Properties

Label 336.2.q.b.193.1
Level $336$
Weight $2$
Character 336.193
Analytic conductor $2.683$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
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 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.2.q.b.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.50000 - 4.33013i) q^{11} +1.00000 q^{15} +(2.00000 - 3.46410i) q^{17} +(4.00000 + 6.92820i) q^{19} +(2.50000 + 0.866025i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} +1.00000 q^{27} -5.00000 q^{29} +(1.50000 - 2.59808i) q^{31} +(2.50000 + 4.33013i) q^{33} +(-2.00000 + 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} -2.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{51} +(4.50000 - 7.79423i) q^{53} -5.00000 q^{55} -8.00000 q^{57} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-2.00000 + 1.73205i) q^{63} +(-1.00000 + 1.73205i) q^{67} +4.00000 q^{69} -2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(2.00000 + 3.46410i) q^{75} +(-12.5000 - 4.33013i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.00000 q^{83} -4.00000 q^{85} +(2.50000 - 4.33013i) q^{87} +(3.00000 + 5.19615i) q^{89} +(1.50000 + 2.59808i) q^{93} +(4.00000 - 6.92820i) q^{95} +7.00000 q^{97} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - q^{5} - q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - q^{5} - q^{7} - q^{9} + 5q^{11} + 2q^{15} + 4q^{17} + 8q^{19} + 5q^{21} - 4q^{23} + 4q^{25} + 2q^{27} - 10q^{29} + 3q^{31} + 5q^{33} - 4q^{35} + 4q^{37} - 4q^{43} - q^{45} - 6q^{47} - 13q^{49} + 4q^{51} + 9q^{53} - 10q^{55} - 16q^{57} - 11q^{59} + 6q^{61} - 4q^{63} - 2q^{67} + 8q^{69} - 4q^{71} - 10q^{73} + 4q^{75} - 25q^{77} + 3q^{79} - q^{81} + 14q^{83} - 8q^{85} + 5q^{87} + 6q^{89} + 3q^{93} + 8q^{95} + 14q^{97} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 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 −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 0 0
\(19\) 4.00000 + 6.92820i 0.917663 + 1.58944i 0.802955 + 0.596040i \(0.203260\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 2.50000 + 0.866025i 0.545545 + 0.188982i
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) 1.50000 2.59808i 0.269408 0.466628i −0.699301 0.714827i \(-0.746505\pi\)
0.968709 + 0.248199i \(0.0798387\pi\)
\(32\) 0 0
\(33\) 2.50000 + 4.33013i 0.435194 + 0.753778i
\(34\) 0 0
\(35\) −2.00000 + 1.73205i −0.338062 + 0.292770i
\(36\) 0 0
\(37\) 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) 2.00000 + 3.46410i 0.280056 + 0.485071i
\(52\) 0 0
\(53\) 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i \(-0.621227\pi\)
0.989828 0.142269i \(-0.0454398\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) −8.00000 −1.05963
\(58\) 0 0
\(59\) −5.50000 + 9.52628i −0.716039 + 1.24022i 0.246518 + 0.969138i \(0.420713\pi\)
−0.962557 + 0.271078i \(0.912620\pi\)
\(60\) 0 0
\(61\) 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) 0 0
\(63\) −2.00000 + 1.73205i −0.251976 + 0.218218i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) −5.00000 + 8.66025i −0.585206 + 1.01361i 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 0 0
\(75\) 2.00000 + 3.46410i 0.230940 + 0.400000i
\(76\) 0 0
\(77\) −12.5000 4.33013i −1.42451 0.493464i
\(78\) 0 0
\(79\) 1.50000 + 2.59808i 0.168763 + 0.292306i 0.937985 0.346675i \(-0.112689\pi\)
−0.769222 + 0.638982i \(0.779356\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 7.00000 0.768350 0.384175 0.923260i \(-0.374486\pi\)
0.384175 + 0.923260i \(0.374486\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) 2.50000 4.33013i 0.268028 0.464238i
\(88\) 0 0
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.50000 + 2.59808i 0.155543 + 0.269408i
\(94\) 0 0
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 0 0
\(99\) −5.00000 −0.502519
\(100\) 0 0
\(101\) −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 0 0
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) 0 0
\(105\) −0.500000 2.59808i −0.0487950 0.253546i
\(106\) 0 0
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 0 0
\(115\) −2.00000 + 3.46410i −0.186501 + 0.323029i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.0000 3.46410i −0.916698 0.317554i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) −9.00000 −0.798621 −0.399310 0.916816i \(-0.630750\pi\)
−0.399310 + 0.916816i \(0.630750\pi\)
\(128\) 0 0
\(129\) 1.00000 1.73205i 0.0880451 0.152499i
\(130\) 0 0
\(131\) 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i \(-0.152757\pi\)
−0.843356 + 0.537355i \(0.819423\pi\)
\(132\) 0 0
\(133\) 16.0000 13.8564i 1.38738 1.20150i
\(134\) 0 0
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) 0 0
\(137\) 1.00000 1.73205i 0.0854358 0.147979i −0.820141 0.572161i \(-0.806105\pi\)
0.905577 + 0.424182i \(0.139438\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 2.50000 + 4.33013i 0.207614 + 0.359597i
\(146\) 0 0
\(147\) 1.00000 6.92820i 0.0824786 0.571429i
\(148\) 0 0
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 9.50000 16.4545i 0.773099 1.33905i −0.162758 0.986666i \(-0.552039\pi\)
0.935857 0.352381i \(-0.114628\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −3.00000 −0.240966
\(156\) 0 0
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) 0 0
\(159\) 4.50000 + 7.79423i 0.356873 + 0.618123i
\(160\) 0 0
\(161\) −8.00000 + 6.92820i −0.630488 + 0.546019i
\(162\) 0 0
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) 0 0
\(165\) 2.50000 4.33013i 0.194625 0.337100i
\(166\) 0 0
\(167\) 14.0000 1.08335 0.541676 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 4.00000 6.92820i 0.305888 0.529813i
\(172\) 0 0
\(173\) −11.0000 19.0526i −0.836315 1.44854i −0.892956 0.450145i \(-0.851372\pi\)
0.0566411 0.998395i \(-0.481961\pi\)
\(174\) 0 0
\(175\) −10.0000 3.46410i −0.755929 0.261861i
\(176\) 0 0
\(177\) −5.50000 9.52628i −0.413405 0.716039i
\(178\) 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
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) 0 0
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) 0 0
\(187\) −10.0000 17.3205i −0.731272 1.26660i
\(188\) 0 0
\(189\) −0.500000 2.59808i −0.0363696 0.188982i
\(190\) 0 0
\(191\) 12.0000 + 20.7846i 0.868290 + 1.50392i 0.863743 + 0.503932i \(0.168114\pi\)
0.00454614 + 0.999990i \(0.498553\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 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
\(201\) −1.00000 1.73205i −0.0705346 0.122169i
\(202\) 0 0
\(203\) 2.50000 + 12.9904i 0.175466 + 0.911746i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2.00000 + 3.46410i −0.139010 + 0.240772i
\(208\) 0 0
\(209\) 40.0000 2.76686
\(210\) 0 0
\(211\) −2.00000 −0.137686 −0.0688428 0.997628i \(-0.521931\pi\)
−0.0688428 + 0.997628i \(0.521931\pi\)
\(212\) 0 0
\(213\) 1.00000 1.73205i 0.0685189 0.118678i
\(214\) 0 0
\(215\) 1.00000 + 1.73205i 0.0681994 + 0.118125i
\(216\) 0 0
\(217\) −7.50000 2.59808i −0.509133 0.176369i
\(218\) 0 0
\(219\) −5.00000 8.66025i −0.337869 0.585206i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 7.00000 0.468755 0.234377 0.972146i \(-0.424695\pi\)
0.234377 + 0.972146i \(0.424695\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) 0 0
\(227\) 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 0 0
\(229\) 10.0000 + 17.3205i 0.660819 + 1.14457i 0.980401 + 0.197013i \(0.0631241\pi\)
−0.319582 + 0.947559i \(0.603543\pi\)
\(230\) 0 0
\(231\) 10.0000 8.66025i 0.657952 0.569803i
\(232\) 0 0
\(233\) 2.00000 + 3.46410i 0.131024 + 0.226941i 0.924072 0.382219i \(-0.124840\pi\)
−0.793047 + 0.609160i \(0.791507\pi\)
\(234\) 0 0
\(235\) −3.00000 + 5.19615i −0.195698 + 0.338960i
\(236\) 0 0
\(237\) −3.00000 −0.194871
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i \(-0.535394\pi\)
0.916159 0.400815i \(-0.131273\pi\)
\(242\) 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
\(247\) 0 0
\(248\) 0 0
\(249\) −3.50000 + 6.06218i −0.221803 + 0.384175i
\(250\) 0 0
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 0 0
\(255\) 2.00000 3.46410i 0.125245 0.216930i
\(256\) 0 0
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) 8.00000 6.92820i 0.497096 0.430498i
\(260\) 0 0
\(261\) 2.50000 + 4.33013i 0.154746 + 0.268028i
\(262\) 0 0
\(263\) −15.0000 + 25.9808i −0.924940 + 1.60204i −0.133281 + 0.991078i \(0.542551\pi\)
−0.791658 + 0.610964i \(0.790782\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) 0 0
\(269\) −15.5000 + 26.8468i −0.945052 + 1.63688i −0.189404 + 0.981899i \(0.560656\pi\)
−0.755648 + 0.654978i \(0.772678\pi\)
\(270\) 0 0
\(271\) 7.50000 + 12.9904i 0.455593 + 0.789109i 0.998722 0.0505395i \(-0.0160941\pi\)
−0.543130 + 0.839649i \(0.682761\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −10.0000 17.3205i −0.603023 1.04447i
\(276\) 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 −0.179605
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 0 0
\(283\) 5.00000 8.66025i 0.297219 0.514799i −0.678280 0.734804i \(-0.737274\pi\)
0.975499 + 0.220005i \(0.0706075\pi\)
\(284\) 0 0
\(285\) 4.00000 + 6.92820i 0.236940 + 0.410391i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) −3.50000 + 6.06218i −0.205174 + 0.355371i
\(292\) 0 0
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 0 0
\(295\) 11.0000 0.640445
\(296\) 0 0
\(297\) 2.50000 4.33013i 0.145065 0.251259i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 1.00000 + 5.19615i 0.0576390 + 0.299501i
\(302\) 0 0
\(303\) −5.00000 8.66025i −0.287242 0.497519i
\(304\) 0 0
\(305\) 3.00000 5.19615i 0.171780 0.297531i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) −16.0000 + 27.7128i −0.907277 + 1.57145i −0.0894452 + 0.995992i \(0.528509\pi\)
−0.817832 + 0.575458i \(0.804824\pi\)
\(312\) 0 0
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) 0 0
\(315\) 2.50000 + 0.866025i 0.140859 + 0.0487950i
\(316\) 0 0
\(317\) −1.50000 2.59808i −0.0842484 0.145922i 0.820822 0.571184i \(-0.193516\pi\)
−0.905071 + 0.425261i \(0.860182\pi\)
\(318\) 0 0
\(319\) −12.5000 + 21.6506i −0.699866 + 1.21220i
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) 0 0
\(323\) 32.0000 1.78053
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.00000 + 1.73205i 0.0553001 + 0.0957826i
\(328\) 0 0
\(329\) −12.0000 + 10.3923i −0.661581 + 0.572946i
\(330\) 0 0
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) 0 0
\(333\) 2.00000 3.46410i 0.109599 0.189832i
\(334\) 0 0
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) 9.00000 0.490261 0.245131 0.969490i \(-0.421169\pi\)
0.245131 + 0.969490i \(0.421169\pi\)
\(338\) 0 0
\(339\) −8.00000 + 13.8564i −0.434500 + 0.752577i
\(340\) 0 0
\(341\) −7.50000 12.9904i −0.406148 0.703469i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) −2.00000 3.46410i −0.107676 0.186501i
\(346\) 0 0
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 0 0
\(355\) 1.00000 + 1.73205i 0.0530745 + 0.0919277i
\(356\) 0 0
\(357\) 8.00000 6.92820i 0.423405 0.366679i
\(358\) 0 0
\(359\) 5.00000 + 8.66025i 0.263890 + 0.457071i 0.967272 0.253741i \(-0.0816611\pi\)
−0.703382 + 0.710812i \(0.748328\pi\)
\(360\) 0 0
\(361\) −22.5000 + 38.9711i −1.18421 + 2.05111i
\(362\) 0 0
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) 0 0
\(367\) 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i \(-0.687000\pi\)
0.997960 + 0.0638362i \(0.0203335\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −22.5000 7.79423i −1.16814 0.404656i
\(372\) 0 0
\(373\) 16.0000 + 27.7128i 0.828449 + 1.43492i 0.899255 + 0.437425i \(0.144109\pi\)
−0.0708063 + 0.997490i \(0.522557\pi\)
\(374\) 0 0
\(375\) 4.50000 7.79423i 0.232379 0.402492i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 4.50000 7.79423i 0.230542 0.399310i
\(382\) 0 0
\(383\) −17.0000 29.4449i −0.868659 1.50456i −0.863367 0.504576i \(-0.831649\pi\)
−0.00529229 0.999986i \(-0.501685\pi\)
\(384\) 0 0
\(385\) 2.50000 + 12.9904i 0.127412 + 0.662051i
\(386\) 0 0
\(387\) 1.00000 + 1.73205i 0.0508329 + 0.0880451i
\(388\) 0 0
\(389\) 1.00000 1.73205i 0.0507020 0.0878185i −0.839561 0.543266i \(-0.817187\pi\)
0.890263 + 0.455448i \(0.150521\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) −1.00000 −0.0504433
\(394\) 0 0
\(395\) 1.50000 2.59808i 0.0754732 0.130723i
\(396\) 0 0
\(397\) −18.0000 31.1769i −0.903394 1.56472i −0.823058 0.567957i \(-0.807734\pi\)
−0.0803356 0.996768i \(-0.525599\pi\)
\(398\) 0 0
\(399\) 4.00000 + 20.7846i 0.200250 + 1.04053i
\(400\) 0 0
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 20.0000 0.991363
\(408\) 0 0
\(409\) 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i \(-0.621242\pi\)
0.989835 0.142222i \(-0.0454247\pi\)
\(410\) 0 0
\(411\) 1.00000 + 1.73205i 0.0493264 + 0.0854358i
\(412\) 0 0
\(413\) 27.5000 + 9.52628i 1.35319 + 0.468758i
\(414\) 0 0
\(415\) −3.50000 6.06218i −0.171808 0.297581i
\(416\) 0 0
\(417\) −7.00000 + 12.1244i −0.342791 + 0.593732i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) −8.00000 13.8564i −0.388057 0.672134i
\(426\) 0 0
\(427\) 12.0000 10.3923i 0.580721 0.502919i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) −5.00000 −0.239732
\(436\) 0 0
\(437\) 16.0000 27.7128i 0.765384 1.32568i
\(438\) 0 0
\(439\) 7.50000 + 12.9904i 0.357955 + 0.619997i 0.987619 0.156871i \(-0.0501406\pi\)
−0.629664 + 0.776868i \(0.716807\pi\)
\(440\) 0 0
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) 8.50000 + 14.7224i 0.403847 + 0.699484i 0.994187 0.107671i \(-0.0343394\pi\)
−0.590339 + 0.807155i \(0.701006\pi\)
\(444\) 0 0
\(445\) 3.00000 5.19615i 0.142214 0.246321i
\(446\) 0 0
\(447\) −18.0000 −0.851371
\(448\) 0 0
\(449\) 16.0000 0.755087 0.377543 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 9.50000 + 16.4545i 0.446349 + 0.773099i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15.5000 26.8468i −0.725059 1.25584i −0.958950 0.283577i \(-0.908479\pi\)
0.233890 0.972263i \(-0.424854\pi\)
\(458\) 0 0
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 1.50000 2.59808i 0.0695608 0.120483i
\(466\) 0 0
\(467\) −10.0000 17.3205i −0.462745 0.801498i 0.536352 0.843995i \(-0.319802\pi\)
−0.999097 + 0.0424970i \(0.986469\pi\)
\(468\) 0 0
\(469\) 5.00000 + 1.73205i 0.230879 + 0.0799787i
\(470\) 0 0
\(471\) 2.00000 + 3.46410i 0.0921551 + 0.159617i
\(472\) 0 0
\(473\) −5.00000 + 8.66025i −0.229900 + 0.398199i
\(474\) 0 0
\(475\) 32.0000 1.46826
\(476\) 0 0
\(477\) −9.00000 −0.412082
\(478\) 0 0
\(479\) 19.0000 32.9090i 0.868132 1.50365i 0.00422900 0.999991i \(-0.498654\pi\)
0.863903 0.503658i \(-0.168013\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −2.00000 10.3923i −0.0910032 0.472866i
\(484\) 0 0
\(485\) −3.50000 6.06218i −0.158927 0.275269i
\(486\) 0 0
\(487\) 2.50000 4.33013i 0.113286 0.196217i −0.803807 0.594890i \(-0.797196\pi\)
0.917093 + 0.398673i \(0.130529\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) −9.00000 −0.406164 −0.203082 0.979162i \(-0.565096\pi\)
−0.203082 + 0.979162i \(0.565096\pi\)
\(492\) 0 0
\(493\) −10.0000 + 17.3205i −0.450377 + 0.780076i
\(494\) 0 0
\(495\) 2.50000 + 4.33013i 0.112367 + 0.194625i
\(496\) 0 0
\(497\) 1.00000 + 5.19615i 0.0448561 + 0.233079i
\(498\) 0 0
\(499\) 5.00000 + 8.66025i 0.223831 + 0.387686i 0.955968 0.293471i \(-0.0948104\pi\)
−0.732137 + 0.681157i \(0.761477\pi\)
\(500\) 0 0
\(501\) −7.00000 + 12.1244i −0.312737 + 0.541676i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) 6.50000 11.2583i 0.288675 0.500000i
\(508\) 0 0
\(509\) −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i \(-0.274536\pi\)
−0.982988 + 0.183669i \(0.941202\pi\)
\(510\) 0 0
\(511\) 25.0000 + 8.66025i 1.10593 + 0.383107i
\(512\) 0 0
\(513\) 4.00000 + 6.92820i 0.176604 + 0.305888i
\(514\) 0 0
\(515\) 4.00000 6.92820i 0.176261 0.305293i
\(516\) 0 0
\(517\) −30.0000 −1.31940
\(518\) 0 0
\(519\) 22.0000 0.965693
\(520\) 0 0
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) 0 0
\(523\) 4.00000 + 6.92820i 0.174908 + 0.302949i 0.940129 0.340818i \(-0.110704\pi\)
−0.765222 + 0.643767i \(0.777371\pi\)
\(524\) 0 0
\(525\) 8.00000 6.92820i 0.349149 0.302372i
\(526\) 0 0
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 11.0000 0.477359
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 1.50000 2.59808i 0.0648507 0.112325i
\(536\) 0 0
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 0 0
\(539\) −5.00000 + 34.6410i −0.215365 + 1.49209i
\(540\) 0 0
\(541\) 9.00000 + 15.5885i 0.386940 + 0.670200i 0.992036 0.125952i \(-0.0401986\pi\)
−0.605096 + 0.796152i \(0.706865\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 0 0
\(549\) 3.00000 5.19615i 0.128037 0.221766i
\(550\) 0 0
\(551\) −20.0000 34.6410i −0.852029 1.47576i
\(552\) 0 0
\(553\) 6.00000 5.19615i 0.255146 0.220963i
\(554\) 0 0
\(555\) 2.00000 + 3.46410i 0.0848953 + 0.147043i
\(556\) 0 0
\(557\) 11.5000 19.9186i 0.487271 0.843978i −0.512622 0.858614i \(-0.671326\pi\)
0.999893 + 0.0146368i \(0.00465919\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 20.0000 0.844401
\(562\) 0 0
\(563\) 8.50000 14.7224i 0.358232 0.620477i −0.629433 0.777055i \(-0.716713\pi\)
0.987666 + 0.156578i \(0.0500463\pi\)
\(564\) 0 0
\(565\) −8.00000 13.8564i −0.336563 0.582943i
\(566\) 0 0
\(567\) 2.50000 + 0.866025i 0.104990 + 0.0363696i
\(568\) 0 0
\(569\) −12.0000 20.7846i −0.503066 0.871336i −0.999994 0.00354413i \(-0.998872\pi\)
0.496928 0.867792i \(-0.334461\pi\)
\(570\) 0 0
\(571\) −15.0000 + 25.9808i −0.627730 + 1.08726i 0.360276 + 0.932846i \(0.382683\pi\)
−0.988006 + 0.154415i \(0.950651\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) 0 0
\(575\) −16.0000 −0.667246
\(576\) 0 0
\(577\) −15.5000 + 26.8468i −0.645273 + 1.11765i 0.338965 + 0.940799i \(0.389923\pi\)
−0.984238 + 0.176847i \(0.943410\pi\)
\(578\) 0 0
\(579\) −2.50000 4.33013i −0.103896 0.179954i
\(580\) 0 0
\(581\) −3.50000 18.1865i −0.145204 0.754505i
\(582\) 0 0
\(583\) −22.5000 38.9711i −0.931855 1.61402i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −35.0000 −1.44460 −0.722302 0.691577i \(-0.756916\pi\)
−0.722302 + 0.691577i \(0.756916\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) 0 0
\(591\) −1.00000 + 1.73205i −0.0411345 + 0.0712470i
\(592\) 0 0
\(593\) −18.0000 31.1769i −0.739171 1.28028i −0.952869 0.303383i \(-0.901884\pi\)
0.213697 0.976900i \(-0.431449\pi\)
\(594\) 0 0
\(595\) 2.00000 + 10.3923i 0.0819920 + 0.426043i
\(596\) 0 0
\(597\) −2.00000 3.46410i −0.0818546 0.141776i
\(598\) 0 0
\(599\) −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(600\) 0 0
\(601\) 35.0000 1.42768 0.713840 0.700309i \(-0.246954\pi\)
0.713840 + 0.700309i \(0.246954\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) 0 0
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 0 0
\(607\) −13.5000 23.3827i −0.547948 0.949074i −0.998415 0.0562808i \(-0.982076\pi\)
0.450467 0.892793i \(-0.351258\pi\)
\(608\) 0 0
\(609\) −12.5000 4.33013i −0.506526 0.175466i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −6.00000 + 10.3923i −0.242338 + 0.419741i −0.961380 0.275225i \(-0.911248\pi\)
0.719042 + 0.694967i \(0.244581\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 0 0
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) 0 0
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) 0 0
\(623\) 12.0000 10.3923i 0.480770 0.416359i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) −20.0000 + 34.6410i −0.798723 + 1.38343i
\(628\) 0 0
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) 19.0000 0.756378 0.378189 0.925728i \(-0.376547\pi\)
0.378189 + 0.925728i \(0.376547\pi\)
\(632\) 0 0
\(633\) 1.00000 1.73205i 0.0397464 0.0688428i
\(634\) 0 0
\(635\) 4.50000 + 7.79423i 0.178577 + 0.309305i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) −13.0000 + 22.5167i −0.513469 + 0.889355i 0.486409 + 0.873731i \(0.338307\pi\)
−0.999878 + 0.0156233i \(0.995027\pi\)
\(642\) 0 0
\(643\) −14.0000 −0.552106 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(644\) 0 0
\(645\) −2.00000 −0.0787499
\(646\) 0 0
\(647\) −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i \(-0.948453\pi\)
0.633090 + 0.774078i \(0.281786\pi\)
\(648\) 0 0
\(649\) 27.5000 + 47.6314i 1.07947 + 1.86970i
\(650\) 0 0
\(651\) 6.00000 5.19615i 0.235159 0.203653i
\(652\) 0 0
\(653\) 19.5000 + 33.7750i 0.763094 + 1.32172i 0.941248 + 0.337715i \(0.109654\pi\)
−0.178154 + 0.984003i \(0.557013\pi\)
\(654\) 0 0
\(655\) 0.500000 0.866025i 0.0195366 0.0338384i
\(656\) 0 0
\(657\) 10.0000 0.390137
\(658\) 0 0
\(659\) 40.0000 1.55818 0.779089 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 0 0
\(661\) −5.00000 + 8.66025i −0.194477 + 0.336845i −0.946729 0.322031i \(-0.895634\pi\)
0.752252 + 0.658876i \(0.228968\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −20.0000 6.92820i −0.775567 0.268664i
\(666\) 0 0
\(667\) 10.0000 + 17.3205i 0.387202 + 0.670653i
\(668\) 0 0
\(669\) −3.50000 + 6.06218i −0.135318 + 0.234377i
\(670\) 0 0
\(671\) 30.0000 1.15814
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 0 0
\(675\) 2.00000 3.46410i 0.0769800 0.133333i
\(676\) 0 0
\(677\) 13.5000 + 23.3827i 0.518847 + 0.898670i 0.999760 + 0.0219013i \(0.00697196\pi\)
−0.480913 + 0.876768i \(0.659695\pi\)
\(678\) 0 0
\(679\) −3.50000 18.1865i −0.134318 0.697935i
\(680\) 0 0
\(681\) 1.50000 + 2.59808i 0.0574801 + 0.0995585i
\(682\) 0 0
\(683\) −4.50000 + 7.79423i −0.172188 + 0.298238i −0.939184 0.343413i \(-0.888417\pi\)
0.766997 + 0.641651i \(0.221750\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) −20.0000 −0.763048
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i \(-0.118041\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 0 0
\(693\) 2.50000 + 12.9904i 0.0949671 + 0.493464i
\(694\) 0 0
\(695\) −7.00000 12.1244i −0.265525 0.459903i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −4.00000 −0.151294
\(700\) 0 0
\(701\) −5.00000 −0.188847 −0.0944237 0.995532i \(-0.530101\pi\)
−0.0944237 + 0.995532i \(0.530101\pi\)
\(702\) 0 0
\(703\) −16.0000 + 27.7128i −0.603451 + 1.04521i
\(704\) 0 0
\(705\) −3.00000 5.19615i −0.112987 0.195698i
\(706\) 0 0
\(707\) 25.0000 + 8.66025i 0.940222 + 0.325702i
\(708\) 0 0
\(709\) −19.0000 32.9090i −0.713560 1.23592i −0.963512 0.267664i \(-0.913748\pi\)
0.249952 0.968258i \(-0.419585\pi\)
\(710\) 0 0
\(711\) 1.50000 2.59808i 0.0562544 0.0974355i
\(712\) 0 0
\(713\) −12.0000 −0.449404
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) 0 0
\(719\) −3.00000 5.19615i −0.111881 0.193784i 0.804648 0.593753i \(-0.202354\pi\)
−0.916529 + 0.399969i \(0.869021\pi\)
\(720\) 0 0
\(721\) 16.0000 13.8564i 0.595871 0.516040i
\(722\) 0 0
\(723\) 12.5000 + 21.6506i 0.464880 + 0.805196i
\(724\) 0 0
\(725\) −10.0000 + 17.3205i −0.371391 + 0.643268i
\(726\) 0 0
\(727\) −7.00000 −0.259616 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.00000 + 6.92820i −0.147945 + 0.256249i
\(732\) 0 0
\(733\) 3.00000 + 5.19615i 0.110808 + 0.191924i 0.916096 0.400959i \(-0.131323\pi\)
−0.805289 + 0.592883i \(0.797990\pi\)
\(734\) 0 0
\(735\) −6.50000 + 2.59808i −0.239756 + 0.0958315i
\(736\) 0 0
\(737\) 5.00000 + 8.66025i 0.184177 + 0.319005i
\(738\) 0 0
\(739\) −15.0000 + 25.9808i −0.551784 + 0.955718i 0.446362 + 0.894852i \(0.352719\pi\)
−0.998146 + 0.0608653i \(0.980614\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30.0000 −1.10059 −0.550297 0.834969i \(-0.685485\pi\)
−0.550297 + 0.834969i \(0.685485\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 0 0
\(747\) −3.50000 6.06218i −0.128058 0.221803i
\(748\) 0 0
\(749\) 6.00000 5.19615i 0.219235 0.189863i
\(750\) 0 0
\(751\) 22.5000 + 38.9711i 0.821037 + 1.42208i 0.904911 + 0.425601i \(0.139937\pi\)
−0.0838743 + 0.996476i \(0.526729\pi\)
\(752\) 0 0
\(753\) 10.5000 18.1865i 0.382641 0.662754i
\(754\) 0 0
\(755\) −19.0000 −0.691481
\(756\) 0 0
\(757\) −54.0000 −1.96266 −0.981332 0.192323i \(-0.938398\pi\)
−0.981332 + 0.192323i \(0.938398\pi\)
\(758\) 0 0
\(759\) 10.0000 17.3205i 0.362977 0.628695i
\(760\) 0 0
\(761\) −4.00000 6.92820i −0.145000 0.251147i 0.784373 0.620289i \(-0.212985\pi\)
−0.929373 + 0.369142i \(0.879652\pi\)
\(762\) 0 0
\(763\) −5.00000 1.73205i −0.181012 0.0627044i
\(764\) 0 0
\(765\) 2.00000 + 3.46410i 0.0723102 + 0.125245i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −35.0000 −1.26213 −0.631066 0.775729i \(-0.717382\pi\)
−0.631066 + 0.775729i \(0.717382\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 0 0
\(773\) −5.00000 + 8.66025i −0.179838 + 0.311488i −0.941825 0.336104i \(-0.890891\pi\)
0.761987 + 0.647592i \(0.224224\pi\)
\(774\) 0 0
\(775\) −6.00000 10.3923i −0.215526 0.373303i
\(776\) 0 0
\(777\) 2.00000 + 10.3923i 0.0717496 + 0.372822i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) 0 0
\(783\) −5.00000 −0.178685
\(784\) 0 0
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) −9.00000 + 15.5885i −0.320815 + 0.555668i −0.980656 0.195737i \(-0.937290\pi\)
0.659841 + 0.751405i \(0.270624\pi\)
\(788\) 0 0
\(789\) −15.0000 25.9808i −0.534014 0.924940i
\(790\) 0 0
\(791\) −8.00000 41.5692i −0.284447 1.47803i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 4.50000 7.79423i 0.159599 0.276433i
\(796\) 0 0
\(797\) 21.0000 0.743858 0.371929 0.928261i \(-0.378696\pi\)
0.371929 + 0.928261i \(0.378696\pi\)
\(798\)