Properties

Label 1053.2.e.b.703.1
Level $1053$
Weight $2$
Character 1053.703
Analytic conductor $8.408$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.40824733284\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 703.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1053.703
Dual form 1053.2.e.b.352.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(2.00000 - 3.46410i) q^{7} -3.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(2.00000 - 3.46410i) q^{7} -3.00000 q^{8} +2.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(2.00000 + 3.46410i) q^{14} +(0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +(1.00000 - 1.73205i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +4.00000 q^{28} +(5.00000 - 8.66025i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{34} -8.00000 q^{35} -2.00000 q^{37} +(3.00000 + 5.19615i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(6.00000 - 10.3923i) q^{43} -4.00000 q^{44} +(-4.50000 - 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.500000 - 0.866025i) q^{52} +6.00000 q^{53} +8.00000 q^{55} +(-6.00000 + 10.3923i) q^{56} +(5.00000 + 8.66025i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +7.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(4.00000 + 6.92820i) q^{67} +(1.00000 + 1.73205i) q^{68} +(4.00000 - 6.92820i) q^{70} +2.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(8.00000 + 13.8564i) q^{77} +(-4.00000 + 6.92820i) q^{79} -2.00000 q^{80} +6.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-2.00000 - 3.46410i) q^{85} +(6.00000 + 10.3923i) q^{86} +(6.00000 - 10.3923i) q^{88} -2.00000 q^{89} -4.00000 q^{91} +(-5.00000 + 8.66025i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} + 4 q^{10} - 4 q^{11} - q^{13} + 4 q^{14} + q^{16} + 4 q^{17} + 2 q^{20} - 4 q^{22} + q^{25} + 2 q^{26} + 8 q^{28} + 10 q^{29} - 4 q^{31} - 5 q^{32} - 2 q^{34} - 16 q^{35} - 4 q^{37} + 6 q^{40} - 6 q^{41} + 12 q^{43} - 8 q^{44} - 9 q^{49} + q^{50} + q^{52} + 12 q^{53} + 16 q^{55} - 12 q^{56} + 10 q^{58} - 12 q^{59} + 2 q^{61} + 8 q^{62} + 14 q^{64} - 2 q^{65} + 8 q^{67} + 2 q^{68} + 8 q^{70} + 4 q^{73} + 2 q^{74} + 16 q^{77} - 8 q^{79} - 4 q^{80} + 12 q^{82} - 4 q^{83} - 4 q^{85} + 12 q^{86} + 12 q^{88} - 4 q^{89} - 8 q^{91} - 10 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(730\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) 2.00000 3.46410i 0.755929 1.30931i −0.188982 0.981981i \(-0.560519\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) −3.00000 −1.06066
\(9\) 0 0
\(10\) 2.00000 0.632456
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 2.00000 + 3.46410i 0.534522 + 0.925820i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) 0 0
\(22\) −2.00000 3.46410i −0.426401 0.738549i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 4.00000 0.755929
\(29\) 5.00000 8.66025i 0.928477 1.60817i 0.142605 0.989780i \(-0.454452\pi\)
0.785872 0.618389i \(-0.212214\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) 0 0
\(34\) −1.00000 + 1.73205i −0.171499 + 0.297044i
\(35\) −8.00000 −1.35225
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 3.00000 + 5.19615i 0.474342 + 0.821584i
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) 0 0
\(43\) 6.00000 10.3923i 0.914991 1.58481i 0.108078 0.994142i \(-0.465531\pi\)
0.806914 0.590669i \(-0.201136\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) −4.50000 7.79423i −0.642857 1.11346i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0 0
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) −6.00000 + 10.3923i −0.801784 + 1.38873i
\(57\) 0 0
\(58\) 5.00000 + 8.66025i 0.656532 + 1.13715i
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 0 0
\(67\) 4.00000 + 6.92820i 0.488678 + 0.846415i 0.999915 0.0130248i \(-0.00414604\pi\)
−0.511237 + 0.859440i \(0.670813\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 0 0
\(70\) 4.00000 6.92820i 0.478091 0.828079i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 0 0
\(76\) 0 0
\(77\) 8.00000 + 13.8564i 0.911685 + 1.57908i
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −2.00000 −0.223607
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) −2.00000 + 3.46410i −0.219529 + 0.380235i −0.954664 0.297686i \(-0.903785\pi\)
0.735135 + 0.677920i \(0.237119\pi\)
\(84\) 0 0
\(85\) −2.00000 3.46410i −0.216930 0.375735i
\(86\) 6.00000 + 10.3923i 0.646997 + 1.12063i
\(87\) 0 0
\(88\) 6.00000 10.3923i 0.639602 1.10782i
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −5.00000 + 8.66025i −0.507673 + 0.879316i 0.492287 + 0.870433i \(0.336161\pi\)
−0.999961 + 0.00888289i \(0.997172\pi\)
\(98\) 9.00000 0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 0 0
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) 1.50000 + 2.59808i 0.147087 + 0.254762i
\(105\) 0 0
\(106\) −3.00000 + 5.19615i −0.291386 + 0.504695i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −4.00000 + 6.92820i −0.381385 + 0.660578i
\(111\) 0 0
\(112\) −2.00000 3.46410i −0.188982 0.327327i
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 4.00000 6.92820i 0.366679 0.635107i
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 1.00000 + 1.73205i 0.0905357 + 0.156813i
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) 0 0
\(130\) −1.00000 1.73205i −0.0877058 0.151911i
\(131\) −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i \(-0.222575\pi\)
−0.940072 + 0.340977i \(0.889242\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) −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
\(139\) −6.00000 10.3923i −0.508913 0.881464i −0.999947 0.0103230i \(-0.996714\pi\)
0.491033 0.871141i \(-0.336619\pi\)
\(140\) −4.00000 6.92820i −0.338062 0.585540i
\(141\) 0 0
\(142\) 0 0
\(143\) 4.00000 0.334497
\(144\) 0 0
\(145\) −20.0000 −1.66091
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 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
\(151\) −2.00000 + 3.46410i −0.162758 + 0.281905i −0.935857 0.352381i \(-0.885372\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −16.0000 −1.28932
\(155\) −4.00000 + 6.92820i −0.321288 + 0.556487i
\(156\) 0 0
\(157\) 9.00000 + 15.5885i 0.718278 + 1.24409i 0.961681 + 0.274169i \(0.0884028\pi\)
−0.243403 + 0.969925i \(0.578264\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) 0 0
\(160\) −5.00000 + 8.66025i −0.395285 + 0.684653i
\(161\) 0 0
\(162\) 0 0
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 0 0
\(166\) −2.00000 3.46410i −0.155230 0.268866i
\(167\) 4.00000 + 6.92820i 0.309529 + 0.536120i 0.978259 0.207385i \(-0.0664952\pi\)
−0.668730 + 0.743505i \(0.733162\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) 12.0000 0.914991
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) −2.00000 3.46410i −0.151186 0.261861i
\(176\) 2.00000 + 3.46410i 0.150756 + 0.261116i
\(177\) 0 0
\(178\) 1.00000 1.73205i 0.0749532 0.129823i
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 2.00000 3.46410i 0.148250 0.256776i
\(183\) 0 0
\(184\) 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
\(189\) 0 0
\(190\) 0 0
\(191\) −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) 0 0
\(193\) −9.00000 15.5885i −0.647834 1.12208i −0.983639 0.180150i \(-0.942342\pi\)
0.335805 0.941932i \(-0.390992\pi\)
\(194\) −5.00000 8.66025i −0.358979 0.621770i
\(195\) 0 0
\(196\) 4.50000 7.79423i 0.321429 0.556731i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −1.50000 + 2.59808i −0.106066 + 0.183712i
\(201\) 0 0
\(202\) 9.00000 + 15.5885i 0.633238 + 1.09680i
\(203\) −20.0000 34.6410i −1.40372 2.43132i
\(204\) 0 0
\(205\) −6.00000 + 10.3923i −0.419058 + 0.725830i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) 10.0000 + 17.3205i 0.688428 + 1.19239i 0.972346 + 0.233544i \(0.0750324\pi\)
−0.283918 + 0.958849i \(0.591634\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −24.0000 −1.63679
\(216\) 0 0
\(217\) −16.0000 −1.08615
\(218\) 1.00000 1.73205i 0.0677285 0.117309i
\(219\) 0 0
\(220\) 4.00000 + 6.92820i 0.269680 + 0.467099i
\(221\) −1.00000 1.73205i −0.0672673 0.116510i
\(222\) 0 0
\(223\) −2.00000 + 3.46410i −0.133930 + 0.231973i −0.925188 0.379509i \(-0.876093\pi\)
0.791258 + 0.611482i \(0.209426\pi\)
\(224\) −20.0000 −1.33631
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 10.0000 17.3205i 0.663723 1.14960i −0.315906 0.948790i \(-0.602309\pi\)
0.979630 0.200812i \(-0.0643581\pi\)
\(228\) 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
\(231\) 0 0
\(232\) −15.0000 + 25.9808i −0.984798 + 1.70572i
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) 0 0
\(238\) 4.00000 + 6.92820i 0.259281 + 0.449089i
\(239\) 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i \(0.116196\pi\)
−0.157893 + 0.987456i \(0.550470\pi\)
\(240\) 0 0
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 5.00000 0.321412
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −9.00000 + 15.5885i −0.574989 + 0.995910i
\(246\) 0 0
\(247\) 0 0
\(248\) 6.00000 + 10.3923i 0.381000 + 0.659912i
\(249\) 0 0
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8.00000 13.8564i 0.501965 0.869428i
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −13.0000 22.5167i −0.810918 1.40455i −0.912222 0.409695i \(-0.865635\pi\)
0.101305 0.994855i \(-0.467698\pi\)
\(258\) 0 0
\(259\) −4.00000 + 6.92820i −0.248548 + 0.430498i
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) 4.00000 0.247121
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 0 0
\(265\) −6.00000 10.3923i −0.368577 0.638394i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.00000 + 6.92820i −0.244339 + 0.423207i
\(269\) 22.0000 1.34136 0.670682 0.741745i \(-0.266002\pi\)
0.670682 + 0.741745i \(0.266002\pi\)
\(270\) 0 0
\(271\) −12.0000 −0.728948 −0.364474 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) 1.00000 1.73205i 0.0606339 0.105021i
\(273\) 0 0
\(274\) −3.00000 5.19615i −0.181237 0.313911i
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 12.0000 0.719712
\(279\) 0 0
\(280\) 24.0000 1.43427
\(281\) 5.00000 8.66025i 0.298275 0.516627i −0.677466 0.735554i \(-0.736922\pi\)
0.975741 + 0.218926i \(0.0702554\pi\)
\(282\) 0 0
\(283\) −6.00000 10.3923i −0.356663 0.617758i 0.630738 0.775996i \(-0.282752\pi\)
−0.987401 + 0.158237i \(0.949419\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −2.00000 + 3.46410i −0.118262 + 0.204837i
\(287\) −24.0000 −1.41668
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 10.0000 17.3205i 0.587220 1.01710i
\(291\) 0 0
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) 0 0
\(295\) −12.0000 + 20.7846i −0.698667 + 1.21013i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −24.0000 41.5692i −1.38334 2.39601i
\(302\) −2.00000 3.46410i −0.115087 0.199337i
\(303\) 0 0
\(304\) 0 0
\(305\) −4.00000 −0.229039
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) −8.00000 + 13.8564i −0.455842 + 0.789542i
\(309\) 0 0
\(310\) −4.00000 6.92820i −0.227185 0.393496i
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i \(-0.779095\pi\)
0.938269 + 0.345907i \(0.112429\pi\)
\(314\) −18.0000 −1.01580
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −13.0000 + 22.5167i −0.730153 + 1.26466i 0.226665 + 0.973973i \(0.427218\pi\)
−0.956818 + 0.290689i \(0.906116\pi\)
\(318\) 0 0
\(319\) 20.0000 + 34.6410i 1.11979 + 1.93952i
\(320\) −7.00000 12.1244i −0.391312 0.677772i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) 0 0
\(328\) 9.00000 + 15.5885i 0.496942 + 0.860729i
\(329\) 0 0
\(330\) 0 0
\(331\) 8.00000 13.8564i 0.439720 0.761617i −0.557948 0.829876i \(-0.688411\pi\)
0.997668 + 0.0682590i \(0.0217444\pi\)
\(332\) −4.00000 −0.219529
\(333\) 0 0
\(334\) −8.00000 −0.437741
\(335\) 8.00000 13.8564i 0.437087 0.757056i
\(336\) 0 0
\(337\) −9.00000 15.5885i −0.490261 0.849157i 0.509676 0.860366i \(-0.329765\pi\)
−0.999937 + 0.0112091i \(0.996432\pi\)
\(338\) −0.500000 0.866025i −0.0271964 0.0471056i
\(339\) 0 0
\(340\) 2.00000 3.46410i 0.108465 0.187867i
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) −18.0000 + 31.1769i −0.970495 + 1.68095i
\(345\) 0 0
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) 13.0000 22.5167i 0.695874 1.20529i −0.274011 0.961727i \(-0.588351\pi\)
0.969885 0.243563i \(-0.0783162\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) 1.00000 1.73205i 0.0532246 0.0921878i −0.838186 0.545385i \(-0.816383\pi\)
0.891410 + 0.453197i \(0.149717\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.00000 1.73205i −0.0529999 0.0917985i
\(357\) 0 0
\(358\) −2.00000 + 3.46410i −0.105703 + 0.183083i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 5.00000 8.66025i 0.262794 0.455173i
\(363\) 0 0
\(364\) −2.00000 3.46410i −0.104828 0.181568i
\(365\) −2.00000 3.46410i −0.104685 0.181319i
\(366\) 0 0
\(367\) −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i \(-0.970461\pi\)
0.578101 + 0.815966i \(0.303794\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) 12.0000 20.7846i 0.623009 1.07908i
\(372\) 0 0
\(373\) 13.0000 + 22.5167i 0.673114 + 1.16587i 0.977016 + 0.213165i \(0.0683772\pi\)
−0.303902 + 0.952703i \(0.598289\pi\)
\(374\) −4.00000 6.92820i −0.206835 0.358249i
\(375\) 0 0
\(376\) 0 0
\(377\) −10.0000 −0.515026
\(378\) 0 0
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.00000 6.92820i −0.204658 0.354478i
\(383\) 8.00000 + 13.8564i 0.408781 + 0.708029i 0.994753 0.102302i \(-0.0326207\pi\)
−0.585973 + 0.810331i \(0.699287\pi\)
\(384\) 0 0
\(385\) 16.0000 27.7128i 0.815436 1.41238i
\(386\) 18.0000 0.916176
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) −11.0000 + 19.0526i −0.557722 + 0.966003i 0.439964 + 0.898015i \(0.354991\pi\)
−0.997686 + 0.0679877i \(0.978342\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 13.5000 + 23.3827i 0.681853 + 1.18100i
\(393\) 0 0
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) 16.0000 0.805047
\(396\) 0 0
\(397\) 38.0000 1.90717 0.953583 0.301131i \(-0.0973643\pi\)
0.953583 + 0.301131i \(0.0973643\pi\)
\(398\) −4.00000 + 6.92820i −0.200502 + 0.347279i
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −11.0000 19.0526i −0.549314 0.951439i −0.998322 0.0579116i \(-0.981556\pi\)
0.449008 0.893528i \(-0.351777\pi\)
\(402\) 0 0
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) 18.0000 0.895533
\(405\) 0 0
\(406\) 40.0000 1.98517
\(407\) 4.00000 6.92820i 0.198273 0.343418i
\(408\) 0 0
\(409\) −17.0000 29.4449i −0.840596 1.45595i −0.889392 0.457146i \(-0.848872\pi\)
0.0487958 0.998809i \(-0.484462\pi\)
\(410\) −6.00000 10.3923i −0.296319 0.513239i
\(411\) 0 0
\(412\) 0 0
\(413\) −48.0000 −2.36193
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) −2.50000 + 4.33013i −0.122573 + 0.212302i
\(417\) 0 0
\(418\) 0 0
\(419\) −2.00000 3.46410i −0.0977064 0.169232i 0.813029 0.582224i \(-0.197817\pi\)
−0.910735 + 0.412991i \(0.864484\pi\)
\(420\) 0 0
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) −20.0000 −0.973585
\(423\) 0 0
\(424\) −18.0000 −0.874157
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) −4.00000 6.92820i −0.193574 0.335279i
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 0 0
\(430\) 12.0000 20.7846i 0.578691 1.00232i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 8.00000 13.8564i 0.384012 0.665129i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 0 0
\(438\) 0 0
\(439\) −16.0000 + 27.7128i −0.763638 + 1.32266i 0.177325 + 0.984152i \(0.443256\pi\)
−0.940963 + 0.338508i \(0.890078\pi\)
\(440\) −24.0000 −1.14416
\(441\) 0 0
\(442\) 2.00000 0.0951303
\(443\) 2.00000 3.46410i 0.0950229 0.164584i −0.814595 0.580030i \(-0.803041\pi\)
0.909618 + 0.415445i \(0.136374\pi\)
\(444\) 0 0
\(445\) 2.00000 + 3.46410i 0.0948091 + 0.164214i
\(446\) −2.00000 3.46410i −0.0947027 0.164030i
\(447\) 0 0
\(448\) 14.0000 24.2487i 0.661438 1.14564i
\(449\) 22.0000 1.03824 0.519122 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) 0 0
\(451\) 24.0000 1.13012
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) 0 0
\(454\) 10.0000 + 17.3205i 0.469323 + 0.812892i
\(455\) 4.00000 + 6.92820i 0.187523 + 0.324799i
\(456\) 0 0
\(457\) −1.00000 + 1.73205i −0.0467780 + 0.0810219i −0.888466 0.458942i \(-0.848229\pi\)
0.841688 + 0.539964i \(0.181562\pi\)
\(458\) −10.0000 −0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) 19.0000 32.9090i 0.884918 1.53272i 0.0391109 0.999235i \(-0.487547\pi\)
0.845807 0.533488i \(-0.179119\pi\)
\(462\) 0 0
\(463\) −2.00000 3.46410i −0.0929479 0.160990i 0.815802 0.578331i \(-0.196296\pi\)
−0.908750 + 0.417340i \(0.862962\pi\)
\(464\) −5.00000 8.66025i −0.232119 0.402042i
\(465\) 0 0
\(466\) 7.00000 12.1244i 0.324269 0.561650i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 32.0000 1.47762
\(470\) 0 0
\(471\) 0 0
\(472\) 18.0000 + 31.1769i 0.828517 + 1.43503i
\(473\) 24.0000 + 41.5692i 1.10352 + 1.91135i
\(474\) 0 0
\(475\) 0 0
\(476\) 8.00000 0.366679
\(477\) 0 0
\(478\) −24.0000 −1.09773
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 0 0
\(481\) 1.00000 + 1.73205i 0.0455961 + 0.0789747i
\(482\) −5.00000 8.66025i −0.227744 0.394464i
\(483\) 0 0
\(484\) 2.50000 4.33013i 0.113636 0.196824i
\(485\) 20.0000 0.908153
\(486\) 0 0
\(487\) 12.0000 0.543772 0.271886 0.962329i \(-0.412353\pi\)
0.271886 + 0.962329i \(0.412353\pi\)
\(488\) −3.00000 + 5.19615i −0.135804 + 0.235219i
\(489\) 0 0
\(490\) −9.00000 15.5885i −0.406579 0.704215i
\(491\) 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) 0 0
\(493\) 10.0000 17.3205i 0.450377 0.780076i
\(494\) 0 0
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 12.0000 + 20.7846i 0.537194 + 0.930447i 0.999054 + 0.0434940i \(0.0138489\pi\)
−0.461860 + 0.886953i \(0.652818\pi\)
\(500\) −6.00000 10.3923i −0.268328 0.464758i
\(501\) 0 0
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) −8.00000 −0.356702 −0.178351 0.983967i \(-0.557076\pi\)
−0.178351 + 0.983967i \(0.557076\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) 0 0
\(507\) 0 0
\(508\) −8.00000 13.8564i −0.354943 0.614779i
\(509\) −5.00000 8.66025i −0.221621 0.383859i 0.733679 0.679496i \(-0.237801\pi\)
−0.955300 + 0.295637i \(0.904468\pi\)
\(510\) 0 0
\(511\) 4.00000 6.92820i 0.176950 0.306486i
\(512\) −11.0000 −0.486136
\(513\) 0 0
\(514\) 26.0000 1.14681
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −4.00000 6.92820i −0.175750 0.304408i
\(519\) 0 0
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 44.0000 1.92399 0.961993 0.273075i \(-0.0880406\pi\)
0.961993 + 0.273075i \(0.0880406\pi\)
\(524\) 2.00000 3.46410i 0.0873704 0.151330i
\(525\) 0 0
\(526\) −12.0000 20.7846i −0.523225 0.906252i
\(527\) −4.00000 6.92820i −0.174243 0.301797i
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 12.0000 0.521247
\(531\) 0 0
\(532\) 0 0
\(533\) −3.00000 + 5.19615i −0.129944 + 0.225070i
\(534\) 0 0
\(535\) −12.0000 20.7846i −0.518805 0.898597i
\(536\) −12.0000 20.7846i −0.518321 0.897758i
\(537\) 0 0
\(538\) −11.0000 + 19.0526i −0.474244 + 0.821414i
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 6.00000 10.3923i 0.257722 0.446388i
\(543\) 0 0
\(544\) −5.00000 8.66025i −0.214373 0.371305i
\(545\) 2.00000 + 3.46410i 0.0856706 + 0.148386i
\(546\) 0 0
\(547\) −2.00000 + 3.46410i −0.0855138 + 0.148114i −0.905610 0.424111i \(-0.860587\pi\)
0.820096 + 0.572226i \(0.193920\pi\)
\(548\) −6.00000 −0.256307
\(549\) 0 0
\(550\) −4.00000 −0.170561
\(551\) 0 0
\(552\) 0 0
\(553\) 16.0000 + 27.7128i 0.680389 + 1.17847i
\(554\) 5.00000 + 8.66025i 0.212430 + 0.367939i
\(555\) 0 0
\(556\) 6.00000 10.3923i 0.254457 0.440732i
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) −4.00000 + 6.92820i −0.169031 + 0.292770i
\(561\) 0 0
\(562\) 5.00000 + 8.66025i 0.210912 + 0.365311i
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) 0 0
\(565\) 6.00000 10.3923i 0.252422 0.437208i
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) 0 0
\(569\) −17.0000 + 29.4449i −0.712677 + 1.23439i 0.251172 + 0.967943i \(0.419184\pi\)
−0.963849 + 0.266450i \(0.914149\pi\)
\(570\) 0 0
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) 2.00000 + 3.46410i 0.0836242 + 0.144841i
\(573\) 0 0
\(574\) 12.0000 20.7846i 0.500870 0.867533i
\(575\) 0 0
\(576\) 0 0
\(577\) −46.0000 −1.91501 −0.957503 0.288425i \(-0.906868\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) 0 0
\(580\) −10.0000 17.3205i −0.415227 0.719195i
\(581\) 8.00000 + 13.8564i 0.331896 + 0.574861i
\(582\) 0 0
\(583\) −12.0000 + 20.7846i −0.496989 + 0.860811i
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −14.0000 + 24.2487i −0.577842 + 1.00085i 0.417885 + 0.908500i \(0.362772\pi\)
−0.995726 + 0.0923513i \(0.970562\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −12.0000 20.7846i −0.494032 0.855689i
\(591\) 0 0
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) −3.00000 + 5.19615i −0.122885 + 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) 20.0000 + 34.6410i 0.817178 + 1.41539i 0.907754 + 0.419504i \(0.137796\pi\)
−0.0905757 + 0.995890i \(0.528871\pi\)
\(600\) 0 0
\(601\) 19.0000 32.9090i 0.775026 1.34238i −0.159754 0.987157i \(-0.551070\pi\)
0.934780 0.355228i \(-0.115597\pi\)
\(602\) 48.0000 1.95633
\(603\) 0 0
\(604\) −4.00000 −0.162758
\(605\) −5.00000 + 8.66025i −0.203279 + 0.352089i
\(606\) 0 0
\(607\) 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i \(-0.0614000\pi\)
−0.656744 + 0.754114i \(0.728067\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 2.00000 3.46410i 0.0809776 0.140257i
\(611\) 0 0
\(612\) 0 0
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 8.00000 13.8564i 0.322854 0.559199i
\(615\) 0 0
\(616\) −24.0000 41.5692i −0.966988 1.67487i
\(617\) −11.0000 19.0526i −0.442843 0.767027i 0.555056 0.831813i \(-0.312697\pi\)
−0.997899 + 0.0647859i \(0.979364\pi\)
\(618\) 0 0
\(619\) −12.0000 + 20.7846i −0.482321 + 0.835404i −0.999794 0.0202954i \(-0.993539\pi\)
0.517473 + 0.855699i \(0.326873\pi\)
\(620\) −8.00000 −0.321288
\(621\) 0 0
\(622\) 0 0
\(623\) −4.00000 + 6.92820i −0.160257 + 0.277573i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 0 0
\(628\) −9.00000 + 15.5885i −0.359139 + 0.622047i
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 12.0000 20.7846i 0.477334 0.826767i
\(633\) 0 0
\(634\) −13.0000 22.5167i −0.516296 0.894251i
\(635\) 16.0000 + 27.7128i 0.634941 + 1.09975i
\(636\) 0 0
\(637\) −4.50000 + 7.79423i −0.178296 + 0.308819i
\(638\) −40.0000 −1.58362
\(639\) 0 0
\(640\) −6.00000 −0.237171
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 0 0
\(643\) 20.0000 + 34.6410i 0.788723 + 1.36611i 0.926750 + 0.375680i \(0.122591\pi\)
−0.138027 + 0.990429i \(0.544076\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) 0 0
\(649\) 48.0000 1.88416
\(650\) 0.500000 0.866025i 0.0196116 0.0339683i
\(651\) 0 0
\(652\) 4.00000 + 6.92820i 0.156652 + 0.271329i
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 0 0
\(655\) −4.00000 + 6.92820i −0.156293 + 0.270707i
\(656\) −6.00000 −0.234261
\(657\) 0 0
\(658\) 0 0
\(659\) −14.0000 + 24.2487i −0.545363 + 0.944596i 0.453221 + 0.891398i \(0.350275\pi\)
−0.998584 + 0.0531977i \(0.983059\pi\)
\(660\) 0 0
\(661\) −15.0000 25.9808i −0.583432 1.01053i −0.995069 0.0991864i \(-0.968376\pi\)
0.411636 0.911348i \(-0.364957\pi\)
\(662\) 8.00000 + 13.8564i 0.310929 + 0.538545i
\(663\) 0 0
\(664\) 6.00000 10.3923i 0.232845 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −4.00000 + 6.92820i −0.154765 + 0.268060i
\(669\) 0 0
\(670\) 8.00000 + 13.8564i 0.309067 + 0.535320i
\(671\) 4.00000 + 6.92820i 0.154418 + 0.267460i
\(672\) 0 0
\(673\) 7.00000 12.1244i 0.269830 0.467360i −0.698988 0.715134i \(-0.746366\pi\)
0.968818 + 0.247774i \(0.0796991\pi\)
\(674\) 18.0000 0.693334
\(675\) 0 0
\(676\) −1.00000 −0.0384615
\(677\) −11.0000 + 19.0526i −0.422764 + 0.732249i −0.996209 0.0869952i \(-0.972274\pi\)
0.573444 + 0.819244i \(0.305607\pi\)
\(678\) 0 0
\(679\) 20.0000 + 34.6410i 0.767530 + 1.32940i
\(680\) 6.00000 + 10.3923i 0.230089 + 0.398527i
\(681\) 0 0
\(682\) −8.00000 + 13.8564i −0.306336 + 0.530589i
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 4.00000 6.92820i 0.152721 0.264520i
\(687\) 0 0
\(688\) −6.00000 10.3923i −0.228748 0.396203i
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 0 0
\(691\) 12.0000 20.7846i 0.456502 0.790684i −0.542272 0.840203i \(-0.682436\pi\)
0.998773 + 0.0495194i \(0.0157690\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −12.0000 + 20.7846i −0.455186 + 0.788405i
\(696\) 0 0
\(697\) −6.00000 10.3923i −0.227266 0.393637i
\(698\) 13.0000 + 22.5167i 0.492057 + 0.852268i
\(699\) 0 0
\(700\) 2.00000 3.46410i 0.0755929 0.130931i
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −14.0000 + 24.2487i −0.527645 + 0.913908i
\(705\) 0 0
\(706\) 1.00000 + 1.73205i 0.0376355 + 0.0651866i
\(707\) −36.0000 62.3538i −1.35392 2.34506i
\(708\) 0 0
\(709\) 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i \(-0.670978\pi\)
0.999908 + 0.0135434i \(0.00431112\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) −4.00000 6.92820i −0.149592 0.259100i
\(716\) 2.00000 + 3.46410i 0.0747435 + 0.129460i
\(717\) 0 0
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 9.50000 16.4545i 0.353553 0.612372i
\(723\) 0 0
\(724\) −5.00000 8.66025i −0.185824 0.321856i
\(725\) −5.00000 8.66025i −0.185695 0.321634i
\(726\) 0 0
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) 12.0000 0.444750
\(729\) 0 0
\(730\) 4.00000 0.148047
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 0 0
\(733\) −15.0000 25.9808i −0.554038 0.959621i −0.997978 0.0635649i \(-0.979753\pi\)
0.443940 0.896056i \(-0.353580\pi\)
\(734\) −8.00000 13.8564i −0.295285 0.511449i
\(735\) 0 0
\(736\) 0 0
\(737\) −32.0000 −1.17874
\(738\) 0 0
\(739\) 32.0000 1.17714 0.588570 0.808447i \(-0.299691\pi\)
0.588570 + 0.808447i \(0.299691\pi\)
\(740\) −2.00000 + 3.46410i −0.0735215 + 0.127343i
\(741\) 0 0
\(742\) 12.0000 + 20.7846i 0.440534 + 0.763027i
\(743\) −24.0000 41.5692i −0.880475 1.52503i −0.850814 0.525467i \(-0.823891\pi\)
−0.0296605 0.999560i \(-0.509443\pi\)
\(744\) 0 0
\(745\) 6.00000 10.3923i 0.219823 0.380745i
\(746\) −26.0000 −0.951928
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) 24.0000 41.5692i 0.876941 1.51891i
\(750\) 0 0
\(751\) −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i \(-0.213294\pi\)
−0.929731 + 0.368238i \(0.879961\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 5.00000 8.66025i 0.182089 0.315388i
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 12.0000 20.7846i 0.435860 0.754931i
\(759\) 0 0
\(760\) 0 0
\(761\) 5.00000 + 8.66025i 0.181250 + 0.313934i 0.942306 0.334752i \(-0.108652\pi\)
−0.761057 + 0.648686i \(0.775319\pi\)
\(762\) 0 0
\(763\) −4.00000 + 6.92820i −0.144810 + 0.250818i
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) −6.00000 + 10.3923i −0.216647 + 0.375244i
\(768\) 0 0
\(769\) 15.0000 + 25.9808i 0.540914 + 0.936890i 0.998852 + 0.0479061i \(0.0152548\pi\)
−0.457938 + 0.888984i \(0.651412\pi\)
\(770\) 16.0000 + 27.7128i 0.576600 + 0.998700i
\(771\) 0 0
\(772\) 9.00000 15.5885i 0.323917 0.561041i
\(773\) 10.0000 0.359675 0.179838 0.983696i \(-0.442443\pi\)
0.179838 + 0.983696i \(0.442443\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 15.0000 25.9808i 0.538469 0.932655i
\(777\) 0 0
\(778\) −11.0000 19.0526i −0.394369 0.683067i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −9.00000 −0.321429
\(785\) 18.0000 31.1769i 0.642448 1.11275i
\(786\) 0 0
\(787\) 16.0000 + 27.7128i 0.570338 + 0.987855i 0.996531 + 0.0832226i \(0.0265213\pi\)
−0.426193 + 0.904632i \(0.640145\pi\)
\(788\) 9.00000 + 15.5885i 0.320612 + 0.555316i
\(789\) 0 0
\(790\) −8.00000 + 13.8564i −0.284627 + 0.492989i
\(791\) 24.0000 0.853342
\(792\) 0