Properties

Label 1008.2.r.d.673.1
Level $1008$
Weight $2$
Character 1008.673
Analytic conductor $8.049$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.d.337.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{3} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-1.73205i q^{3} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +(-3.00000 + 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(4.50000 - 2.59808i) q^{15} +6.00000 q^{17} +7.00000 q^{19} +(-1.50000 - 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} +(1.00000 + 1.73205i) q^{31} +(9.00000 + 5.19615i) q^{33} +3.00000 q^{35} +2.00000 q^{37} +(-3.00000 + 1.73205i) q^{39} +(1.00000 - 1.73205i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(-0.500000 - 0.866025i) q^{49} -10.3923i q^{51} +6.00000 q^{53} -18.0000 q^{55} -12.1244i q^{57} +(-2.50000 + 4.33013i) q^{61} +(-1.50000 + 2.59808i) q^{63} +(3.00000 - 5.19615i) q^{65} +(4.00000 + 6.92820i) q^{67} +(4.50000 - 2.59808i) q^{69} -3.00000 q^{71} +2.00000 q^{73} +(6.00000 + 3.46410i) q^{75} +(3.00000 + 5.19615i) q^{77} +(2.50000 - 4.33013i) q^{79} +9.00000 q^{81} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(9.00000 + 5.19615i) q^{87} -2.00000 q^{91} +(3.00000 - 1.73205i) q^{93} +(10.5000 + 18.1865i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(9.00000 - 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{5} + q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + 3q^{5} + q^{7} - 6q^{9} - 6q^{11} - 2q^{13} + 9q^{15} + 12q^{17} + 14q^{19} - 3q^{21} + 3q^{23} - 4q^{25} - 6q^{29} + 2q^{31} + 18q^{33} + 6q^{35} + 4q^{37} - 6q^{39} + 2q^{43} - 9q^{45} - q^{49} + 12q^{53} - 36q^{55} - 5q^{61} - 3q^{63} + 6q^{65} + 8q^{67} + 9q^{69} - 6q^{71} + 4q^{73} + 12q^{75} + 6q^{77} + 5q^{79} + 18q^{81} + 12q^{83} + 18q^{85} + 18q^{87} - 4q^{91} + 6q^{93} + 21q^{95} - 2q^{97} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 4.50000 2.59808i 1.16190 0.670820i
\(16\) 0 0
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) −1.50000 0.866025i −0.327327 0.188982i
\(22\) 0 0
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) 0 0
\(33\) 9.00000 + 5.19615i 1.56670 + 0.904534i
\(34\) 0 0
\(35\) 3.00000 0.507093
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) −3.00000 + 1.73205i −0.480384 + 0.277350i
\(40\) 0 0
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) 1.00000 1.73205i 0.152499 0.264135i −0.779647 0.626219i \(-0.784601\pi\)
0.932145 + 0.362084i \(0.117935\pi\)
\(44\) 0 0
\(45\) −4.50000 7.79423i −0.670820 1.16190i
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 10.3923i 1.45521i
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −18.0000 −2.42712
\(56\) 0 0
\(57\) 12.1244i 1.60591i
\(58\) 0 0
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) 0 0
\(63\) −1.50000 + 2.59808i −0.188982 + 0.327327i
\(64\) 0 0
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 0 0
\(67\) 4.00000 + 6.92820i 0.488678 + 0.846415i 0.999915 0.0130248i \(-0.00414604\pi\)
−0.511237 + 0.859440i \(0.670813\pi\)
\(68\) 0 0
\(69\) 4.50000 2.59808i 0.541736 0.312772i
\(70\) 0 0
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) 6.00000 + 3.46410i 0.692820 + 0.400000i
\(76\) 0 0
\(77\) 3.00000 + 5.19615i 0.341882 + 0.592157i
\(78\) 0 0
\(79\) 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i \(-0.742577\pi\)
0.971698 + 0.236225i \(0.0759104\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) 9.00000 + 15.5885i 0.976187 + 1.69081i
\(86\) 0 0
\(87\) 9.00000 + 5.19615i 0.964901 + 0.557086i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) 0 0
\(93\) 3.00000 1.73205i 0.311086 0.179605i
\(94\) 0 0
\(95\) 10.5000 + 18.1865i 1.07728 + 1.86590i
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 0 0
\(99\) 9.00000 15.5885i 0.904534 1.56670i
\(100\) 0 0
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 0 0
\(103\) −5.00000 8.66025i −0.492665 0.853320i 0.507300 0.861770i \(-0.330644\pi\)
−0.999964 + 0.00844953i \(0.997310\pi\)
\(104\) 0 0
\(105\) 5.19615i 0.507093i
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 3.46410i 0.328798i
\(112\) 0 0
\(113\) −7.50000 12.9904i −0.705541 1.22203i −0.966496 0.256681i \(-0.917371\pi\)
0.260955 0.965351i \(-0.415962\pi\)
\(114\) 0 0
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) 0 0
\(117\) 3.00000 + 5.19615i 0.277350 + 0.480384i
\(118\) 0 0
\(119\) 3.00000 5.19615i 0.275010 0.476331i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −17.0000 −1.50851 −0.754253 0.656584i \(-0.772001\pi\)
−0.754253 + 0.656584i \(0.772001\pi\)
\(128\) 0 0
\(129\) −3.00000 1.73205i −0.264135 0.152499i
\(130\) 0 0
\(131\) −4.50000 7.79423i −0.393167 0.680985i 0.599699 0.800226i \(-0.295287\pi\)
−0.992865 + 0.119241i \(0.961954\pi\)
\(132\) 0 0
\(133\) 3.50000 6.06218i 0.303488 0.525657i
\(134\) 0 0
\(135\) −13.5000 + 7.79423i −1.16190 + 0.670820i
\(136\) 0 0
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) −18.0000 −1.49482
\(146\) 0 0
\(147\) −1.50000 + 0.866025i −0.123718 + 0.0714286i
\(148\) 0 0
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 11.5000 19.9186i 0.935857 1.62095i 0.162758 0.986666i \(-0.447961\pi\)
0.773099 0.634285i \(-0.218706\pi\)
\(152\) 0 0
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) −3.00000 + 5.19615i −0.240966 + 0.417365i
\(156\) 0 0
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 0 0
\(159\) 10.3923i 0.824163i
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) −2.00000 −0.156652 −0.0783260 0.996928i \(-0.524958\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) 0 0
\(165\) 31.1769i 2.42712i
\(166\) 0 0
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) −21.0000 −1.60591
\(172\) 0 0
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) 7.50000 + 4.33013i 0.554416 + 0.320092i
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) −18.0000 + 31.1769i −1.31629 + 2.27988i
\(188\) 0 0
\(189\) 4.50000 + 2.59808i 0.327327 + 0.188982i
\(190\) 0 0
\(191\) −4.50000 + 7.79423i −0.325609 + 0.563971i −0.981635 0.190767i \(-0.938902\pi\)
0.656027 + 0.754738i \(0.272236\pi\)
\(192\) 0 0
\(193\) −8.50000 14.7224i −0.611843 1.05974i −0.990930 0.134382i \(-0.957095\pi\)
0.379086 0.925361i \(-0.376238\pi\)
\(194\) 0 0
\(195\) −9.00000 5.19615i −0.644503 0.372104i
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 0 0
\(201\) 12.0000 6.92820i 0.846415 0.488678i
\(202\) 0 0
\(203\) 3.00000 + 5.19615i 0.210559 + 0.364698i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −4.50000 7.79423i −0.312772 0.541736i
\(208\) 0 0
\(209\) −21.0000 + 36.3731i −1.45260 + 2.51598i
\(210\) 0 0
\(211\) 4.00000 + 6.92820i 0.275371 + 0.476957i 0.970229 0.242190i \(-0.0778659\pi\)
−0.694857 + 0.719148i \(0.744533\pi\)
\(212\) 0 0
\(213\) 5.19615i 0.356034i
\(214\) 0 0
\(215\) 6.00000 0.409197
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) 3.46410i 0.234082i
\(220\) 0 0
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) 0 0
\(223\) −14.0000 + 24.2487i −0.937509 + 1.62381i −0.167412 + 0.985887i \(0.553541\pi\)
−0.770097 + 0.637927i \(0.779792\pi\)
\(224\) 0 0
\(225\) 6.00000 10.3923i 0.400000 0.692820i
\(226\) 0 0
\(227\) −7.50000 + 12.9904i −0.497792 + 0.862202i −0.999997 0.00254715i \(-0.999189\pi\)
0.502204 + 0.864749i \(0.332523\pi\)
\(228\) 0 0
\(229\) 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i \(-0.156147\pi\)
−0.849032 + 0.528341i \(0.822814\pi\)
\(230\) 0 0
\(231\) 9.00000 5.19615i 0.592157 0.341882i
\(232\) 0 0
\(233\) 9.00000 0.589610 0.294805 0.955557i \(-0.404745\pi\)
0.294805 + 0.955557i \(0.404745\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −7.50000 4.33013i −0.487177 0.281272i
\(238\) 0 0
\(239\) −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i \(-0.327896\pi\)
−0.999854 + 0.0170808i \(0.994563\pi\)
\(240\) 0 0
\(241\) −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) 0 0
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) 1.50000 2.59808i 0.0958315 0.165985i
\(246\) 0 0
\(247\) −7.00000 12.1244i −0.445399 0.771454i
\(248\) 0 0
\(249\) −18.0000 10.3923i −1.14070 0.658586i
\(250\) 0 0
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 0 0
\(255\) 27.0000 15.5885i 1.69081 0.976187i
\(256\) 0 0
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 0 0
\(259\) 1.00000 1.73205i 0.0621370 0.107624i
\(260\) 0 0
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) 0 0
\(263\) −10.5000 + 18.1865i −0.647458 + 1.12143i 0.336270 + 0.941766i \(0.390834\pi\)
−0.983728 + 0.179664i \(0.942499\pi\)
\(264\) 0 0
\(265\) 9.00000 + 15.5885i 0.552866 + 0.957591i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.00000 −0.548740 −0.274370 0.961624i \(-0.588469\pi\)
−0.274370 + 0.961624i \(0.588469\pi\)
\(270\) 0 0
\(271\) 28.0000 1.70088 0.850439 0.526073i \(-0.176336\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) 0 0
\(273\) 3.46410i 0.209657i
\(274\) 0 0
\(275\) −12.0000 20.7846i −0.723627 1.25336i
\(276\) 0 0
\(277\) 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) 0 0
\(279\) −3.00000 5.19615i −0.179605 0.311086i
\(280\) 0 0
\(281\) 13.5000 23.3827i 0.805342 1.39489i −0.110717 0.993852i \(-0.535315\pi\)
0.916060 0.401042i \(-0.131352\pi\)
\(282\) 0 0
\(283\) −9.50000 16.4545i −0.564716 0.978117i −0.997076 0.0764162i \(-0.975652\pi\)
0.432360 0.901701i \(-0.357681\pi\)
\(284\) 0 0
\(285\) 31.5000 18.1865i 1.86590 1.07728i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 3.00000 + 1.73205i 0.175863 + 0.101535i
\(292\) 0 0
\(293\) 1.50000 + 2.59808i 0.0876309 + 0.151781i 0.906509 0.422186i \(-0.138737\pi\)
−0.818878 + 0.573967i \(0.805404\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −27.0000 15.5885i −1.56670 0.904534i
\(298\) 0 0
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) −1.00000 1.73205i −0.0576390 0.0998337i
\(302\) 0 0
\(303\) 13.5000 + 7.79423i 0.775555 + 0.447767i
\(304\) 0 0
\(305\) −15.0000 −0.858898
\(306\) 0 0
\(307\) 25.0000 1.42683 0.713413 0.700744i \(-0.247149\pi\)
0.713413 + 0.700744i \(0.247149\pi\)
\(308\) 0 0
\(309\) −15.0000 + 8.66025i −0.853320 + 0.492665i
\(310\) 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
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 0 0
\(315\) −9.00000 −0.507093
\(316\) 0 0
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) −18.0000 31.1769i −1.00781 1.74557i
\(320\) 0 0
\(321\) 20.7846i 1.16008i
\(322\) 0 0
\(323\) 42.0000 2.33694
\(324\) 0 0
\(325\) 8.00000 0.443760
\(326\) 0 0
\(327\) 17.3205i 0.957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 13.0000 22.5167i 0.714545 1.23763i −0.248590 0.968609i \(-0.579967\pi\)
0.963135 0.269019i \(-0.0866994\pi\)
\(332\) 0 0
\(333\) −6.00000 −0.328798
\(334\) 0 0
\(335\) −12.0000 + 20.7846i −0.655630 + 1.13558i
\(336\) 0 0
\(337\) 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i \(0.0378512\pi\)
−0.393730 + 0.919226i \(0.628816\pi\)
\(338\) 0 0
\(339\) −22.5000 + 12.9904i −1.22203 + 0.705541i
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 13.5000 + 7.79423i 0.726816 + 0.419627i
\(346\) 0 0
\(347\) −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i \(-0.943860\pi\)
0.340293 0.940319i \(-0.389474\pi\)
\(348\) 0 0
\(349\) −13.0000 + 22.5167i −0.695874 + 1.20529i 0.274011 + 0.961727i \(0.411649\pi\)
−0.969885 + 0.243563i \(0.921684\pi\)
\(350\) 0 0
\(351\) 9.00000 5.19615i 0.480384 0.277350i
\(352\) 0 0
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) 0 0
\(355\) −4.50000 7.79423i −0.238835 0.413675i
\(356\) 0 0
\(357\) −9.00000 5.19615i −0.476331 0.275010i
\(358\) 0 0
\(359\) 3.00000 0.158334 0.0791670 0.996861i \(-0.474774\pi\)
0.0791670 + 0.996861i \(0.474774\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) −37.5000 + 21.6506i −1.96824 + 1.13636i
\(364\) 0 0
\(365\) 3.00000 + 5.19615i 0.157027 + 0.271979i
\(366\) 0 0
\(367\) 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 0 0
\(373\) −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i \(-0.284725\pi\)
−0.988363 + 0.152115i \(0.951392\pi\)
\(374\) 0 0
\(375\) 5.19615i 0.268328i
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) −2.00000 −0.102733 −0.0513665 0.998680i \(-0.516358\pi\)
−0.0513665 + 0.998680i \(0.516358\pi\)
\(380\) 0 0
\(381\) 29.4449i 1.50851i
\(382\) 0 0
\(383\) −9.00000 15.5885i −0.459879 0.796533i 0.539076 0.842257i \(-0.318774\pi\)
−0.998954 + 0.0457244i \(0.985440\pi\)
\(384\) 0 0
\(385\) −9.00000 + 15.5885i −0.458682 + 0.794461i
\(386\) 0 0
\(387\) −3.00000 + 5.19615i −0.152499 + 0.264135i
\(388\) 0 0
\(389\) −12.0000 + 20.7846i −0.608424 + 1.05382i 0.383076 + 0.923717i \(0.374865\pi\)
−0.991500 + 0.130105i \(0.958469\pi\)
\(390\) 0 0
\(391\) 9.00000 + 15.5885i 0.455150 + 0.788342i
\(392\) 0 0
\(393\) −13.5000 + 7.79423i −0.680985 + 0.393167i
\(394\) 0 0
\(395\) 15.0000 0.754732
\(396\) 0 0
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 0 0
\(399\) −10.5000 6.06218i −0.525657 0.303488i
\(400\) 0 0
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) 2.00000 3.46410i 0.0996271 0.172559i
\(404\) 0 0
\(405\) 13.5000 + 23.3827i 0.670820 + 1.16190i
\(406\) 0 0
\(407\) −6.00000 + 10.3923i −0.297409 + 0.515127i
\(408\) 0 0
\(409\) −16.0000 27.7128i −0.791149 1.37031i −0.925256 0.379344i \(-0.876150\pi\)
0.134107 0.990967i \(-0.457183\pi\)
\(410\) 0 0
\(411\) 9.00000 + 5.19615i 0.443937 + 0.256307i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 36.0000 1.76717
\(416\) 0 0
\(417\) 7.50000 4.33013i 0.367277 0.212047i
\(418\) 0 0
\(419\) 7.50000 + 12.9904i 0.366399 + 0.634622i 0.989000 0.147918i \(-0.0472572\pi\)
−0.622601 + 0.782540i \(0.713924\pi\)
\(420\) 0 0
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.0000 + 20.7846i −0.582086 + 1.00820i
\(426\) 0 0
\(427\) 2.50000 + 4.33013i 0.120983 + 0.209550i
\(428\) 0 0
\(429\) 20.7846i 1.00349i
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 31.1769i 1.49482i
\(436\) 0 0
\(437\) 10.5000 + 18.1865i 0.502283 + 0.869980i
\(438\) 0 0
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) 1.50000 + 2.59808i 0.0714286 + 0.123718i
\(442\) 0 0
\(443\) 9.00000 15.5885i 0.427603 0.740630i −0.569057 0.822298i \(-0.692691\pi\)
0.996660 + 0.0816684i \(0.0260248\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 9.00000 5.19615i 0.425685 0.245770i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −34.5000 19.9186i −1.62095 0.935857i
\(454\) 0 0
\(455\) −3.00000 5.19615i −0.140642 0.243599i
\(456\) 0 0
\(457\) −14.5000 + 25.1147i −0.678281 + 1.17482i 0.297217 + 0.954810i \(0.403942\pi\)
−0.975498 + 0.220008i \(0.929392\pi\)
\(458\) 0 0
\(459\) 31.1769i 1.45521i
\(460\) 0 0
\(461\) 16.5000 28.5788i 0.768482 1.33105i −0.169904 0.985461i \(-0.554346\pi\)
0.938386 0.345589i \(-0.112321\pi\)
\(462\) 0 0
\(463\) −6.50000 11.2583i −0.302081 0.523219i 0.674526 0.738251i \(-0.264348\pi\)
−0.976607 + 0.215032i \(0.931015\pi\)
\(464\) 0 0
\(465\) 9.00000 + 5.19615i 0.417365 + 0.240966i
\(466\) 0 0
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 8.00000 0.369406
\(470\) 0 0
\(471\) 19.5000 11.2583i 0.898513 0.518756i
\(472\) 0 0
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) 0 0
\(475\) −14.0000 + 24.2487i −0.642364 + 1.11261i
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) 0 0
\(479\) −3.00000 + 5.19615i −0.137073 + 0.237418i −0.926388 0.376571i \(-0.877103\pi\)
0.789314 + 0.613990i \(0.210436\pi\)
\(480\) 0 0
\(481\) −2.00000 3.46410i −0.0911922 0.157949i
\(482\) 0 0
\(483\) 5.19615i 0.236433i
\(484\) 0 0
\(485\) −6.00000 −0.272446
\(486\) 0 0
\(487\) −29.0000 −1.31412 −0.657058 0.753840i \(-0.728199\pi\)
−0.657058 + 0.753840i \(0.728199\pi\)
\(488\) 0 0
\(489\) 3.46410i 0.156652i
\(490\) 0 0
\(491\) 9.00000 + 15.5885i 0.406164 + 0.703497i 0.994456 0.105151i \(-0.0335327\pi\)
−0.588292 + 0.808649i \(0.700199\pi\)
\(492\) 0 0
\(493\) −18.0000 + 31.1769i −0.810679 + 1.40414i
\(494\) 0 0
\(495\) 54.0000 2.42712
\(496\) 0 0
\(497\) −1.50000 + 2.59808i −0.0672842 + 0.116540i
\(498\) 0 0
\(499\) 16.0000 + 27.7128i 0.716258 + 1.24060i 0.962472 + 0.271380i \(0.0874801\pi\)
−0.246214 + 0.969216i \(0.579187\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −27.0000 −1.20148
\(506\) 0 0
\(507\) −13.5000 7.79423i −0.599556 0.346154i
\(508\) 0 0
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) 1.00000 1.73205i 0.0442374 0.0766214i
\(512\) 0 0
\(513\) 36.3731i 1.60591i
\(514\) 0 0
\(515\) 15.0000 25.9808i 0.660979 1.14485i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −9.00000 5.19615i −0.395056 0.228086i
\(520\) 0 0
\(521\) 24.0000 1.05146 0.525730 0.850652i \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) 0 0
\(523\) 13.0000 0.568450 0.284225 0.958758i \(-0.408264\pi\)
0.284225 + 0.958758i \(0.408264\pi\)
\(524\) 0 0
\(525\) 6.00000 3.46410i 0.261861 0.151186i
\(526\) 0 0
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 18.0000 + 31.1769i 0.778208 + 1.34790i
\(536\) 0 0
\(537\) 31.1769i 1.34538i
\(538\) 0 0
\(539\) 6.00000 0.258438
\(540\) 0 0
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 0 0
\(543\) 43.3013i 1.85824i
\(544\) 0 0
\(545\) −15.0000 25.9808i −0.642529 1.11289i
\(546\) 0 0
\(547\) 16.0000 27.7128i 0.684111 1.18491i −0.289605 0.957146i \(-0.593524\pi\)
0.973715 0.227768i \(-0.0731428\pi\)
\(548\) 0 0
\(549\) 7.50000 12.9904i 0.320092 0.554416i
\(550\) 0 0
\(551\) −21.0000 + 36.3731i −0.894630 + 1.54954i
\(552\) 0 0
\(553\) −2.50000 4.33013i −0.106311 0.184136i
\(554\) 0 0
\(555\) 9.00000 5.19615i 0.382029 0.220564i
\(556\) 0 0
\(557\) −24.0000 −1.01691 −0.508456 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 54.0000 + 31.1769i 2.27988 + 1.31629i
\(562\) 0 0
\(563\) −16.5000 28.5788i −0.695392 1.20445i −0.970048 0.242912i \(-0.921897\pi\)
0.274656 0.961542i \(-0.411436\pi\)
\(564\) 0 0
\(565\) 22.5000 38.9711i 0.946582 1.63953i
\(566\) 0 0
\(567\) 4.50000 7.79423i 0.188982 0.327327i
\(568\) 0 0
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 0 0
\(571\) 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i \(0.0668588\pi\)
−0.308443 + 0.951243i \(0.599808\pi\)
\(572\) 0 0
\(573\) 13.5000 + 7.79423i 0.563971 + 0.325609i
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −4.00000 −0.166522 −0.0832611 0.996528i \(-0.526534\pi\)
−0.0832611 + 0.996528i \(0.526534\pi\)
\(578\) 0 0
\(579\) −25.5000 + 14.7224i −1.05974 + 0.611843i
\(580\) 0 0
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) −18.0000 + 31.1769i −0.745484 + 1.29122i
\(584\) 0 0
\(585\) −9.00000 + 15.5885i −0.372104 + 0.644503i
\(586\) 0 0
\(587\) −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i \(-0.853053\pi\)
0.833408 + 0.552658i \(0.186386\pi\)
\(588\) 0 0
\(589\) 7.00000 + 12.1244i 0.288430 + 0.499575i
\(590\) 0 0
\(591\) 31.1769i 1.28245i
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 18.0000 0.737928
\(596\) 0 0
\(597\) 24.2487i 0.992434i
\(598\) 0 0
\(599\) −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) 0 0
\(601\) −7.00000 + 12.1244i −0.285536 + 0.494563i −0.972739 0.231903i \(-0.925505\pi\)
0.687203 + 0.726465i \(0.258838\pi\)
\(602\) 0 0
\(603\) −12.0000 20.7846i −0.488678 0.846415i
\(604\) 0 0
\(605\) 37.5000 64.9519i 1.52459 2.64067i
\(606\) 0 0
\(607\) −11.0000 19.0526i −0.446476 0.773320i 0.551678 0.834058i \(-0.313988\pi\)
−0.998154 + 0.0607380i \(0.980655\pi\)
\(608\) 0 0
\(609\) 9.00000 5.19615i 0.364698 0.210559i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 8.00000 0.323117 0.161558 0.986863i \(-0.448348\pi\)
0.161558 + 0.986863i \(0.448348\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.0000 36.3731i −0.845428 1.46432i −0.885249 0.465118i \(-0.846012\pi\)
0.0398207 0.999207i \(-0.487321\pi\)
\(618\) 0 0
\(619\) −3.50000 + 6.06218i −0.140677 + 0.243659i −0.927752 0.373198i \(-0.878261\pi\)
0.787075 + 0.616858i \(0.211595\pi\)
\(620\) 0 0
\(621\) −13.5000 + 7.79423i −0.541736 + 0.312772i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) 63.0000 + 36.3731i 2.51598 + 1.45260i
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) 0 0
\(633\) 12.0000 6.92820i 0.476957 0.275371i
\(634\) 0 0
\(635\) −25.5000 44.1673i −1.01194 1.75273i
\(636\) 0 0
\(637\) −1.00000 + 1.73205i −0.0396214 + 0.0686264i
\(638\) 0 0
\(639\) 9.00000 0.356034
\(640\) 0 0
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) 0 0
\(643\) −2.00000 3.46410i −0.0788723 0.136611i 0.823891 0.566748i \(-0.191799\pi\)
−0.902764 + 0.430137i \(0.858465\pi\)
\(644\) 0 0
\(645\) 10.3923i 0.409197i
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 3.46410i 0.135769i
\(652\) 0 0
\(653\) 18.0000 + 31.1769i 0.704394 + 1.22005i 0.966910 + 0.255119i \(0.0821147\pi\)
−0.262515 + 0.964928i \(0.584552\pi\)
\(654\) 0 0
\(655\) 13.5000 23.3827i 0.527489 0.913637i
\(656\) 0 0
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) 21.0000 36.3731i 0.818044 1.41689i −0.0890776 0.996025i \(-0.528392\pi\)
0.907122 0.420869i \(-0.138275\pi\)
\(660\) 0 0
\(661\) −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i \(-0.197668\pi\)
−0.910541 + 0.413419i \(0.864334\pi\)
\(662\) 0 0
\(663\) −18.0000 + 10.3923i −0.699062 + 0.403604i
\(664\) 0 0
\(665\) 21.0000 0.814345
\(666\) 0 0
\(667\) −18.0000 −0.696963
\(668\) 0 0
\(669\) 42.0000 + 24.2487i 1.62381 + 0.937509i
\(670\) 0 0
\(671\) −15.0000 25.9808i −0.579069 1.00298i
\(672\) 0 0
\(673\) 18.5000 32.0429i 0.713123 1.23516i −0.250557 0.968102i \(-0.580614\pi\)
0.963679 0.267063i \(-0.0860531\pi\)
\(674\) 0 0
\(675\) −18.0000 10.3923i −0.692820 0.400000i
\(676\) 0 0
\(677\) −21.0000 + 36.3731i −0.807096 + 1.39793i 0.107772 + 0.994176i \(0.465628\pi\)
−0.914867 + 0.403755i \(0.867705\pi\)
\(678\) 0 0
\(679\) 1.00000 + 1.73205i 0.0383765 + 0.0664700i
\(680\) 0 0
\(681\) 22.5000 + 12.9904i 0.862202 + 0.497792i
\(682\) 0 0
\(683\) 6.00000 0.229584 0.114792 0.993390i \(-0.463380\pi\)
0.114792 + 0.993390i \(0.463380\pi\)
\(684\) 0 0
\(685\) −18.0000 −0.687745
\(686\) 0 0
\(687\) 1.50000 0.866025i 0.0572286 0.0330409i
\(688\) 0 0
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) 23.5000 40.7032i 0.893982 1.54842i 0.0589228 0.998263i \(-0.481233\pi\)
0.835059 0.550160i \(-0.185433\pi\)
\(692\) 0 0
\(693\) −9.00000 15.5885i −0.341882 0.592157i
\(694\) 0 0
\(695\) −7.50000 + 12.9904i −0.284491 + 0.492753i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 15.5885i 0.589610i
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 14.0000 0.528020
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.50000 + 7.79423i 0.169240 + 0.293132i
\(708\) 0 0
\(709\) 26.0000 45.0333i 0.976450 1.69126i 0.301388 0.953502i \(-0.402550\pi\)
0.675063 0.737760i \(-0.264116\pi\)
\(710\) 0 0
\(711\) −7.50000 + 12.9904i −0.281272 + 0.487177i
\(712\) 0 0
\(713\) −3.00000 + 5.19615i −0.112351 + 0.194597i
\(714\) 0 0
\(715\) 18.0000 + 31.1769i 0.673162 + 1.16595i
\(716\) 0 0
\(717\) −22.5000 + 12.9904i −0.840278 + 0.485135i
\(718\) 0 0
\(719\) 36.0000 1.34257 0.671287 0.741198i \(-0.265742\pi\)
0.671287 + 0.741198i \(0.265742\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) 0 0
\(723\) 12.0000 + 6.92820i 0.446285 + 0.257663i
\(724\) 0 0
\(725\) −12.0000 20.7846i −0.445669 0.771921i
\(726\) 0 0
\(727\) 4.00000 6.92820i 0.148352 0.256953i −0.782267 0.622944i \(-0.785937\pi\)
0.930618 + 0.365991i \(0.119270\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 6.00000 10.3923i 0.221918 0.384373i
\(732\) 0 0
\(733\) −14.5000 25.1147i −0.535570 0.927634i −0.999136 0.0415715i \(-0.986764\pi\)
0.463566 0.886062i \(-0.346570\pi\)
\(734\) 0 0
\(735\) −4.50000 2.59808i −0.165985 0.0958315i
\(736\) 0 0
\(737\) −48.0000 −1.76810
\(738\) 0 0
\(739\) −26.0000 −0.956425 −0.478213 0.878244i \(-0.658715\pi\)
−0.478213 + 0.878244i \(0.658715\pi\)
\(740\) 0 0
\(741\) −21.0000 + 12.1244i −0.771454 + 0.445399i
\(742\) 0 0
\(743\) 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i \(0.0629279\pi\)
−0.320166 + 0.947361i \(0.603739\pi\)
\(744\) 0 0
\(745\) −9.00000 + 15.5885i −0.329734 + 0.571117i
\(746\) 0 0
\(747\) −18.0000 + 31.1769i −0.658586 + 1.14070i
\(748\) 0 0
\(749\) 6.00000 10.3923i 0.219235 0.379727i
\(750\) 0 0
\(751\) −15.5000 26.8468i −0.565603 0.979653i −0.996993 0.0774878i \(-0.975310\pi\)
0.431390 0.902165i \(-0.358023\pi\)
\(752\) 0 0
\(753\) 5.19615i 0.189358i
\(754\) 0 0
\(755\) 69.0000 2.51117
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 0 0
\(759\) 31.1769i 1.13165i
\(760\) 0 0
\(761\) 21.0000 + 36.3731i 0.761249 + 1.31852i 0.942207 + 0.335032i \(0.108747\pi\)
−0.180957 + 0.983491i \(0.557920\pi\)
\(762\) 0 0
\(763\) −5.00000 + 8.66025i −0.181012 + 0.313522i
\(764\) 0 0
\(765\) −27.0000 46.7654i −0.976187 1.69081i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) 0 0
\(771\) −27.0000 + 15.5885i −0.972381 + 0.561405i
\(772\) 0 0
\(773\) −51.0000 −1.83434 −0.917171 0.398493i \(-0.869533\pi\)
−0.917171 + 0.398493i \(0.869533\pi\)
\(774\) 0 0
\(775\) −8.00000 −0.287368
\(776\) 0 0
\(777\) −3.00000 1.73205i −0.107624 0.0621370i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 15.5885i 0.322045 0.557799i
\(782\) 0 0
\(783\) −27.0000 15.5885i −0.964901 0.557086i
\(784\) 0 0
\(785\) −19.5000 + 33.7750i −0.695985 + 1.20548i
\(786\) 0 0
\(787\) 10.0000 + 17.3205i 0.356462 + 0.617409i 0.987367 0.158450i \(-0.0506498\pi\)
−0.630905 + 0.775860i \(0.717316\pi\)
\(788\) 0 0
\(789\) 31.5000 + 18.1865i 1.12143 + 0.647458i
\(790\) 0 0
\(791\) −15.0000 −0.533339
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) 0 0
\(795\) 27.0000 15.5885i 0.957591 0.552866i
\(796\) 0 0
\(797\) −1.50000 2.59808i −0.0531327 0.0920286i 0.838236 0.545308i \(-0.183587\pi\)
−0.891368 + 0.453279i \(0.850254\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −6.00000 + 10.3923i −0.211735 + 0.366736i
\(804\) 0 0
\(805\) 4.50000 + 7.79423i 0.158604 + 0.274710i
\(806\) 0 0
\(807\) 15.5885i 0.548740i
\(808\) 0 0
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 0 0
\(811\) 16.0000 0.561836 0.280918 0.959732i