Properties

Label 560.2.q.h.81.1
Level $560$
Weight $2$
Character 560.81
Analytic conductor $4.472$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) 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 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 560.81
Dual form 560.2.q.h.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.50000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.00000 - 1.73205i) q^{11} +1.00000 q^{15} +(-2.00000 + 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 2.59808i) q^{21} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{27} +9.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(2.00000 + 1.73205i) q^{35} +(-2.00000 - 3.46410i) q^{37} +1.00000 q^{41} -9.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(5.50000 - 4.33013i) q^{49} +(2.00000 + 3.46410i) q^{51} +(5.00000 - 8.66025i) q^{53} +2.00000 q^{55} -2.00000 q^{57} +(-5.00000 + 8.66025i) q^{59} +(-4.50000 - 7.79423i) q^{61} +(4.00000 + 3.46410i) q^{63} +(2.50000 - 4.33013i) q^{67} +1.00000 q^{69} -14.0000 q^{71} +(-6.00000 + 10.3923i) q^{73} +(0.500000 + 0.866025i) q^{75} +(1.00000 - 5.19615i) q^{77} +(7.00000 + 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{81} -11.0000 q^{83} -4.00000 q^{85} +(4.50000 - 7.79423i) q^{87} +(7.50000 + 12.9904i) q^{89} +(-2.00000 - 3.46410i) q^{93} +(1.00000 - 1.73205i) q^{95} -18.0000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + q^{5} + 5 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} + q^{5} + 5 q^{7} + 2 q^{9} + 2 q^{11} + 2 q^{15} - 4 q^{17} - 2 q^{19} + q^{21} + q^{23} - q^{25} + 10 q^{27} + 18 q^{29} + 4 q^{31} - 2 q^{33} + 4 q^{35} - 4 q^{37} + 2 q^{41} - 18 q^{43} - 2 q^{45} + 11 q^{49} + 4 q^{51} + 10 q^{53} + 4 q^{55} - 4 q^{57} - 10 q^{59} - 9 q^{61} + 8 q^{63} + 5 q^{67} + 2 q^{69} - 28 q^{71} - 12 q^{73} + q^{75} + 2 q^{77} + 14 q^{79} - q^{81} - 22 q^{83} - 8 q^{85} + 9 q^{87} + 15 q^{89} - 4 q^{93} + 2 q^{95} - 36 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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 −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) 0.500000 2.59808i 0.109109 0.566947i
\(22\) 0 0
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0 0
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) 0 0
\(35\) 2.00000 + 1.73205i 0.338062 + 0.292770i
\(36\) 0 0
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.00000 0.156174 0.0780869 0.996947i \(-0.475119\pi\)
0.0780869 + 0.996947i \(0.475119\pi\)
\(42\) 0 0
\(43\) −9.00000 −1.37249 −0.686244 0.727372i \(-0.740742\pi\)
−0.686244 + 0.727372i \(0.740742\pi\)
\(44\) 0 0
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0 0
\(51\) 2.00000 + 3.46410i 0.280056 + 0.485071i
\(52\) 0 0
\(53\) 5.00000 8.66025i 0.686803 1.18958i −0.286064 0.958211i \(-0.592347\pi\)
0.972867 0.231367i \(-0.0743197\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −5.00000 + 8.66025i −0.650945 + 1.12747i 0.331949 + 0.943297i \(0.392294\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(60\) 0 0
\(61\) −4.50000 7.79423i −0.576166 0.997949i −0.995914 0.0903080i \(-0.971215\pi\)
0.419748 0.907641i \(-0.362118\pi\)
\(62\) 0 0
\(63\) 4.00000 + 3.46410i 0.503953 + 0.436436i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i \(-0.734535\pi\)
0.977356 + 0.211604i \(0.0678686\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −14.0000 −1.66149 −0.830747 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) 0 0
\(73\) −6.00000 + 10.3923i −0.702247 + 1.21633i 0.265429 + 0.964130i \(0.414486\pi\)
−0.967676 + 0.252197i \(0.918847\pi\)
\(74\) 0 0
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 1.00000 5.19615i 0.113961 0.592157i
\(78\) 0 0
\(79\) 7.00000 + 12.1244i 0.787562 + 1.36410i 0.927457 + 0.373930i \(0.121990\pi\)
−0.139895 + 0.990166i \(0.544677\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −11.0000 −1.20741 −0.603703 0.797209i \(-0.706309\pi\)
−0.603703 + 0.797209i \(0.706309\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) 4.50000 7.79423i 0.482451 0.835629i
\(88\) 0 0
\(89\) 7.50000 + 12.9904i 0.794998 + 1.37698i 0.922840 + 0.385183i \(0.125862\pi\)
−0.127842 + 0.991795i \(0.540805\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.00000 3.46410i −0.207390 0.359211i
\(94\) 0 0
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 0 0
\(97\) −18.0000 −1.82762 −0.913812 0.406138i \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 0 0
\(103\) −6.50000 11.2583i −0.640464 1.10932i −0.985329 0.170664i \(-0.945409\pi\)
0.344865 0.938652i \(-0.387925\pi\)
\(104\) 0 0
\(105\) 2.50000 0.866025i 0.243975 0.0845154i
\(106\) 0 0
\(107\) 4.50000 + 7.79423i 0.435031 + 0.753497i 0.997298 0.0734594i \(-0.0234039\pi\)
−0.562267 + 0.826956i \(0.690071\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) −0.500000 + 0.866025i −0.0466252 + 0.0807573i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.00000 + 10.3923i −0.183340 + 0.952661i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0 0
\(123\) 0.500000 0.866025i 0.0450835 0.0780869i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) −4.50000 + 7.79423i −0.396203 + 0.686244i
\(130\) 0 0
\(131\) −4.00000 6.92820i −0.349482 0.605320i 0.636676 0.771132i \(-0.280309\pi\)
−0.986157 + 0.165812i \(0.946976\pi\)
\(132\) 0 0
\(133\) −4.00000 3.46410i −0.346844 0.300376i
\(134\) 0 0
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 4.50000 + 7.79423i 0.373705 + 0.647275i
\(146\) 0 0
\(147\) −1.00000 6.92820i −0.0824786 0.571429i
\(148\) 0 0
\(149\) 2.50000 + 4.33013i 0.204808 + 0.354738i 0.950072 0.312032i \(-0.101010\pi\)
−0.745264 + 0.666770i \(0.767676\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 0 0
\(153\) −8.00000 −0.646762
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) 0 0
\(159\) −5.00000 8.66025i −0.396526 0.686803i
\(160\) 0 0
\(161\) 2.00000 + 1.73205i 0.157622 + 0.136505i
\(162\) 0 0
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 0 0
\(165\) 1.00000 1.73205i 0.0778499 0.134840i
\(166\) 0 0
\(167\) −17.0000 −1.31550 −0.657750 0.753237i \(-0.728492\pi\)
−0.657750 + 0.753237i \(0.728492\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) 0 0
\(173\) −8.00000 13.8564i −0.608229 1.05348i −0.991532 0.129861i \(-0.958547\pi\)
0.383304 0.923622i \(-0.374786\pi\)
\(174\) 0 0
\(175\) −0.500000 + 2.59808i −0.0377964 + 0.196396i
\(176\) 0 0
\(177\) 5.00000 + 8.66025i 0.375823 + 0.650945i
\(178\) 0 0
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) −9.00000 −0.665299
\(184\) 0 0
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) 0 0
\(187\) 4.00000 + 6.92820i 0.292509 + 0.506640i
\(188\) 0 0
\(189\) 12.5000 4.33013i 0.909241 0.314970i
\(190\) 0 0
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 0 0
\(193\) 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i \(-0.665242\pi\)
0.999990 0.00447566i \(-0.00142465\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 0 0
\(201\) −2.50000 4.33013i −0.176336 0.305424i
\(202\) 0 0
\(203\) 22.5000 7.79423i 1.57919 0.547048i
\(204\) 0 0
\(205\) 0.500000 + 0.866025i 0.0349215 + 0.0604858i
\(206\) 0 0
\(207\) −1.00000 + 1.73205i −0.0695048 + 0.120386i
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −2.00000 −0.137686 −0.0688428 0.997628i \(-0.521931\pi\)
−0.0688428 + 0.997628i \(0.521931\pi\)
\(212\) 0 0
\(213\) −7.00000 + 12.1244i −0.479632 + 0.830747i
\(214\) 0 0
\(215\) −4.50000 7.79423i −0.306897 0.531562i
\(216\) 0 0
\(217\) 2.00000 10.3923i 0.135769 0.705476i
\(218\) 0 0
\(219\) 6.00000 + 10.3923i 0.405442 + 0.702247i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0 0
\(225\) −2.00000 −0.133333
\(226\) 0 0
\(227\) −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 0 0
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 0 0
\(231\) −4.00000 3.46410i −0.263181 0.227921i
\(232\) 0 0
\(233\) −4.00000 6.92820i −0.262049 0.453882i 0.704737 0.709468i \(-0.251065\pi\)
−0.966786 + 0.255586i \(0.917731\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 14.0000 0.909398
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 11.0000 19.0526i 0.708572 1.22728i −0.256814 0.966461i \(-0.582673\pi\)
0.965387 0.260822i \(-0.0839937\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 0 0
\(245\) 6.50000 + 2.59808i 0.415270 + 0.165985i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −5.50000 + 9.52628i −0.348548 + 0.603703i
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) 2.00000 0.125739
\(254\) 0 0
\(255\) −2.00000 + 3.46410i −0.125245 + 0.216930i
\(256\) 0 0
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) −8.00000 6.92820i −0.497096 0.430498i
\(260\) 0 0
\(261\) 9.00000 + 15.5885i 0.557086 + 0.964901i
\(262\) 0 0
\(263\) −0.500000 + 0.866025i −0.0308313 + 0.0534014i −0.881029 0.473062i \(-0.843149\pi\)
0.850198 + 0.526463i \(0.176482\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) 0 0
\(267\) 15.0000 0.917985
\(268\) 0 0
\(269\) 10.5000 18.1865i 0.640196 1.10885i −0.345192 0.938532i \(-0.612186\pi\)
0.985389 0.170321i \(-0.0544803\pi\)
\(270\) 0 0
\(271\) 11.0000 + 19.0526i 0.668202 + 1.15736i 0.978406 + 0.206691i \(0.0662693\pi\)
−0.310204 + 0.950670i \(0.600397\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 + 1.73205i 0.0603023 + 0.104447i
\(276\) 0 0
\(277\) 14.0000 24.2487i 0.841178 1.45696i −0.0477206 0.998861i \(-0.515196\pi\)
0.888899 0.458103i \(-0.151471\pi\)
\(278\) 0 0
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) 0 0
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) 0 0
\(287\) 2.50000 0.866025i 0.147570 0.0511199i
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) −9.00000 + 15.5885i −0.527589 + 0.913812i
\(292\) 0 0
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) −10.0000 −0.582223
\(296\) 0 0
\(297\) 5.00000 8.66025i 0.290129 0.502519i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −22.5000 + 7.79423i −1.29688 + 0.449252i
\(302\) 0 0
\(303\) 1.50000 + 2.59808i 0.0861727 + 0.149256i
\(304\) 0 0
\(305\) 4.50000 7.79423i 0.257669 0.446296i
\(306\) 0 0
\(307\) −21.0000 −1.19853 −0.599267 0.800549i \(-0.704541\pi\)
−0.599267 + 0.800549i \(0.704541\pi\)
\(308\) 0 0
\(309\) −13.0000 −0.739544
\(310\) 0 0
\(311\) 13.0000 22.5167i 0.737162 1.27680i −0.216606 0.976259i \(-0.569499\pi\)
0.953768 0.300544i \(-0.0971681\pi\)
\(312\) 0 0
\(313\) −8.00000 13.8564i −0.452187 0.783210i 0.546335 0.837567i \(-0.316023\pi\)
−0.998522 + 0.0543564i \(0.982689\pi\)
\(314\) 0 0
\(315\) −1.00000 + 5.19615i −0.0563436 + 0.292770i
\(316\) 0 0
\(317\) 8.00000 + 13.8564i 0.449325 + 0.778253i 0.998342 0.0575576i \(-0.0183313\pi\)
−0.549017 + 0.835811i \(0.684998\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) 0 0
\(321\) 9.00000 0.502331
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −0.500000 0.866025i −0.0276501 0.0478913i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(332\) 0 0
\(333\) 4.00000 6.92820i 0.219199 0.379663i
\(334\) 0 0
\(335\) 5.00000 0.273179
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 0 0
\(339\) 1.00000 1.73205i 0.0543125 0.0940721i
\(340\) 0 0
\(341\) −4.00000 6.92820i −0.216612 0.375183i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0.500000 + 0.866025i 0.0269191 + 0.0466252i
\(346\) 0 0
\(347\) −3.50000 + 6.06218i −0.187890 + 0.325435i −0.944547 0.328378i \(-0.893498\pi\)
0.756657 + 0.653812i \(0.226831\pi\)
\(348\) 0 0
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7.00000 + 12.1244i −0.372572 + 0.645314i −0.989960 0.141344i \(-0.954858\pi\)
0.617388 + 0.786659i \(0.288191\pi\)
\(354\) 0 0
\(355\) −7.00000 12.1244i −0.371521 0.643494i
\(356\) 0 0
\(357\) 8.00000 + 6.92820i 0.423405 + 0.366679i
\(358\) 0 0
\(359\) 6.00000 + 10.3923i 0.316668 + 0.548485i 0.979791 0.200026i \(-0.0641026\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −12.0000 −0.628109
\(366\) 0 0
\(367\) 3.50000 6.06218i 0.182699 0.316443i −0.760100 0.649806i \(-0.774850\pi\)
0.942799 + 0.333363i \(0.108183\pi\)
\(368\) 0 0
\(369\) 1.00000 + 1.73205i 0.0520579 + 0.0901670i
\(370\) 0 0
\(371\) 5.00000 25.9808i 0.259587 1.34885i
\(372\) 0 0
\(373\) 14.0000 + 24.2487i 0.724893 + 1.25555i 0.959018 + 0.283344i \(0.0914439\pi\)
−0.234126 + 0.972206i \(0.575223\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 30.0000 1.54100 0.770498 0.637442i \(-0.220007\pi\)
0.770498 + 0.637442i \(0.220007\pi\)
\(380\) 0 0
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 0 0
\(383\) 10.5000 + 18.1865i 0.536525 + 0.929288i 0.999088 + 0.0427020i \(0.0135966\pi\)
−0.462563 + 0.886586i \(0.653070\pi\)
\(384\) 0 0
\(385\) 5.00000 1.73205i 0.254824 0.0882735i
\(386\) 0 0
\(387\) −9.00000 15.5885i −0.457496 0.792406i
\(388\) 0 0
\(389\) −13.0000 + 22.5167i −0.659126 + 1.14164i 0.321716 + 0.946836i \(0.395740\pi\)
−0.980842 + 0.194804i \(0.937593\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 0 0
\(393\) −8.00000 −0.403547
\(394\) 0 0
\(395\) −7.00000 + 12.1244i −0.352208 + 0.610043i
\(396\) 0 0
\(397\) −3.00000 5.19615i −0.150566 0.260787i 0.780870 0.624694i \(-0.214776\pi\)
−0.931436 + 0.363906i \(0.881443\pi\)
\(398\) 0 0
\(399\) −5.00000 + 1.73205i −0.250313 + 0.0867110i
\(400\) 0 0
\(401\) 8.50000 + 14.7224i 0.424470 + 0.735203i 0.996371 0.0851195i \(-0.0271272\pi\)
−0.571901 + 0.820323i \(0.693794\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) 10.5000 18.1865i 0.519192 0.899266i −0.480560 0.876962i \(-0.659566\pi\)
0.999751 0.0223042i \(-0.00710022\pi\)
\(410\) 0 0
\(411\) 6.00000 + 10.3923i 0.295958 + 0.512615i
\(412\) 0 0
\(413\) −5.00000 + 25.9808i −0.246034 + 1.27843i
\(414\) 0 0
\(415\) −5.50000 9.52628i −0.269984 0.467627i
\(416\) 0 0
\(417\) 1.00000 1.73205i 0.0489702 0.0848189i
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) 0 0
\(421\) −27.0000 −1.31590 −0.657950 0.753062i \(-0.728576\pi\)
−0.657950 + 0.753062i \(0.728576\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.00000 3.46410i −0.0970143 0.168034i
\(426\) 0 0
\(427\) −18.0000 15.5885i −0.871081 0.754378i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.00000 12.1244i 0.337178 0.584010i −0.646723 0.762725i \(-0.723861\pi\)
0.983901 + 0.178716i \(0.0571942\pi\)
\(432\) 0 0
\(433\) 30.0000 1.44171 0.720854 0.693087i \(-0.243750\pi\)
0.720854 + 0.693087i \(0.243750\pi\)
\(434\) 0 0
\(435\) 9.00000 0.431517
\(436\) 0 0
\(437\) 1.00000 1.73205i 0.0478365 0.0828552i
\(438\) 0 0
\(439\) −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) 0 0
\(441\) 13.0000 + 5.19615i 0.619048 + 0.247436i
\(442\) 0 0
\(443\) −5.50000 9.52628i −0.261313 0.452607i 0.705278 0.708931i \(-0.250822\pi\)
−0.966591 + 0.256323i \(0.917489\pi\)
\(444\) 0 0
\(445\) −7.50000 + 12.9904i −0.355534 + 0.615803i
\(446\) 0 0
\(447\) 5.00000 0.236492
\(448\) 0 0
\(449\) −41.0000 −1.93491 −0.967455 0.253044i \(-0.918568\pi\)
−0.967455 + 0.253044i \(0.918568\pi\)
\(450\) 0 0
\(451\) 1.00000 1.73205i 0.0470882 0.0815591i
\(452\) 0 0
\(453\) −4.00000 6.92820i −0.187936 0.325515i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.00000 6.92820i −0.187112 0.324088i 0.757174 0.653213i \(-0.226579\pi\)
−0.944286 + 0.329125i \(0.893246\pi\)
\(458\) 0 0
\(459\) −10.0000 + 17.3205i −0.466760 + 0.808452i
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −39.0000 −1.81248 −0.906242 0.422760i \(-0.861061\pi\)
−0.906242 + 0.422760i \(0.861061\pi\)
\(464\) 0 0
\(465\) 2.00000 3.46410i 0.0927478 0.160644i
\(466\) 0 0
\(467\) −3.50000 6.06218i −0.161961 0.280524i 0.773611 0.633661i \(-0.218448\pi\)
−0.935572 + 0.353137i \(0.885115\pi\)
\(468\) 0 0
\(469\) 2.50000 12.9904i 0.115439 0.599840i
\(470\) 0 0
\(471\) 1.00000 + 1.73205i 0.0460776 + 0.0798087i
\(472\) 0 0
\(473\) −9.00000 + 15.5885i −0.413820 + 0.716758i
\(474\) 0 0
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) 20.0000 0.915737
\(478\) 0 0
\(479\) −8.00000 + 13.8564i −0.365529 + 0.633115i −0.988861 0.148842i \(-0.952445\pi\)
0.623332 + 0.781958i \(0.285779\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 2.50000 0.866025i 0.113754 0.0394055i
\(484\) 0 0
\(485\) −9.00000 15.5885i −0.408669 0.707835i
\(486\) 0 0
\(487\) −4.00000 + 6.92820i −0.181257 + 0.313947i −0.942309 0.334744i \(-0.891350\pi\)
0.761052 + 0.648691i \(0.224683\pi\)
\(488\) 0 0
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 0 0
\(493\) −18.0000 + 31.1769i −0.810679 + 1.40414i
\(494\) 0 0
\(495\) 2.00000 + 3.46410i 0.0898933 + 0.155700i
\(496\) 0 0
\(497\) −35.0000 + 12.1244i −1.56996 + 0.543852i
\(498\) 0 0
\(499\) −19.0000 32.9090i −0.850557 1.47321i −0.880707 0.473662i \(-0.842932\pi\)
0.0301498 0.999545i \(-0.490402\pi\)
\(500\) 0 0
\(501\) −8.50000 + 14.7224i −0.379752 + 0.657750i
\(502\) 0 0
\(503\) 23.0000 1.02552 0.512760 0.858532i \(-0.328623\pi\)
0.512760 + 0.858532i \(0.328623\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) −6.50000 + 11.2583i −0.288675 + 0.500000i
\(508\) 0 0
\(509\) 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) 0 0
\(511\) −6.00000 + 31.1769i −0.265424 + 1.37919i
\(512\) 0 0
\(513\) −5.00000 8.66025i −0.220755 0.382360i
\(514\) 0 0
\(515\) 6.50000 11.2583i 0.286424 0.496101i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −16.0000 −0.702322
\(520\) 0 0
\(521\) 21.0000 36.3731i 0.920027 1.59353i 0.120656 0.992694i \(-0.461500\pi\)
0.799370 0.600839i \(-0.205167\pi\)
\(522\) 0 0
\(523\) 14.0000 + 24.2487i 0.612177 + 1.06032i 0.990873 + 0.134801i \(0.0430394\pi\)
−0.378695 + 0.925521i \(0.623627\pi\)
\(524\) 0 0
\(525\) 2.00000 + 1.73205i 0.0872872 + 0.0755929i
\(526\) 0 0
\(527\) 8.00000 + 13.8564i 0.348485 + 0.603595i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 0 0
\(531\) −20.0000 −0.867926
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −4.50000 + 7.79423i −0.194552 + 0.336974i
\(536\) 0 0
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) 0 0
\(539\) −2.00000 13.8564i −0.0861461 0.596838i
\(540\) 0 0
\(541\) 6.50000 + 11.2583i 0.279457 + 0.484033i 0.971250 0.238062i \(-0.0765123\pi\)
−0.691793 + 0.722096i \(0.743179\pi\)
\(542\) 0 0
\(543\) −12.5000 + 21.6506i −0.536426 + 0.929118i
\(544\) 0 0
\(545\) 1.00000 0.0428353
\(546\) 0 0
\(547\) 35.0000 1.49649 0.748246 0.663421i \(-0.230896\pi\)
0.748246 + 0.663421i \(0.230896\pi\)
\(548\) 0 0
\(549\) 9.00000 15.5885i 0.384111 0.665299i
\(550\) 0 0
\(551\) −9.00000 15.5885i −0.383413 0.664091i
\(552\) 0 0
\(553\) 28.0000 + 24.2487i 1.19068 + 1.03116i
\(554\) 0 0
\(555\) −2.00000 3.46410i −0.0848953 0.147043i
\(556\) 0 0
\(557\) −15.0000 + 25.9808i −0.635570 + 1.10084i 0.350824 + 0.936442i \(0.385902\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 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
\(565\) 1.00000 + 1.73205i 0.0420703 + 0.0728679i
\(566\) 0 0
\(567\) −0.500000 + 2.59808i −0.0209980 + 0.109109i
\(568\) 0 0
\(569\) −23.0000 39.8372i −0.964210 1.67006i −0.711722 0.702461i \(-0.752085\pi\)
−0.252488 0.967600i \(-0.581249\pi\)
\(570\) 0 0
\(571\) −13.0000 + 22.5167i −0.544033 + 0.942293i 0.454634 + 0.890678i \(0.349770\pi\)
−0.998667 + 0.0516146i \(0.983563\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −1.00000 + 1.73205i −0.0416305 + 0.0721062i −0.886090 0.463513i \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) 0 0
\(579\) −7.00000 12.1244i −0.290910 0.503871i
\(580\) 0 0
\(581\) −27.5000 + 9.52628i −1.14089 + 0.395217i
\(582\) 0 0
\(583\) −10.0000 17.3205i −0.414158 0.717342i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 9.00000 15.5885i 0.370211 0.641223i
\(592\) 0 0
\(593\) −9.00000 15.5885i −0.369586 0.640141i 0.619915 0.784669i \(-0.287167\pi\)
−0.989501 + 0.144528i \(0.953834\pi\)
\(594\) 0 0
\(595\) −10.0000 + 3.46410i −0.409960 + 0.142014i
\(596\) 0 0
\(597\) 2.00000 + 3.46410i 0.0818546 + 0.141776i
\(598\) 0 0
\(599\) 2.00000 3.46410i 0.0817178 0.141539i −0.822270 0.569097i \(-0.807293\pi\)
0.903988 + 0.427558i \(0.140626\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 10.0000 0.407231
\(604\) 0 0
\(605\) −3.50000 + 6.06218i −0.142295 + 0.246463i
\(606\) 0 0
\(607\) 13.5000 + 23.3827i 0.547948 + 0.949074i 0.998415 + 0.0562808i \(0.0179242\pi\)
−0.450467 + 0.892793i \(0.648742\pi\)
\(608\) 0 0
\(609\) 4.50000 23.3827i 0.182349 0.947514i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 10.0000 17.3205i 0.403896 0.699569i −0.590296 0.807187i \(-0.700989\pi\)
0.994192 + 0.107618i \(0.0343224\pi\)
\(614\) 0 0
\(615\) 1.00000 0.0403239
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 0 0
\(619\) −17.0000 + 29.4449i −0.683288 + 1.18349i 0.290684 + 0.956819i \(0.406117\pi\)
−0.973972 + 0.226670i \(0.927216\pi\)
\(620\) 0 0
\(621\) 2.50000 + 4.33013i 0.100322 + 0.173762i
\(622\) 0 0
\(623\) 30.0000 + 25.9808i 1.20192 + 1.04090i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −2.00000 + 3.46410i −0.0798723 + 0.138343i
\(628\) 0 0
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) 0 0
\(633\) −1.00000 + 1.73205i −0.0397464 + 0.0688428i
\(634\) 0 0
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −14.0000 24.2487i −0.553831 0.959264i
\(640\) 0 0
\(641\) 9.50000 16.4545i 0.375227 0.649913i −0.615134 0.788423i \(-0.710898\pi\)
0.990361 + 0.138510i \(0.0442313\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) −9.00000 −0.354375
\(646\) 0 0
\(647\) 11.5000 19.9186i 0.452112 0.783080i −0.546405 0.837521i \(-0.684004\pi\)
0.998517 + 0.0544405i \(0.0173375\pi\)
\(648\) 0 0
\(649\) 10.0000 + 17.3205i 0.392534 + 0.679889i
\(650\) 0 0
\(651\) −8.00000 6.92820i −0.313545 0.271538i
\(652\) 0 0
\(653\) −18.0000 31.1769i −0.704394 1.22005i −0.966910 0.255119i \(-0.917885\pi\)
0.262515 0.964928i \(-0.415448\pi\)
\(654\) 0 0
\(655\) 4.00000 6.92820i 0.156293 0.270707i
\(656\) 0 0
\(657\) −24.0000 −0.936329
\(658\) 0 0
\(659\) −2.00000 −0.0779089 −0.0389545 0.999241i \(-0.512403\pi\)
−0.0389545 + 0.999241i \(0.512403\pi\)
\(660\) 0 0
\(661\) 1.50000 2.59808i 0.0583432 0.101053i −0.835379 0.549675i \(-0.814752\pi\)
0.893722 + 0.448622i \(0.148085\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.00000 5.19615i 0.0387783 0.201498i
\(666\) 0 0
\(667\) 4.50000 + 7.79423i 0.174241 + 0.301794i
\(668\) 0 0
\(669\) 2.00000 3.46410i 0.0773245 0.133930i
\(670\) 0 0
\(671\) −18.0000 −0.694882
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) −2.50000 + 4.33013i −0.0962250 + 0.166667i
\(676\) 0 0
\(677\) 12.0000 + 20.7846i 0.461197 + 0.798817i 0.999021 0.0442400i \(-0.0140866\pi\)
−0.537823 + 0.843057i \(0.680753\pi\)
\(678\) 0 0
\(679\) −45.0000 + 15.5885i −1.72694 + 0.598230i
\(680\) 0 0
\(681\) 10.0000 + 17.3205i 0.383201 + 0.663723i
\(682\) 0 0
\(683\) 4.50000 7.79423i 0.172188 0.298238i −0.766997 0.641651i \(-0.778250\pi\)
0.939184 + 0.343413i \(0.111583\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 10.0000 0.381524
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 25.0000 + 43.3013i 0.951045 + 1.64726i 0.743170 + 0.669102i \(0.233321\pi\)
0.207875 + 0.978155i \(0.433345\pi\)
\(692\) 0 0
\(693\) 10.0000 3.46410i 0.379869 0.131590i
\(694\) 0 0
\(695\) 1.00000 + 1.73205i 0.0379322 + 0.0657004i
\(696\) 0 0
\(697\) −2.00000 + 3.46410i −0.0757554 + 0.131212i
\(698\) 0 0
\(699\) −8.00000 −0.302588
\(700\) 0 0
\(701\) 9.00000 0.339925 0.169963 0.985451i \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 0 0
\(703\) −4.00000 + 6.92820i −0.150863 + 0.261302i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.50000 + 7.79423i −0.0564133 + 0.293132i
\(708\) 0 0
\(709\) −10.5000 18.1865i −0.394336 0.683010i 0.598680 0.800988i \(-0.295692\pi\)
−0.993016 + 0.117978i \(0.962359\pi\)
\(710\) 0 0
\(711\) −14.0000 + 24.2487i −0.525041 + 0.909398i
\(712\) 0 0
\(713\) 4.00000 0.149801
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 12.0000 20.7846i 0.448148 0.776215i
\(718\) 0 0
\(719\) −21.0000 36.3731i −0.783168 1.35649i −0.930087 0.367338i \(-0.880269\pi\)
0.146920 0.989148i \(-0.453064\pi\)
\(720\) 0 0
\(721\) −26.0000 22.5167i −0.968291 0.838564i
\(722\) 0 0
\(723\) −11.0000 19.0526i −0.409094 0.708572i
\(724\) 0 0
\(725\) −4.50000 + 7.79423i −0.167126 + 0.289470i
\(726\) 0 0
\(727\) 31.0000 1.14973 0.574863 0.818250i \(-0.305055\pi\)
0.574863 + 0.818250i \(0.305055\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 18.0000 31.1769i 0.665754 1.15312i
\(732\) 0 0
\(733\) 13.0000 + 22.5167i 0.480166 + 0.831672i 0.999741 0.0227529i \(-0.00724310\pi\)
−0.519575 + 0.854425i \(0.673910\pi\)
\(734\) 0 0
\(735\) 5.50000 4.33013i 0.202871 0.159719i
\(736\) 0 0
\(737\) −5.00000 8.66025i −0.184177 0.319005i
\(738\) 0 0
\(739\) 5.00000 8.66025i 0.183928 0.318573i −0.759287 0.650756i \(-0.774452\pi\)
0.943215 + 0.332184i \(0.107785\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27.0000 −0.990534 −0.495267 0.868741i \(-0.664930\pi\)
−0.495267 + 0.868741i \(0.664930\pi\)
\(744\) 0 0
\(745\) −2.50000 + 4.33013i −0.0915929 + 0.158644i
\(746\) 0 0
\(747\) −11.0000 19.0526i −0.402469 0.697097i
\(748\) 0 0
\(749\) 18.0000 + 15.5885i 0.657706 + 0.569590i
\(750\) 0 0
\(751\) 6.00000 + 10.3923i 0.218943 + 0.379221i 0.954485 0.298259i \(-0.0964058\pi\)
−0.735542 + 0.677479i \(0.763072\pi\)
\(752\) 0 0
\(753\) −4.00000 + 6.92820i −0.145768 + 0.252478i
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −24.0000 −0.872295 −0.436147 0.899875i \(-0.643657\pi\)
−0.436147 + 0.899875i \(0.643657\pi\)
\(758\) 0 0
\(759\) 1.00000 1.73205i 0.0362977 0.0628695i
\(760\) 0 0
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) 0 0
\(763\) 0.500000 2.59808i 0.0181012 0.0940567i
\(764\) 0 0
\(765\) −4.00000 6.92820i −0.144620 0.250490i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(774\) 0 0
\(775\) 2.00000 + 3.46410i 0.0718421 + 0.124434i
\(776\) 0 0
\(777\) −10.0000 + 3.46410i −0.358748 + 0.124274i
\(778\) 0 0
\(779\) −1.00000 1.73205i −0.0358287 0.0620572i
\(780\) 0 0
\(781\) −14.0000 + 24.2487i −0.500959 + 0.867687i
\(782\) 0 0
\(783\) 45.0000 1.60817
\(784\) 0 0
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) 22.5000 38.9711i 0.802038 1.38917i −0.116234 0.993222i \(-0.537082\pi\)
0.918272 0.395949i \(-0.129584\pi\)
\(788\) 0 0
\(789\) 0.500000 + 0.866025i 0.0178005 + 0.0308313i
\(790\) 0 0
\(791\) 5.00000 1.73205i 0.177780 0.0615846i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 5.00000 8.66025i 0.177332 0.307148i
\(796\) 0 0
\(797\) 8.00000