Properties

Label 1680.2.bg.g.961.1
Level $1680$
Weight $2$
Character 1680.961
Analytic conductor $13.415$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.bg (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1680.961
Dual form 1680.2.bg.g.1201.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +1.00000 q^{13} -1.00000 q^{15} +(-1.50000 + 2.59808i) q^{19} +(2.50000 + 0.866025i) q^{21} +(3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -8.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(0.500000 + 2.59808i) q^{35} +(-5.50000 + 9.52628i) q^{37} +(-0.500000 - 0.866025i) q^{39} -11.0000 q^{41} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(-2.50000 + 4.33013i) q^{47} +(1.00000 - 6.92820i) q^{49} +(5.50000 + 9.52628i) q^{53} -1.00000 q^{55} +3.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-0.500000 - 2.59808i) q^{63} +(0.500000 - 0.866025i) q^{65} -7.00000 q^{69} +6.00000 q^{71} +(3.00000 + 5.19615i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(2.50000 + 0.866025i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.00000 q^{83} +(4.00000 + 6.92820i) q^{87} +(5.00000 - 8.66025i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(-1.00000 + 1.73205i) q^{93} +(1.50000 + 2.59808i) q^{95} -16.0000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} + q^{5} - 4q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} + q^{5} - 4q^{7} - q^{9} - q^{11} + 2q^{13} - 2q^{15} - 3q^{19} + 5q^{21} + 7q^{23} - q^{25} + 2q^{27} - 16q^{29} - 2q^{31} - q^{33} + q^{35} - 11q^{37} - q^{39} - 22q^{41} - 16q^{43} + q^{45} - 5q^{47} + 2q^{49} + 11q^{53} - 2q^{55} + 6q^{57} + 4q^{59} - q^{63} + q^{65} - 14q^{69} + 12q^{71} + 6q^{73} - q^{75} + 5q^{77} - 8q^{79} - q^{81} - 16q^{83} + 8q^{87} + 10q^{89} - 4q^{91} - 2q^{93} + 3q^{95} - 32q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\) \(1\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) −1.50000 + 2.59808i −0.344124 + 0.596040i −0.985194 0.171442i \(-0.945157\pi\)
0.641071 + 0.767482i \(0.278491\pi\)
\(20\) 0 0
\(21\) 2.50000 + 0.866025i 0.545545 + 0.188982i
\(22\) 0 0
\(23\) 3.50000 6.06218i 0.729800 1.26405i −0.227167 0.973856i \(-0.572946\pi\)
0.956967 0.290196i \(-0.0937204\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) 0 0
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 0 0
\(35\) 0.500000 + 2.59808i 0.0845154 + 0.439155i
\(36\) 0 0
\(37\) −5.50000 + 9.52628i −0.904194 + 1.56611i −0.0821995 + 0.996616i \(0.526194\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) 0 0
\(41\) −11.0000 −1.71791 −0.858956 0.512050i \(-0.828886\pi\)
−0.858956 + 0.512050i \(0.828886\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 0 0
\(47\) −2.50000 + 4.33013i −0.364662 + 0.631614i −0.988722 0.149763i \(-0.952149\pi\)
0.624059 + 0.781377i \(0.285482\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.50000 + 9.52628i 0.755483 + 1.30854i 0.945134 + 0.326683i \(0.105931\pi\)
−0.189651 + 0.981852i \(0.560736\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) 0 0
\(65\) 0.500000 0.866025i 0.0620174 0.107417i
\(66\) 0 0
\(67\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 0 0
\(69\) −7.00000 −0.842701
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 3.00000 + 5.19615i 0.351123 + 0.608164i 0.986447 0.164083i \(-0.0524664\pi\)
−0.635323 + 0.772246i \(0.719133\pi\)
\(74\) 0 0
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 2.50000 + 0.866025i 0.284901 + 0.0986928i
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.00000 + 6.92820i 0.428845 + 0.742781i
\(88\) 0 0
\(89\) 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) 0 0
\(91\) −2.00000 + 1.73205i −0.209657 + 0.181568i
\(92\) 0 0
\(93\) −1.00000 + 1.73205i −0.103695 + 0.179605i
\(94\) 0 0
\(95\) 1.50000 + 2.59808i 0.153897 + 0.266557i
\(96\) 0 0
\(97\) −16.0000 −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) 0 0
\(99\) 1.00000 0.100504
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i \(0.455686\pi\)
−0.927030 + 0.374987i \(0.877647\pi\)
\(104\) 0 0
\(105\) 2.00000 1.73205i 0.195180 0.169031i
\(106\) 0 0
\(107\) −5.00000 + 8.66025i −0.483368 + 0.837218i −0.999818 0.0190994i \(-0.993920\pi\)
0.516449 + 0.856318i \(0.327253\pi\)
\(108\) 0 0
\(109\) −3.00000 5.19615i −0.287348 0.497701i 0.685828 0.727764i \(-0.259440\pi\)
−0.973176 + 0.230063i \(0.926107\pi\)
\(110\) 0 0
\(111\) 11.0000 1.04407
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −3.50000 6.06218i −0.326377 0.565301i
\(116\) 0 0
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) 5.50000 + 9.52628i 0.495918 + 0.858956i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) 0 0
\(129\) 4.00000 + 6.92820i 0.352180 + 0.609994i
\(130\) 0 0
\(131\) −2.50000 + 4.33013i −0.218426 + 0.378325i −0.954327 0.298764i \(-0.903426\pi\)
0.735901 + 0.677089i \(0.236759\pi\)
\(132\) 0 0
\(133\) −1.50000 7.79423i −0.130066 0.675845i
\(134\) 0 0
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 0 0
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 0 0
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 5.00000 0.421076
\(142\) 0 0
\(143\) −0.500000 0.866025i −0.0418121 0.0724207i
\(144\) 0 0
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) 0 0
\(147\) −6.50000 + 2.59808i −0.536111 + 0.214286i
\(148\) 0 0
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0 0
\(151\) 3.00000 + 5.19615i 0.244137 + 0.422857i 0.961888 0.273442i \(-0.0881622\pi\)
−0.717752 + 0.696299i \(0.754829\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) 3.50000 + 6.06218i 0.279330 + 0.483814i 0.971219 0.238190i \(-0.0765542\pi\)
−0.691888 + 0.722005i \(0.743221\pi\)
\(158\) 0 0
\(159\) 5.50000 9.52628i 0.436178 0.755483i
\(160\) 0 0
\(161\) 3.50000 + 18.1865i 0.275839 + 1.43330i
\(162\) 0 0
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 0 0
\(165\) 0.500000 + 0.866025i 0.0389249 + 0.0674200i
\(166\) 0 0
\(167\) 3.00000 0.232147 0.116073 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −1.50000 2.59808i −0.114708 0.198680i
\(172\) 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
\(175\) 2.50000 + 0.866025i 0.188982 + 0.0654654i
\(176\) 0 0
\(177\) 2.00000 3.46410i 0.150329 0.260378i
\(178\) 0 0
\(179\) −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i \(-0.915333\pi\)
0.254770 0.967002i \(-0.418000\pi\)
\(180\) 0 0
\(181\) −24.0000 −1.78391 −0.891953 0.452128i \(-0.850665\pi\)
−0.891953 + 0.452128i \(0.850665\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.50000 + 9.52628i 0.404368 + 0.700386i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −2.00000 + 1.73205i −0.145479 + 0.125988i
\(190\) 0 0
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 0 0
\(193\) −11.0000 19.0526i −0.791797 1.37143i −0.924853 0.380325i \(-0.875812\pi\)
0.133056 0.991109i \(-0.457521\pi\)
\(194\) 0 0
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) −1.00000 −0.0712470 −0.0356235 0.999365i \(-0.511342\pi\)
−0.0356235 + 0.999365i \(0.511342\pi\)
\(198\) 0 0
\(199\) −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i \(-0.842871\pi\)
0.0299585 0.999551i \(-0.490462\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 16.0000 13.8564i 1.12298 0.972529i
\(204\) 0 0
\(205\) −5.50000 + 9.52628i −0.384137 + 0.665344i
\(206\) 0 0
\(207\) 3.50000 + 6.06218i 0.243267 + 0.421350i
\(208\) 0 0
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) −5.00000 −0.344214 −0.172107 0.985078i \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) 0 0
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) 0 0
\(215\) −4.00000 + 6.92820i −0.272798 + 0.472500i
\(216\) 0 0
\(217\) 5.00000 + 1.73205i 0.339422 + 0.117579i
\(218\) 0 0
\(219\) 3.00000 5.19615i 0.202721 0.351123i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 4.00000 + 6.92820i 0.265489 + 0.459841i 0.967692 0.252136i \(-0.0811332\pi\)
−0.702202 + 0.711977i \(0.747800\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) −0.500000 2.59808i −0.0328976 0.170941i
\(232\) 0 0
\(233\) −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) 0 0
\(235\) 2.50000 + 4.33013i 0.163082 + 0.282466i
\(236\) 0 0
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) 0 0
\(247\) −1.50000 + 2.59808i −0.0954427 + 0.165312i
\(248\) 0 0
\(249\) 4.00000 + 6.92820i 0.253490 + 0.439057i
\(250\) 0 0
\(251\) −13.0000 −0.820553 −0.410276 0.911961i \(-0.634568\pi\)
−0.410276 + 0.911961i \(0.634568\pi\)
\(252\) 0 0
\(253\) −7.00000 −0.440086
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.0000 17.3205i 0.623783 1.08042i −0.364992 0.931011i \(-0.618928\pi\)
0.988775 0.149413i \(-0.0477384\pi\)
\(258\) 0 0
\(259\) −5.50000 28.5788i −0.341753 1.77580i
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) 0 0
\(263\) 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) 0 0
\(265\) 11.0000 0.675725
\(266\) 0 0
\(267\) −10.0000 −0.611990
\(268\) 0 0
\(269\) −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i \(-0.957952\pi\)
0.381577 0.924337i \(-0.375381\pi\)
\(270\) 0 0
\(271\) 16.0000 27.7128i 0.971931 1.68343i 0.282218 0.959350i \(-0.408930\pi\)
0.689713 0.724083i \(-0.257737\pi\)
\(272\) 0 0
\(273\) 2.50000 + 0.866025i 0.151307 + 0.0524142i
\(274\) 0 0
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) 0 0
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −1.00000 −0.0596550 −0.0298275 0.999555i \(-0.509496\pi\)
−0.0298275 + 0.999555i \(0.509496\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 0 0
\(285\) 1.50000 2.59808i 0.0888523 0.153897i
\(286\) 0 0
\(287\) 22.0000 19.0526i 1.29862 1.12464i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) 8.00000 + 13.8564i 0.468968 + 0.812277i
\(292\) 0 0
\(293\) 27.0000 1.57736 0.788678 0.614806i \(-0.210766\pi\)
0.788678 + 0.614806i \(0.210766\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) 0 0
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) 0 0
\(299\) 3.50000 6.06218i 0.202410 0.350585i
\(300\) 0 0
\(301\) 16.0000 13.8564i 0.922225 0.798670i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i \(-0.0561621\pi\)
−0.644246 + 0.764818i \(0.722829\pi\)
\(312\) 0 0
\(313\) 6.00000 10.3923i 0.339140 0.587408i −0.645131 0.764072i \(-0.723197\pi\)
0.984271 + 0.176664i \(0.0565306\pi\)
\(314\) 0 0
\(315\) −2.50000 0.866025i −0.140859 0.0487950i
\(316\) 0 0
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 0 0
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 0 0
\(321\) 10.0000 0.558146
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −0.500000 0.866025i −0.0277350 0.0480384i
\(326\) 0 0
\(327\) −3.00000 + 5.19615i −0.165900 + 0.287348i
\(328\) 0 0
\(329\) −2.50000 12.9904i −0.137829 0.716183i
\(330\) 0 0
\(331\) −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 0 0
\(333\) −5.50000 9.52628i −0.301398 0.522037i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) 0 0
\(339\) −3.00000 5.19615i −0.162938 0.282216i
\(340\) 0 0
\(341\) −1.00000 + 1.73205i −0.0541530 + 0.0937958i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) −3.50000 + 6.06218i −0.188434 + 0.326377i
\(346\) 0 0
\(347\) 7.00000 + 12.1244i 0.375780 + 0.650870i 0.990443 0.137920i \(-0.0440416\pi\)
−0.614664 + 0.788789i \(0.710708\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 0 0
\(355\) 3.00000 5.19615i 0.159223 0.275783i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.00000 3.46410i 0.105556 0.182828i −0.808409 0.588621i \(-0.799671\pi\)
0.913965 + 0.405793i \(0.133004\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) 0 0
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) 12.5000 + 21.6506i 0.652495 + 1.13015i 0.982516 + 0.186180i \(0.0596109\pi\)
−0.330021 + 0.943974i \(0.607056\pi\)
\(368\) 0 0
\(369\) 5.50000 9.52628i 0.286319 0.495918i
\(370\) 0 0
\(371\) −27.5000 9.52628i −1.42773 0.494580i
\(372\) 0 0
\(373\) −3.00000 + 5.19615i −0.155334 + 0.269047i −0.933181 0.359408i \(-0.882979\pi\)
0.777847 + 0.628454i \(0.216312\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) −8.00000 −0.412021
\(378\) 0 0
\(379\) 19.0000 0.975964 0.487982 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(380\) 0 0
\(381\) −8.50000 14.7224i −0.435468 0.754253i
\(382\) 0 0
\(383\) 17.5000 30.3109i 0.894208 1.54881i 0.0594268 0.998233i \(-0.481073\pi\)
0.834781 0.550581i \(-0.185594\pi\)
\(384\) 0 0
\(385\) 2.00000 1.73205i 0.101929 0.0882735i
\(386\) 0 0
\(387\) 4.00000 6.92820i 0.203331 0.352180i
\(388\) 0 0
\(389\) −5.00000 8.66025i −0.253510 0.439092i 0.710980 0.703213i \(-0.248252\pi\)
−0.964490 + 0.264120i \(0.914918\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 5.00000 0.252217
\(394\) 0 0
\(395\) 4.00000 + 6.92820i 0.201262 + 0.348596i
\(396\) 0 0
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) 0 0
\(399\) −6.00000 + 5.19615i −0.300376 + 0.260133i
\(400\) 0 0
\(401\) 2.50000 4.33013i 0.124844 0.216236i −0.796828 0.604206i \(-0.793490\pi\)
0.921672 + 0.387970i \(0.126824\pi\)
\(402\) 0 0
\(403\) −1.00000 1.73205i −0.0498135 0.0862796i
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 11.0000 0.545250
\(408\) 0 0
\(409\) −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i \(-0.182412\pi\)
−0.889689 + 0.456566i \(0.849079\pi\)
\(410\) 0 0
\(411\) 9.00000 15.5885i 0.443937 0.768922i
\(412\) 0 0
\(413\) −10.0000 3.46410i −0.492068 0.170457i
\(414\) 0 0
\(415\) −4.00000 + 6.92820i −0.196352 + 0.340092i
\(416\) 0 0
\(417\) 10.0000 + 17.3205i 0.489702 + 0.848189i
\(418\) 0 0
\(419\) 5.00000 0.244266 0.122133 0.992514i \(-0.461027\pi\)
0.122133 + 0.992514i \(0.461027\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 0 0
\(423\) −2.50000 4.33013i −0.121554 0.210538i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −0.500000 + 0.866025i −0.0241402 + 0.0418121i
\(430\) 0 0
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) −32.0000 −1.53782 −0.768911 0.639356i \(-0.779201\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) 0 0
\(437\) 10.5000 + 18.1865i 0.502283 + 0.869980i
\(438\) 0 0
\(439\) 16.0000 27.7128i 0.763638 1.32266i −0.177325 0.984152i \(-0.556744\pi\)
0.940963 0.338508i \(-0.109922\pi\)
\(440\) 0 0
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) 8.00000 13.8564i 0.380091 0.658338i −0.610984 0.791643i \(-0.709226\pi\)
0.991075 + 0.133306i \(0.0425592\pi\)
\(444\) 0 0
\(445\) −5.00000 8.66025i −0.237023 0.410535i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 11.0000 0.519122 0.259561 0.965727i \(-0.416422\pi\)
0.259561 + 0.965727i \(0.416422\pi\)
\(450\) 0 0
\(451\) 5.50000 + 9.52628i 0.258985 + 0.448575i
\(452\) 0 0
\(453\) 3.00000 5.19615i 0.140952 0.244137i
\(454\) 0 0
\(455\) 0.500000 + 2.59808i 0.0234404 + 0.121800i
\(456\) 0 0
\(457\) 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i \(-0.695012\pi\)
0.996038 + 0.0889312i \(0.0283451\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) 0 0
\(465\) 1.00000 + 1.73205i 0.0463739 + 0.0803219i
\(466\) 0 0
\(467\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 3.50000 6.06218i 0.161271 0.279330i
\(472\) 0 0
\(473\) 4.00000 + 6.92820i 0.183920 + 0.318559i
\(474\) 0 0
\(475\) 3.00000 0.137649
\(476\) 0 0
\(477\) −11.0000 −0.503655
\(478\) 0 0
\(479\) 11.0000 + 19.0526i 0.502603 + 0.870534i 0.999995 + 0.00300810i \(0.000957509\pi\)
−0.497393 + 0.867526i \(0.665709\pi\)
\(480\) 0 0
\(481\) −5.50000 + 9.52628i −0.250778 + 0.434361i
\(482\) 0 0
\(483\) 14.0000 12.1244i 0.637022 0.551677i
\(484\) 0 0
\(485\) −8.00000 + 13.8564i −0.363261 + 0.629187i
\(486\) 0 0
\(487\) −8.00000 13.8564i −0.362515 0.627894i 0.625859 0.779936i \(-0.284748\pi\)
−0.988374 + 0.152042i \(0.951415\pi\)
\(488\) 0 0
\(489\) −16.0000 −0.723545
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0.500000 0.866025i 0.0224733 0.0389249i
\(496\) 0 0
\(497\) −12.0000 + 10.3923i −0.538274 + 0.466159i
\(498\) 0 0
\(499\) −16.0000 + 27.7128i −0.716258 + 1.24060i 0.246214 + 0.969216i \(0.420813\pi\)
−0.962472 + 0.271380i \(0.912520\pi\)
\(500\) 0 0
\(501\) −1.50000 2.59808i −0.0670151 0.116073i
\(502\) 0 0
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 0 0
\(509\) 17.0000 29.4449i 0.753512 1.30512i −0.192599 0.981278i \(-0.561692\pi\)
0.946111 0.323843i \(-0.104975\pi\)
\(510\) 0 0
\(511\) −15.0000 5.19615i −0.663561 0.229864i
\(512\) 0 0
\(513\) −1.50000 + 2.59808i −0.0662266 + 0.114708i
\(514\) 0 0
\(515\) 8.00000 + 13.8564i 0.352522 + 0.610586i
\(516\) 0 0
\(517\) 5.00000 0.219900
\(518\) 0 0
\(519\) −15.0000 −0.658427
\(520\) 0 0
\(521\) 16.5000 + 28.5788i 0.722878 + 1.25206i 0.959841 + 0.280543i \(0.0905145\pi\)
−0.236963 + 0.971519i \(0.576152\pi\)
\(522\) 0 0
\(523\) 1.00000 1.73205i 0.0437269 0.0757373i −0.843334 0.537390i \(-0.819410\pi\)
0.887061 + 0.461653i \(0.152744\pi\)
\(524\) 0 0
\(525\) −0.500000 2.59808i −0.0218218 0.113389i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −13.0000 22.5167i −0.565217 0.978985i
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) −11.0000 −0.476463
\(534\) 0 0
\(535\) 5.00000 + 8.66025i 0.216169 + 0.374415i
\(536\) 0 0
\(537\) −9.50000 + 16.4545i −0.409955 + 0.710063i
\(538\) 0 0
\(539\) −6.50000 + 2.59808i −0.279975 + 0.111907i
\(540\) 0 0
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) 0 0
\(543\) 12.0000 + 20.7846i 0.514969 + 0.891953i
\(544\) 0 0
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) −16.0000 −0.684111 −0.342055 0.939680i \(-0.611123\pi\)
−0.342055 + 0.939680i \(0.611123\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 12.0000 20.7846i 0.511217 0.885454i
\(552\) 0 0
\(553\) −4.00000 20.7846i −0.170097 0.883852i
\(554\) 0 0
\(555\) 5.50000 9.52628i 0.233462 0.404368i
\(556\) 0 0
\(557\) 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i \(0.0797613\pi\)
−0.269642 + 0.962961i \(0.586905\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −19.0000 32.9090i −0.800755 1.38695i −0.919120 0.393977i \(-0.871099\pi\)
0.118366 0.992970i \(-0.462235\pi\)
\(564\) 0 0
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 0 0
\(567\) 2.50000 + 0.866025i 0.104990 + 0.0363696i
\(568\) 0 0
\(569\) 4.50000 7.79423i 0.188650 0.326751i −0.756151 0.654398i \(-0.772922\pi\)
0.944800 + 0.327647i \(0.106256\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) −7.00000 −0.291920
\(576\) 0 0
\(577\) 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i \(-0.0725410\pi\)
−0.682730 + 0.730670i \(0.739208\pi\)
\(578\) 0 0
\(579\) −11.0000 + 19.0526i −0.457144 + 0.791797i
\(580\) 0 0
\(581\) 16.0000 13.8564i 0.663792 0.574861i
\(582\) 0 0
\(583\) 5.50000 9.52628i 0.227787 0.394538i
\(584\) 0 0
\(585\) 0.500000 + 0.866025i 0.0206725 + 0.0358057i
\(586\) 0 0
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) 0.500000 + 0.866025i 0.0205673 + 0.0356235i
\(592\) 0 0
\(593\) −8.00000 + 13.8564i −0.328521 + 0.569014i −0.982219 0.187741i \(-0.939883\pi\)
0.653698 + 0.756756i \(0.273217\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −12.0000 + 20.7846i −0.491127 + 0.850657i
\(598\) 0 0
\(599\) 1.00000 + 1.73205i 0.0408589 + 0.0707697i 0.885732 0.464198i \(-0.153657\pi\)
−0.844873 + 0.534967i \(0.820324\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 0 0
\(607\) −18.5000 + 32.0429i −0.750892 + 1.30058i 0.196499 + 0.980504i \(0.437043\pi\)
−0.947391 + 0.320079i \(0.896291\pi\)
\(608\) 0 0
\(609\) −20.0000 6.92820i −0.810441 0.280745i
\(610\) 0 0
\(611\) −2.50000 + 4.33013i −0.101139 + 0.175178i
\(612\) 0 0
\(613\) 20.5000 + 35.5070i 0.827987 + 1.43412i 0.899615 + 0.436684i \(0.143847\pi\)
−0.0716275 + 0.997431i \(0.522819\pi\)
\(614\) 0 0
\(615\) 11.0000 0.443563
\(616\) 0 0
\(617\) 28.0000 1.12724 0.563619 0.826035i \(-0.309409\pi\)
0.563619 + 0.826035i \(0.309409\pi\)
\(618\) 0 0
\(619\) 14.5000 + 25.1147i 0.582804 + 1.00945i 0.995145 + 0.0984169i \(0.0313779\pi\)
−0.412341 + 0.911030i \(0.635289\pi\)
\(620\) 0 0
\(621\) 3.50000 6.06218i 0.140450 0.243267i
\(622\) 0 0
\(623\) 5.00000 + 25.9808i 0.200321 + 1.04090i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −1.50000 2.59808i −0.0599042 0.103757i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 26.0000 1.03504 0.517522 0.855670i \(-0.326855\pi\)
0.517522 + 0.855670i \(0.326855\pi\)
\(632\) 0 0
\(633\) 2.50000 + 4.33013i 0.0993661 + 0.172107i
\(634\) 0 0
\(635\) 8.50000 14.7224i 0.337312 0.584242i
\(636\) 0 0
\(637\) 1.00000 6.92820i 0.0396214 0.274505i
\(638\) 0 0
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) 0 0
\(643\) 10.0000 0.394362 0.197181 0.980367i \(-0.436821\pi\)
0.197181 + 0.980367i \(0.436821\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) −8.50000 14.7224i −0.334169 0.578799i 0.649155 0.760656i \(-0.275122\pi\)
−0.983325 + 0.181857i \(0.941789\pi\)
\(648\) 0 0
\(649\) 2.00000 3.46410i 0.0785069 0.135978i
\(650\) 0 0
\(651\) −1.00000 5.19615i −0.0391931 0.203653i
\(652\) 0 0
\(653\) −3.50000 + 6.06218i −0.136966 + 0.237231i −0.926347 0.376672i \(-0.877068\pi\)
0.789381 + 0.613904i \(0.210402\pi\)
\(654\) 0 0
\(655\) 2.50000 + 4.33013i 0.0976831 + 0.169192i
\(656\) 0 0
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 12.0000 + 20.7846i 0.466746 + 0.808428i 0.999278 0.0379819i \(-0.0120929\pi\)
−0.532533 + 0.846410i \(0.678760\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.50000 2.59808i −0.290838 0.100749i
\(666\) 0 0
\(667\) −28.0000 + 48.4974i −1.08416 + 1.87783i
\(668\) 0 0
\(669\) 6.00000 + 10.3923i 0.231973 + 0.401790i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 0 0
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 0 0
\(677\) 6.50000 11.2583i 0.249815 0.432693i −0.713659 0.700493i \(-0.752963\pi\)
0.963474 + 0.267800i \(0.0862968\pi\)
\(678\) 0 0
\(679\) 32.0000 27.7128i 1.22805 1.06352i
\(680\) 0 0
\(681\) 4.00000 6.92820i 0.153280 0.265489i
\(682\) 0 0
\(683\) 2.00000 + 3.46410i 0.0765279 + 0.132550i 0.901750 0.432259i \(-0.142283\pi\)
−0.825222 + 0.564809i \(0.808950\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) 0 0
\(689\) 5.50000 + 9.52628i 0.209533 + 0.362922i
\(690\) 0 0
\(691\) −6.00000 + 10.3923i −0.228251 + 0.395342i −0.957290 0.289130i \(-0.906634\pi\)
0.729039 + 0.684472i \(0.239967\pi\)
\(692\) 0 0
\(693\) −2.00000 + 1.73205i −0.0759737 + 0.0657952i
\(694\) 0 0
\(695\) −10.0000 + 17.3205i −0.379322 + 0.657004i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −16.5000 28.5788i −0.622309 1.07787i
\(704\) 0 0
\(705\) 2.50000 4.33013i 0.0941554 0.163082i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) 0 0
\(711\) −4.00000 6.92820i −0.150012 0.259828i
\(712\) 0 0
\(713\) −14.0000 −0.524304
\(714\) 0 0
\(715\) −1.00000 −0.0373979
\(716\) 0 0
\(717\) −9.00000 15.5885i −0.336111 0.582162i
\(718\) 0 0
\(719\) 1.00000 1.73205i 0.0372937 0.0645946i −0.846776 0.531949i \(-0.821460\pi\)
0.884070 + 0.467355i \(0.154793\pi\)
\(720\) 0 0
\(721\) −8.00000 41.5692i −0.297936 1.54812i
\(722\) 0 0
\(723\) −3.50000 + 6.06218i −0.130166 + 0.225455i
\(724\) 0 0
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) 0 0
\(727\) −11.0000 −0.407967 −0.203984 0.978974i \(-0.565389\pi\)
−0.203984 + 0.978974i \(0.565389\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i \(-0.898450\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(734\) 0 0
\(735\) −1.00000 + 6.92820i −0.0368856 + 0.255551i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −9.50000 16.4545i −0.349463 0.605288i 0.636691 0.771119i \(-0.280303\pi\)
−0.986154 + 0.165831i \(0.946969\pi\)
\(740\) 0 0
\(741\) 3.00000 0.110208
\(742\) 0 0
\(743\) −49.0000 −1.79764 −0.898818 0.438322i \(-0.855573\pi\)
−0.898818 + 0.438322i \(0.855573\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 4.00000 6.92820i 0.146352 0.253490i
\(748\) 0 0
\(749\) −5.00000 25.9808i −0.182696 0.949316i
\(750\) 0 0
\(751\) 13.0000 22.5167i 0.474377 0.821645i −0.525193 0.850983i \(-0.676007\pi\)
0.999570 + 0.0293387i \(0.00934013\pi\)
\(752\) 0 0
\(753\) 6.50000 + 11.2583i 0.236873 + 0.410276i
\(754\) 0 0
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 3.50000 + 6.06218i 0.127042 + 0.220043i
\(760\) 0 0
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 0 0
\(763\) 15.0000 + 5.19615i 0.543036 + 0.188113i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.00000 + 3.46410i 0.0722158 + 0.125081i
\(768\) 0 0
\(769\) −5.00000 −0.180305 −0.0901523 0.995928i \(-0.528735\pi\)
−0.0901523 + 0.995928i \(0.528735\pi\)
\(770\) 0 0
\(771\) −20.0000 −0.720282
\(772\) 0 0
\(773\) −16.5000 28.5788i −0.593464 1.02791i −0.993762 0.111524i \(-0.964427\pi\)
0.400298 0.916385i \(-0.368907\pi\)
\(774\) 0 0
\(775\) −1.00000 + 1.73205i −0.0359211 + 0.0622171i
\(776\) 0 0
\(777\) −22.0000 + 19.0526i −0.789246 + 0.683507i
\(778\) 0 0
\(779\) 16.5000 28.5788i 0.591174 1.02394i
\(780\) 0 0
\(781\) −3.00000 5.19615i −0.107348 0.185933i
\(782\) 0 0
\(783\) −8.00000 −0.285897
\(784\) 0 0
\(785\) 7.00000 0.249841
\(786\) 0 0
\(787\) 11.0000 + 19.0526i 0.392108 + 0.679150i 0.992727 0.120384i \(-0.0384127\pi\)
−0.600620 + 0.799535i \(0.705079\pi\)
\(788\) 0 0
\(789\) 12.0000 20.7846i 0.427211 0.739952i
\(790\) 0 0
\(791\) −12.0000 + 10.3923i −0.426671 + 0.369508i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −5.50000 9.52628i −0.195065 0.337862i
\(796\) 0 0
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\)