Properties

Label 1040.2.q.b.81.1
Level $1040$
Weight $2$
Character 1040.81
Analytic conductor $8.304$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1040.81
Dual form 1040.2.q.b.321.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} +1.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} +1.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(1.50000 + 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(-1.50000 - 2.59808i) q^{15} +(3.50000 - 6.06218i) q^{17} +(0.500000 - 0.866025i) q^{19} -9.00000 q^{21} +(-3.50000 - 6.06218i) q^{23} +1.00000 q^{25} +9.00000 q^{27} +(2.50000 + 4.33013i) q^{29} +4.00000 q^{31} +(4.50000 - 7.79423i) q^{33} +(1.50000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{37} +(-10.5000 + 2.59808i) q^{39} +(-3.50000 - 6.06218i) q^{41} +(-4.50000 + 7.79423i) q^{43} +(-3.00000 + 5.19615i) q^{45} -8.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} -21.0000 q^{51} -6.00000 q^{53} +(1.50000 + 2.59808i) q^{55} -3.00000 q^{57} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(9.00000 + 15.5885i) q^{63} +(1.00000 - 3.46410i) q^{65} +(6.50000 + 11.2583i) q^{67} +(-10.5000 + 18.1865i) q^{69} +(-1.50000 + 2.59808i) q^{71} -14.0000 q^{73} +(-1.50000 - 2.59808i) q^{75} +9.00000 q^{77} +8.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000 q^{83} +(3.50000 - 6.06218i) q^{85} +(7.50000 - 12.9904i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(-7.50000 - 7.79423i) q^{91} +(-6.00000 - 10.3923i) q^{93} +(0.500000 - 0.866025i) q^{95} +(5.50000 - 9.52628i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} + 2 q^{5} + 3 q^{7} - 6 q^{9} + O(q^{10}) \) \( 2 q - 3 q^{3} + 2 q^{5} + 3 q^{7} - 6 q^{9} + 3 q^{11} + 2 q^{13} - 3 q^{15} + 7 q^{17} + q^{19} - 18 q^{21} - 7 q^{23} + 2 q^{25} + 18 q^{27} + 5 q^{29} + 8 q^{31} + 9 q^{33} + 3 q^{35} + 3 q^{37} - 21 q^{39} - 7 q^{41} - 9 q^{43} - 6 q^{45} - 16 q^{47} - 2 q^{49} - 42 q^{51} - 12 q^{53} + 3 q^{55} - 6 q^{57} + 5 q^{59} + 5 q^{61} + 18 q^{63} + 2 q^{65} + 13 q^{67} - 21 q^{69} - 3 q^{71} - 28 q^{73} - 3 q^{75} + 18 q^{77} + 16 q^{79} - 9 q^{81} - 24 q^{83} + 7 q^{85} + 15 q^{87} - 7 q^{89} - 15 q^{91} - 12 q^{93} + q^{95} + 11 q^{97} - 36 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 2.59808i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.50000 2.59808i 0.566947 0.981981i −0.429919 0.902867i \(-0.641458\pi\)
0.996866 0.0791130i \(-0.0252088\pi\)
\(8\) 0 0
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) 0 0
\(15\) −1.50000 2.59808i −0.387298 0.670820i
\(16\) 0 0
\(17\) 3.50000 6.06218i 0.848875 1.47029i −0.0333386 0.999444i \(-0.510614\pi\)
0.882213 0.470850i \(-0.156053\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) −9.00000 −1.96396
\(22\) 0 0
\(23\) −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i \(-0.906280\pi\)
0.227167 0.973856i \(-0.427054\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i \(-0.0129948\pi\)
−0.534928 + 0.844897i \(0.679661\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 4.50000 7.79423i 0.783349 1.35680i
\(34\) 0 0
\(35\) 1.50000 2.59808i 0.253546 0.439155i
\(36\) 0 0
\(37\) 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i \(-0.0873538\pi\)
−0.715981 + 0.698119i \(0.754020\pi\)
\(38\) 0 0
\(39\) −10.5000 + 2.59808i −1.68135 + 0.416025i
\(40\) 0 0
\(41\) −3.50000 6.06218i −0.546608 0.946753i −0.998504 0.0546823i \(-0.982585\pi\)
0.451896 0.892071i \(-0.350748\pi\)
\(42\) 0 0
\(43\) −4.50000 + 7.79423i −0.686244 + 1.18861i 0.286801 + 0.957990i \(0.407408\pi\)
−0.973044 + 0.230618i \(0.925925\pi\)
\(44\) 0 0
\(45\) −3.00000 + 5.19615i −0.447214 + 0.774597i
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 0 0
\(51\) −21.0000 −2.94059
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 1.50000 + 2.59808i 0.202260 + 0.350325i
\(56\) 0 0
\(57\) −3.00000 −0.397360
\(58\) 0 0
\(59\) 2.50000 4.33013i 0.325472 0.563735i −0.656136 0.754643i \(-0.727810\pi\)
0.981608 + 0.190909i \(0.0611434\pi\)
\(60\) 0 0
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 0 0
\(63\) 9.00000 + 15.5885i 1.13389 + 1.96396i
\(64\) 0 0
\(65\) 1.00000 3.46410i 0.124035 0.429669i
\(66\) 0 0
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 0 0
\(69\) −10.5000 + 18.1865i −1.26405 + 2.18940i
\(70\) 0 0
\(71\) −1.50000 + 2.59808i −0.178017 + 0.308335i −0.941201 0.337846i \(-0.890302\pi\)
0.763184 + 0.646181i \(0.223635\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) −1.50000 2.59808i −0.173205 0.300000i
\(76\) 0 0
\(77\) 9.00000 1.02565
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 3.50000 6.06218i 0.379628 0.657536i
\(86\) 0 0
\(87\) 7.50000 12.9904i 0.804084 1.39272i
\(88\) 0 0
\(89\) −3.50000 6.06218i −0.370999 0.642590i 0.618720 0.785611i \(-0.287651\pi\)
−0.989720 + 0.143022i \(0.954318\pi\)
\(90\) 0 0
\(91\) −7.50000 7.79423i −0.786214 0.817057i
\(92\) 0 0
\(93\) −6.00000 10.3923i −0.622171 1.07763i
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) 5.50000 9.52628i 0.558440 0.967247i −0.439187 0.898396i \(-0.644733\pi\)
0.997627 0.0688512i \(-0.0219334\pi\)
\(98\) 0 0
\(99\) −18.0000 −1.80907
\(100\) 0 0
\(101\) 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 0 0
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) −9.00000 −0.878310
\(106\) 0 0
\(107\) −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i \(-0.212988\pi\)
−0.929377 + 0.369132i \(0.879655\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 4.50000 7.79423i 0.427121 0.739795i
\(112\) 0 0
\(113\) −6.50000 + 11.2583i −0.611469 + 1.05909i 0.379525 + 0.925182i \(0.376088\pi\)
−0.990993 + 0.133913i \(0.957246\pi\)
\(114\) 0 0
\(115\) −3.50000 6.06218i −0.326377 0.565301i
\(116\) 0 0
\(117\) 15.0000 + 15.5885i 1.38675 + 1.44115i
\(118\) 0 0
\(119\) −10.5000 18.1865i −0.962533 1.66716i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) −10.5000 + 18.1865i −0.946753 + 1.63982i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 0.500000 + 0.866025i 0.0443678 + 0.0768473i 0.887357 0.461084i \(-0.152539\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0 0
\(129\) 27.0000 2.37722
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) −1.50000 2.59808i −0.130066 0.225282i
\(134\) 0 0
\(135\) 9.00000 0.774597
\(136\) 0 0
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 0 0
\(139\) 6.50000 11.2583i 0.551323 0.954919i −0.446857 0.894606i \(-0.647457\pi\)
0.998179 0.0603135i \(-0.0192101\pi\)
\(140\) 0 0
\(141\) 12.0000 + 20.7846i 1.01058 + 1.75038i
\(142\) 0 0
\(143\) 10.5000 2.59808i 0.878054 0.217262i
\(144\) 0 0
\(145\) 2.50000 + 4.33013i 0.207614 + 0.359597i
\(146\) 0 0
\(147\) −3.00000 + 5.19615i −0.247436 + 0.428571i
\(148\) 0 0
\(149\) −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i \(-0.872548\pi\)
0.798019 + 0.602632i \(0.205881\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) 21.0000 + 36.3731i 1.69775 + 2.94059i
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) 6.00000 0.478852 0.239426 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) 0 0
\(159\) 9.00000 + 15.5885i 0.713746 + 1.23625i
\(160\) 0 0
\(161\) −21.0000 −1.65503
\(162\) 0 0
\(163\) 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i \(-0.691567\pi\)
0.996942 + 0.0781474i \(0.0249005\pi\)
\(164\) 0 0
\(165\) 4.50000 7.79423i 0.350325 0.606780i
\(166\) 0 0
\(167\) 0.500000 + 0.866025i 0.0386912 + 0.0670151i 0.884723 0.466118i \(-0.154348\pi\)
−0.846031 + 0.533133i \(0.821014\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) 3.00000 + 5.19615i 0.229416 + 0.397360i
\(172\) 0 0
\(173\) 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i \(-0.640193\pi\)
0.996544 0.0830722i \(-0.0264732\pi\)
\(174\) 0 0
\(175\) 1.50000 2.59808i 0.113389 0.196396i
\(176\) 0 0
\(177\) −15.0000 −1.12747
\(178\) 0 0
\(179\) 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i \(0.0846670\pi\)
−0.254770 + 0.967002i \(0.582000\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) −15.0000 −1.10883
\(184\) 0 0
\(185\) 1.50000 + 2.59808i 0.110282 + 0.191014i
\(186\) 0 0
\(187\) 21.0000 1.53567
\(188\) 0 0
\(189\) 13.5000 23.3827i 0.981981 1.70084i
\(190\) 0 0
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) 0 0
\(193\) 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i \(0.0148568\pi\)
−0.459049 + 0.888411i \(0.651810\pi\)
\(194\) 0 0
\(195\) −10.5000 + 2.59808i −0.751921 + 0.186052i
\(196\) 0 0
\(197\) 11.5000 + 19.9186i 0.819341 + 1.41914i 0.906168 + 0.422917i \(0.138994\pi\)
−0.0868274 + 0.996223i \(0.527673\pi\)
\(198\) 0 0
\(199\) 4.50000 7.79423i 0.318997 0.552518i −0.661282 0.750137i \(-0.729987\pi\)
0.980279 + 0.197619i \(0.0633208\pi\)
\(200\) 0 0
\(201\) 19.5000 33.7750i 1.37542 2.38230i
\(202\) 0 0
\(203\) 15.0000 1.05279
\(204\) 0 0
\(205\) −3.50000 6.06218i −0.244451 0.423401i
\(206\) 0 0
\(207\) 42.0000 2.91920
\(208\) 0 0
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i \(-0.221724\pi\)
−0.939156 + 0.343490i \(0.888391\pi\)
\(212\) 0 0
\(213\) 9.00000 0.616670
\(214\) 0 0
\(215\) −4.50000 + 7.79423i −0.306897 + 0.531562i
\(216\) 0 0
\(217\) 6.00000 10.3923i 0.407307 0.705476i
\(218\) 0 0
\(219\) 21.0000 + 36.3731i 1.41905 + 2.45786i
\(220\) 0 0
\(221\) −17.5000 18.1865i −1.17718 1.22336i
\(222\) 0 0
\(223\) −11.5000 19.9186i −0.770097 1.33385i −0.937509 0.347960i \(-0.886874\pi\)
0.167412 0.985887i \(-0.446459\pi\)
\(224\) 0 0
\(225\) −3.00000 + 5.19615i −0.200000 + 0.346410i
\(226\) 0 0
\(227\) −0.500000 + 0.866025i −0.0331862 + 0.0574801i −0.882141 0.470985i \(-0.843899\pi\)
0.848955 + 0.528465i \(0.177232\pi\)
\(228\) 0 0
\(229\) 26.0000 1.71813 0.859064 0.511868i \(-0.171046\pi\)
0.859064 + 0.511868i \(0.171046\pi\)
\(230\) 0 0
\(231\) −13.5000 23.3827i −0.888235 1.53847i
\(232\) 0 0
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) −12.0000 20.7846i −0.779484 1.35011i
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.00000 1.73205i −0.0638877 0.110657i
\(246\) 0 0
\(247\) −2.50000 2.59808i −0.159071 0.165312i
\(248\) 0 0
\(249\) 18.0000 + 31.1769i 1.14070 + 1.97576i
\(250\) 0 0
\(251\) 2.50000 4.33013i 0.157799 0.273315i −0.776276 0.630393i \(-0.782894\pi\)
0.934075 + 0.357078i \(0.116227\pi\)
\(252\) 0 0
\(253\) 10.5000 18.1865i 0.660129 1.14338i
\(254\) 0 0
\(255\) −21.0000 −1.31507
\(256\) 0 0
\(257\) 9.50000 + 16.4545i 0.592594 + 1.02640i 0.993882 + 0.110450i \(0.0352294\pi\)
−0.401288 + 0.915952i \(0.631437\pi\)
\(258\) 0 0
\(259\) 9.00000 0.559233
\(260\) 0 0
\(261\) −30.0000 −1.85695
\(262\) 0 0
\(263\) −3.50000 6.06218i −0.215819 0.373810i 0.737706 0.675122i \(-0.235909\pi\)
−0.953526 + 0.301312i \(0.902576\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) −10.5000 + 18.1865i −0.642590 + 1.11300i
\(268\) 0 0
\(269\) −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i \(-0.862486\pi\)
0.816668 + 0.577108i \(0.195819\pi\)
\(270\) 0 0
\(271\) 11.5000 + 19.9186i 0.698575 + 1.20997i 0.968960 + 0.247216i \(0.0795156\pi\)
−0.270385 + 0.962752i \(0.587151\pi\)
\(272\) 0 0
\(273\) −9.00000 + 31.1769i −0.544705 + 1.88691i
\(274\) 0 0
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 0 0
\(277\) 11.5000 19.9186i 0.690968 1.19679i −0.280553 0.959839i \(-0.590518\pi\)
0.971521 0.236953i \(-0.0761488\pi\)
\(278\) 0 0
\(279\) −12.0000 + 20.7846i −0.718421 + 1.24434i
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) 0.500000 + 0.866025i 0.0297219 + 0.0514799i 0.880504 0.474039i \(-0.157204\pi\)
−0.850782 + 0.525519i \(0.823871\pi\)
\(284\) 0 0
\(285\) −3.00000 −0.177705
\(286\) 0 0
\(287\) −21.0000 −1.23959
\(288\) 0 0
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) 0 0
\(291\) −33.0000 −1.93449
\(292\) 0 0
\(293\) −4.50000 + 7.79423i −0.262893 + 0.455344i −0.967009 0.254741i \(-0.918010\pi\)
0.704117 + 0.710084i \(0.251343\pi\)
\(294\) 0 0
\(295\) 2.50000 4.33013i 0.145556 0.252110i
\(296\) 0 0
\(297\) 13.5000 + 23.3827i 0.783349 + 1.35680i
\(298\) 0 0
\(299\) −24.5000 + 6.06218i −1.41687 + 0.350585i
\(300\) 0 0
\(301\) 13.5000 + 23.3827i 0.778127 + 1.34776i
\(302\) 0 0
\(303\) 13.5000 23.3827i 0.775555 1.34330i
\(304\) 0 0
\(305\) 2.50000 4.33013i 0.143150 0.247942i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) −24.0000 41.5692i −1.36531 2.36479i
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 0 0
\(315\) 9.00000 + 15.5885i 0.507093 + 0.878310i
\(316\) 0 0
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) 0 0
\(319\) −7.50000 + 12.9904i −0.419919 + 0.727322i
\(320\) 0 0
\(321\) −4.50000 + 7.79423i −0.251166 + 0.435031i
\(322\) 0 0
\(323\) −3.50000 6.06218i −0.194745 0.337309i
\(324\) 0 0
\(325\) 1.00000 3.46410i 0.0554700 0.192154i
\(326\) 0 0
\(327\) 21.0000 + 36.3731i 1.16130 + 2.01144i
\(328\) 0 0
\(329\) −12.0000 + 20.7846i −0.661581 + 1.14589i
\(330\) 0 0
\(331\) 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503735\pi\)
\(332\) 0 0
\(333\) −18.0000 −0.986394
\(334\) 0 0
\(335\) 6.50000 + 11.2583i 0.355133 + 0.615108i
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 39.0000 2.11819
\(340\) 0 0
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) −10.5000 + 18.1865i −0.565301 + 0.979130i
\(346\) 0 0
\(347\) −6.50000 + 11.2583i −0.348938 + 0.604379i −0.986061 0.166383i \(-0.946791\pi\)
0.637123 + 0.770762i \(0.280124\pi\)
\(348\) 0 0
\(349\) 12.5000 + 21.6506i 0.669110 + 1.15893i 0.978153 + 0.207884i \(0.0666577\pi\)
−0.309044 + 0.951048i \(0.600009\pi\)
\(350\) 0 0
\(351\) 9.00000 31.1769i 0.480384 1.66410i
\(352\) 0 0
\(353\) −10.5000 18.1865i −0.558859 0.967972i −0.997592 0.0693543i \(-0.977906\pi\)
0.438733 0.898617i \(-0.355427\pi\)
\(354\) 0 0
\(355\) −1.50000 + 2.59808i −0.0796117 + 0.137892i
\(356\) 0 0
\(357\) −31.5000 + 54.5596i −1.66716 + 2.88760i
\(358\) 0 0
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) −6.00000 −0.314918
\(364\) 0 0
\(365\) −14.0000 −0.732793
\(366\) 0 0
\(367\) 4.50000 + 7.79423i 0.234898 + 0.406855i 0.959243 0.282582i \(-0.0911910\pi\)
−0.724345 + 0.689438i \(0.757858\pi\)
\(368\) 0 0
\(369\) 42.0000 2.18643
\(370\) 0 0
\(371\) −9.00000 + 15.5885i −0.467257 + 0.809312i
\(372\) 0 0
\(373\) 13.5000 23.3827i 0.699004 1.21071i −0.269809 0.962914i \(-0.586961\pi\)
0.968812 0.247796i \(-0.0797062\pi\)
\(374\) 0 0
\(375\) −1.50000 2.59808i −0.0774597 0.134164i
\(376\) 0 0
\(377\) 17.5000 4.33013i 0.901296 0.223013i
\(378\) 0 0
\(379\) −4.50000 7.79423i −0.231149 0.400363i 0.726997 0.686640i \(-0.240915\pi\)
−0.958147 + 0.286278i \(0.907582\pi\)
\(380\) 0 0
\(381\) 1.50000 2.59808i 0.0768473 0.133103i
\(382\) 0 0
\(383\) −6.50000 + 11.2583i −0.332134 + 0.575274i −0.982930 0.183979i \(-0.941102\pi\)
0.650796 + 0.759253i \(0.274435\pi\)
\(384\) 0 0
\(385\) 9.00000 0.458682
\(386\) 0 0
\(387\) −27.0000 46.7654i −1.37249 2.37722i
\(388\) 0 0
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) −49.0000 −2.47804
\(392\) 0 0
\(393\) 6.00000 + 10.3923i 0.302660 + 0.524222i
\(394\) 0 0
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) −16.5000 + 28.5788i −0.828111 + 1.43433i 0.0714068 + 0.997447i \(0.477251\pi\)
−0.899518 + 0.436884i \(0.856082\pi\)
\(398\) 0 0
\(399\) −4.50000 + 7.79423i −0.225282 + 0.390199i
\(400\) 0 0
\(401\) −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i \(-0.288863\pi\)
−0.990257 + 0.139253i \(0.955530\pi\)
\(402\) 0 0
\(403\) 4.00000 13.8564i 0.199254 0.690237i
\(404\) 0 0
\(405\) −4.50000 7.79423i −0.223607 0.387298i
\(406\) 0 0
\(407\) −4.50000 + 7.79423i −0.223057 + 0.386346i
\(408\) 0 0
\(409\) 0.500000 0.866025i 0.0247234 0.0428222i −0.853399 0.521258i \(-0.825463\pi\)
0.878122 + 0.478436i \(0.158796\pi\)
\(410\) 0 0
\(411\) −9.00000 −0.443937
\(412\) 0 0
\(413\) −7.50000 12.9904i −0.369051 0.639215i
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) −39.0000 −1.90984
\(418\) 0 0
\(419\) −16.5000 28.5788i −0.806078 1.39617i −0.915561 0.402179i \(-0.868253\pi\)
0.109483 0.993989i \(-0.465080\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 24.0000 41.5692i 1.16692 2.02116i
\(424\) 0 0
\(425\) 3.50000 6.06218i 0.169775 0.294059i
\(426\) 0 0
\(427\) −7.50000 12.9904i −0.362950 0.628649i
\(428\) 0 0
\(429\) −22.5000 23.3827i −1.08631 1.12893i
\(430\) 0 0
\(431\) −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i \(-0.236215\pi\)
−0.953815 + 0.300395i \(0.902881\pi\)
\(432\) 0 0
\(433\) −0.500000 + 0.866025i −0.0240285 + 0.0416185i −0.877790 0.479046i \(-0.840983\pi\)
0.853761 + 0.520665i \(0.174316\pi\)
\(434\) 0 0
\(435\) 7.50000 12.9904i 0.359597 0.622841i
\(436\) 0 0
\(437\) −7.00000 −0.334855
\(438\) 0 0
\(439\) 1.50000 + 2.59808i 0.0715911 + 0.123999i 0.899599 0.436717i \(-0.143859\pi\)
−0.828008 + 0.560717i \(0.810526\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 0 0
\(445\) −3.50000 6.06218i −0.165916 0.287375i
\(446\) 0 0
\(447\) 9.00000 0.425685
\(448\) 0 0
\(449\) 10.5000 18.1865i 0.495526 0.858276i −0.504461 0.863434i \(-0.668309\pi\)
0.999987 + 0.00515887i \(0.00164213\pi\)
\(450\) 0 0
\(451\) 10.5000 18.1865i 0.494426 0.856370i
\(452\) 0 0
\(453\) −12.0000 20.7846i −0.563809 0.976546i
\(454\) 0 0
\(455\) −7.50000 7.79423i −0.351605 0.365399i
\(456\) 0 0
\(457\) 11.5000 + 19.9186i 0.537947 + 0.931752i 0.999014 + 0.0443868i \(0.0141334\pi\)
−0.461067 + 0.887365i \(0.652533\pi\)
\(458\) 0 0
\(459\) 31.5000 54.5596i 1.47029 2.54662i
\(460\) 0 0
\(461\) −5.50000 + 9.52628i −0.256161 + 0.443683i −0.965210 0.261476i \(-0.915791\pi\)
0.709050 + 0.705159i \(0.249124\pi\)
\(462\) 0 0
\(463\) 28.0000 1.30127 0.650635 0.759390i \(-0.274503\pi\)
0.650635 + 0.759390i \(0.274503\pi\)
\(464\) 0 0
\(465\) −6.00000 10.3923i −0.278243 0.481932i
\(466\) 0 0
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) 39.0000 1.80085
\(470\) 0 0
\(471\) −9.00000 15.5885i −0.414698 0.718278i
\(472\) 0 0
\(473\) −27.0000 −1.24146
\(474\) 0 0
\(475\) 0.500000 0.866025i 0.0229416 0.0397360i
\(476\) 0 0
\(477\) 18.0000 31.1769i 0.824163 1.42749i
\(478\) 0 0
\(479\) −0.500000 0.866025i −0.0228456 0.0395697i 0.854377 0.519654i \(-0.173939\pi\)
−0.877222 + 0.480085i \(0.840606\pi\)
\(480\) 0 0
\(481\) 10.5000 2.59808i 0.478759 0.118462i
\(482\) 0 0
\(483\) 31.5000 + 54.5596i 1.43330 + 2.48255i
\(484\) 0 0
\(485\) 5.50000 9.52628i 0.249742 0.432566i
\(486\) 0 0
\(487\) −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i \(-0.959191\pi\)
0.606621 + 0.794991i \(0.292524\pi\)
\(488\) 0 0
\(489\) −33.0000 −1.49231
\(490\) 0 0
\(491\) 11.5000 + 19.9186i 0.518988 + 0.898913i 0.999757 + 0.0220657i \(0.00702431\pi\)
−0.480769 + 0.876847i \(0.659642\pi\)
\(492\) 0 0
\(493\) 35.0000 1.57632
\(494\) 0 0
\(495\) −18.0000 −0.809040
\(496\) 0 0
\(497\) 4.50000 + 7.79423i 0.201853 + 0.349619i
\(498\) 0 0
\(499\) 16.0000 0.716258 0.358129 0.933672i \(-0.383415\pi\)
0.358129 + 0.933672i \(0.383415\pi\)
\(500\) 0 0
\(501\) 1.50000 2.59808i 0.0670151 0.116073i
\(502\) 0 0
\(503\) 5.50000 9.52628i 0.245233 0.424756i −0.716964 0.697110i \(-0.754469\pi\)
0.962197 + 0.272354i \(0.0878022\pi\)
\(504\) 0 0
\(505\) 4.50000 + 7.79423i 0.200247 + 0.346839i
\(506\) 0 0
\(507\) −1.50000 + 38.9711i −0.0666173 + 1.73077i
\(508\) 0 0
\(509\) −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i \(-0.274536\pi\)
−0.982988 + 0.183669i \(0.941202\pi\)
\(510\) 0 0
\(511\) −21.0000 + 36.3731i −0.928985 + 1.60905i
\(512\) 0 0
\(513\) 4.50000 7.79423i 0.198680 0.344124i
\(514\) 0 0
\(515\) 16.0000 0.705044
\(516\) 0 0
\(517\) −12.0000 20.7846i −0.527759 0.914106i
\(518\) 0 0
\(519\) −45.0000 −1.97528
\(520\) 0 0
\(521\) −34.0000 −1.48957 −0.744784 0.667306i \(-0.767447\pi\)
−0.744784 + 0.667306i \(0.767447\pi\)
\(522\) 0 0
\(523\) −11.5000 19.9186i −0.502860 0.870979i −0.999995 0.00330547i \(-0.998948\pi\)
0.497135 0.867673i \(-0.334385\pi\)
\(524\) 0 0
\(525\) −9.00000 −0.392792
\(526\) 0 0
\(527\) 14.0000 24.2487i 0.609850 1.05629i
\(528\) 0 0
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) 0 0
\(531\) 15.0000 + 25.9808i 0.650945 + 1.12747i
\(532\) 0 0
\(533\) −24.5000 + 6.06218i −1.06121 + 0.262582i
\(534\) 0 0
\(535\) −1.50000 2.59808i −0.0648507 0.112325i
\(536\) 0 0
\(537\) 28.5000 49.3634i 1.22987 2.13019i
\(538\) 0 0
\(539\) 3.00000 5.19615i 0.129219 0.223814i
\(540\) 0 0
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) 0 0
\(543\) 21.0000 + 36.3731i 0.901196 + 1.56092i
\(544\) 0 0
\(545\) −14.0000 −0.599694
\(546\) 0 0
\(547\) 16.0000 0.684111 0.342055 0.939680i \(-0.388877\pi\)
0.342055 + 0.939680i \(0.388877\pi\)
\(548\) 0 0
\(549\) 15.0000 + 25.9808i 0.640184 + 1.10883i
\(550\) 0 0
\(551\) 5.00000 0.213007
\(552\) 0 0
\(553\) 12.0000 20.7846i 0.510292 0.883852i
\(554\) 0 0
\(555\) 4.50000 7.79423i 0.191014 0.330847i
\(556\) 0 0
\(557\) 9.50000 + 16.4545i 0.402528 + 0.697199i 0.994030 0.109104i \(-0.0347983\pi\)
−0.591502 + 0.806303i \(0.701465\pi\)
\(558\) 0 0
\(559\) 22.5000 + 23.3827i 0.951649 + 0.988982i
\(560\) 0 0
\(561\) −31.5000 54.5596i −1.32993 2.30351i
\(562\) 0 0
\(563\) −22.5000 + 38.9711i −0.948262 + 1.64244i −0.199177 + 0.979963i \(0.563827\pi\)
−0.749085 + 0.662474i \(0.769506\pi\)
\(564\) 0 0
\(565\) −6.50000 + 11.2583i −0.273457 + 0.473642i
\(566\) 0 0
\(567\) −27.0000 −1.13389
\(568\) 0 0
\(569\) −9.50000 16.4545i −0.398261 0.689808i 0.595251 0.803540i \(-0.297053\pi\)
−0.993511 + 0.113732i \(0.963719\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 0 0
\(573\) 9.00000 0.375980
\(574\) 0 0
\(575\) −3.50000 6.06218i −0.145960 0.252810i
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 0 0
\(579\) 22.5000 38.9711i 0.935068 1.61959i
\(580\) 0 0
\(581\) −18.0000 + 31.1769i −0.746766 + 1.29344i
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) 0 0
\(585\) 15.0000 + 15.5885i 0.620174 + 0.644503i
\(586\) 0 0
\(587\) 18.5000 + 32.0429i 0.763577 + 1.32255i 0.940996 + 0.338418i \(0.109892\pi\)
−0.177419 + 0.984135i \(0.556775\pi\)
\(588\) 0 0
\(589\) 2.00000 3.46410i 0.0824086 0.142736i
\(590\) 0 0
\(591\) 34.5000 59.7558i 1.41914 2.45802i
\(592\) 0 0
\(593\) 26.0000 1.06769 0.533846 0.845582i \(-0.320746\pi\)
0.533846 + 0.845582i \(0.320746\pi\)
\(594\) 0 0
\(595\) −10.5000 18.1865i −0.430458 0.745575i
\(596\) 0 0
\(597\) −27.0000 −1.10504
\(598\) 0 0
\(599\) −8.00000 −0.326871 −0.163436 0.986554i \(-0.552258\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(600\) 0 0
\(601\) 6.50000 + 11.2583i 0.265141 + 0.459237i 0.967600 0.252486i \(-0.0812483\pi\)
−0.702460 + 0.711723i \(0.747915\pi\)
\(602\) 0 0
\(603\) −78.0000 −3.17641
\(604\) 0 0
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) −4.50000 + 7.79423i −0.182649 + 0.316358i −0.942782 0.333410i \(-0.891801\pi\)
0.760133 + 0.649768i \(0.225134\pi\)
\(608\) 0 0
\(609\) −22.5000 38.9711i −0.911746 1.57919i
\(610\) 0 0
\(611\) −8.00000 + 27.7128i −0.323645 + 1.12114i
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) 0 0
\(615\) −10.5000 + 18.1865i −0.423401 + 0.733352i
\(616\) 0 0
\(617\) −14.5000 + 25.1147i −0.583748 + 1.01108i 0.411282 + 0.911508i \(0.365081\pi\)
−0.995030 + 0.0995732i \(0.968252\pi\)
\(618\) 0 0
\(619\) −12.0000 −0.482321 −0.241160 0.970485i \(-0.577528\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(620\) 0 0
\(621\) −31.5000 54.5596i −1.26405 2.18940i
\(622\) 0 0
\(623\) −21.0000 −0.841347
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −4.50000 7.79423i −0.179713 0.311272i
\(628\) 0 0
\(629\) 21.0000 0.837325
\(630\) 0 0
\(631\) −7.50000 + 12.9904i −0.298570 + 0.517139i −0.975809 0.218624i \(-0.929843\pi\)
0.677239 + 0.735763i \(0.263176\pi\)
\(632\) 0 0
\(633\) −7.50000 + 12.9904i −0.298098 + 0.516321i
\(634\) 0 0
\(635\) 0.500000 + 0.866025i 0.0198419 + 0.0343672i
\(636\) 0 0
\(637\) −7.00000 + 1.73205i −0.277350 + 0.0686264i
\(638\) 0 0
\(639\) −9.00000 15.5885i −0.356034 0.616670i
\(640\) 0 0
\(641\) 10.5000 18.1865i 0.414725 0.718325i −0.580674 0.814136i \(-0.697211\pi\)
0.995400 + 0.0958109i \(0.0305444\pi\)
\(642\) 0 0
\(643\) 3.50000 6.06218i 0.138027 0.239069i −0.788723 0.614749i \(-0.789257\pi\)
0.926750 + 0.375680i \(0.122591\pi\)
\(644\) 0 0
\(645\) 27.0000 1.06312
\(646\) 0 0
\(647\) 8.50000 + 14.7224i 0.334169 + 0.578799i 0.983325 0.181857i \(-0.0582109\pi\)
−0.649155 + 0.760656i \(0.724878\pi\)
\(648\) 0 0
\(649\) 15.0000 0.588802
\(650\) 0 0
\(651\) −36.0000 −1.41095
\(652\) 0 0
\(653\) 5.50000 + 9.52628i 0.215232 + 0.372792i 0.953344 0.301885i \(-0.0976160\pi\)
−0.738113 + 0.674678i \(0.764283\pi\)
\(654\) 0 0
\(655\) −4.00000 −0.156293
\(656\) 0 0
\(657\) 42.0000 72.7461i 1.63858 2.83810i
\(658\) 0 0
\(659\) −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) 0 0
\(661\) 8.50000 + 14.7224i 0.330612 + 0.572636i 0.982632 0.185565i \(-0.0594116\pi\)
−0.652020 + 0.758202i \(0.726078\pi\)
\(662\) 0 0
\(663\) −21.0000 + 72.7461i −0.815572 + 2.82523i
\(664\) 0 0
\(665\) −1.50000 2.59808i −0.0581675 0.100749i
\(666\) 0 0
\(667\) 17.5000 30.3109i 0.677603 1.17364i
\(668\) 0 0
\(669\) −34.5000 + 59.7558i −1.33385 + 2.31029i
\(670\) 0 0
\(671\) 15.0000 0.579069
\(672\) 0 0
\(673\) −6.50000 11.2583i −0.250557 0.433977i 0.713123 0.701039i \(-0.247280\pi\)
−0.963679 + 0.267063i \(0.913947\pi\)
\(674\) 0 0
\(675\) 9.00000 0.346410
\(676\) 0 0
\(677\) 22.0000 0.845529 0.422764 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) 0 0
\(679\) −16.5000 28.5788i −0.633212 1.09676i
\(680\) 0 0
\(681\) 3.00000 0.114960
\(682\) 0 0
\(683\) 15.5000 26.8468i 0.593091 1.02726i −0.400722 0.916200i \(-0.631241\pi\)
0.993813 0.111064i \(-0.0354259\pi\)
\(684\) 0 0
\(685\) 1.50000 2.59808i 0.0573121 0.0992674i
\(686\) 0 0
\(687\) −39.0000 67.5500i −1.48794 2.57719i
\(688\) 0 0
\(689\) −6.00000 + 20.7846i −0.228582 + 0.791831i
\(690\) 0 0
\(691\) −12.5000 21.6506i −0.475522 0.823629i 0.524084 0.851666i \(-0.324408\pi\)
−0.999607 + 0.0280373i \(0.991074\pi\)
\(692\) 0 0
\(693\) −27.0000 + 46.7654i −1.02565 + 1.77647i
\(694\) 0 0
\(695\) 6.50000 11.2583i 0.246559 0.427053i
\(696\) 0 0
\(697\) −49.0000 −1.85601
\(698\) 0 0
\(699\) −27.0000 46.7654i −1.02123 1.76883i
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) 3.00000 0.113147
\(704\) 0 0
\(705\) 12.0000 + 20.7846i 0.451946 + 0.782794i
\(706\) 0 0
\(707\) 27.0000 1.01544
\(708\) 0 0
\(709\) −17.5000 + 30.3109i −0.657226 + 1.13835i 0.324104 + 0.946021i \(0.394937\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(710\) 0 0
\(711\) −24.0000 + 41.5692i −0.900070 + 1.55897i
\(712\) 0 0
\(713\) −14.0000 24.2487i −0.524304 0.908121i
\(714\) 0 0
\(715\) 10.5000 2.59808i 0.392678 0.0971625i
\(716\) 0 0
\(717\) −24.0000 41.5692i −0.896296 1.55243i
\(718\) 0 0
\(719\) 0.500000 0.866025i 0.0186469 0.0322973i −0.856551 0.516062i \(-0.827398\pi\)
0.875198 + 0.483764i \(0.160731\pi\)
\(720\) 0 0
\(721\) 24.0000 41.5692i 0.893807 1.54812i
\(722\) 0 0
\(723\) −3.00000 −0.111571
\(724\) 0 0
\(725\) 2.50000 + 4.33013i 0.0928477 + 0.160817i
\(726\) 0 0
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 31.5000 + 54.5596i 1.16507 + 2.01796i
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 0 0
\(735\) −3.00000 + 5.19615i −0.110657 + 0.191663i
\(736\) 0 0
\(737\) −19.5000 + 33.7750i −0.718292 + 1.24412i
\(738\) 0 0
\(739\) 19.5000 + 33.7750i 0.717319 + 1.24243i 0.962058 + 0.272844i \(0.0879643\pi\)
−0.244739 + 0.969589i \(0.578702\pi\)
\(740\) 0 0
\(741\) −3.00000 + 10.3923i −0.110208 + 0.381771i
\(742\) 0 0
\(743\) 0.500000 + 0.866025i 0.0183432 + 0.0317714i 0.875051 0.484030i \(-0.160828\pi\)
−0.856708 + 0.515802i \(0.827494\pi\)
\(744\) 0 0
\(745\) −1.50000 + 2.59808i −0.0549557 + 0.0951861i
\(746\) 0 0
\(747\) 36.0000 62.3538i 1.31717 2.28141i
\(748\) 0 0
\(749\) −9.00000 −0.328853
\(750\) 0 0
\(751\) −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i \(-0.242893\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(752\) 0 0
\(753\) −15.0000 −0.546630
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −0.500000 0.866025i −0.0181728 0.0314762i 0.856796 0.515656i \(-0.172452\pi\)
−0.874969 + 0.484179i \(0.839118\pi\)
\(758\) 0 0
\(759\) −63.0000 −2.28676
\(760\) 0 0
\(761\) −25.5000 + 44.1673i −0.924374 + 1.60106i −0.131810 + 0.991275i \(0.542079\pi\)
−0.792564 + 0.609788i \(0.791255\pi\)
\(762\) 0 0
\(763\) −21.0000 + 36.3731i −0.760251 + 1.31679i
\(764\) 0 0
\(765\) 21.0000 + 36.3731i 0.759257 + 1.31507i
\(766\) 0 0
\(767\) −12.5000 12.9904i −0.451349 0.469055i
\(768\) 0 0
\(769\) 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) 0 0
\(771\) 28.5000 49.3634i 1.02640 1.77778i
\(772\) 0 0
\(773\) −12.5000 + 21.6506i −0.449594 + 0.778719i −0.998359 0.0572570i \(-0.981765\pi\)
0.548766 + 0.835976i \(0.315098\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) −13.5000 23.3827i −0.484310 0.838849i
\(778\) 0 0
\(779\) −7.00000 −0.250801
\(780\) 0 0
\(781\) −9.00000 −0.322045
\(782\) 0 0
\(783\) 22.5000 + 38.9711i 0.804084 + 1.39272i
\(784\) 0 0
\(785\) 6.00000 0.214149
\(786\) 0 0
\(787\) −0.500000 + 0.866025i −0.0178231 + 0.0308705i −0.874799 0.484485i \(-0.839007\pi\)
0.856976 + 0.515356i \(0.172340\pi\)
\(788\) 0 0
\(789\) −10.5000 + 18.1865i −0.373810 + 0.647458i
\(790\) 0 0
\(791\) 19.5000 + 33.7750i 0.693340 + 1.20090i
\(792\) 0 0
\(793\) −12.5000 12.9904i −0.443888 0.461302i
\(794\) 0 0
\(795\) 9.00000 + 15.5885i 0.319197 +