092 + 0.999411i \(0.489077\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −34.1769 + 34.1769i −1.31353 + 1.31353i −0.394727 + 0.918798i \(0.629161\pi\)
−0.918798 + 0.394727i \(0.870839\pi\)
\(678\) 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 −0.839455 0.543429i \(-0.817126\pi\)
0.890351 + 0.455275i \(0.150459\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 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
\(695\) 0 0
\(696\) 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
\(705\) 0 0
\(706\) 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
\(715\) 0 0
\(716\) 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
\(725\) 0 0
\(726\) 0 0
\(727\) 2.41154 + 2.41154i 0.0894392 + 0.0894392i 0.750411 0.660972i \(-0.229856\pi\)
−0.660972 + 0.750411i \(0.729856\pi\)
\(728\) 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 \(0.0880295\pi\)
−0.962002 + 0.273041i \(0.911971\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 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 −0.291344 0.956618i \(-0.594102\pi\)
0.682784 + 0.730621i \(0.260769\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 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
\(755\) 0 0
\(756\) 0 0
\(757\) 22.1603 + 5.93782i 0.805428 + 0.215814i 0.637966 0.770065i \(-0.279776\pi\)
0.167462 + 0.985878i \(0.446443\pi\)
\(758\) 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
\(765\) 0 0
\(766\) 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 \(0.0980960\pi\)
0.739129 + 0.673564i \(0.235237\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 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
\(785\) 0 0
\(786\) 0 0
\(787\) 4.54552 + 2.62436i 0.162030 + 0.0935482i 0.578822 0.815454i \(-0.303512\pi\)
−0.416792 + 0.909002i \(0.636846\pi\)
\(788\) 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 0
\(793\) −14.3827 29.0885i −0.510744 1.03296i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0