Properties

Label 1386.2.k.a.793.1
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.a.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.00000 - 3.46410i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{19} +4.00000 q^{20} +1.00000 q^{22} +(-1.00000 + 1.73205i) q^{23} +(-5.50000 - 9.52628i) q^{25} +(0.500000 - 0.866025i) q^{26} +(2.00000 + 1.73205i) q^{28} -1.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} -2.00000 q^{34} +(2.00000 - 10.3923i) q^{35} +(1.00000 - 1.73205i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-2.00000 + 3.46410i) q^{40} +2.00000 q^{41} +4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.00000 - 1.73205i) q^{46} +(1.00000 - 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +11.0000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +(4.50000 + 7.79423i) q^{59} +(2.50000 - 4.33013i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(4.50000 + 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} +(8.00000 + 6.92820i) q^{70} -4.00000 q^{71} +(1.00000 + 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +6.00000 q^{76} +(2.00000 + 1.73205i) q^{77} +(7.50000 - 12.9904i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-1.00000 + 1.73205i) q^{82} +6.00000 q^{83} -8.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(2.50000 - 0.866025i) q^{91} +2.00000 q^{92} +(1.00000 + 1.73205i) q^{94} +(-12.0000 - 20.7846i) q^{95} -5.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - 4q^{5} - 5q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - 4q^{5} - 5q^{7} + 2q^{8} - 4q^{10} - q^{11} - 2q^{13} + q^{14} - q^{16} + 2q^{17} - 6q^{19} + 8q^{20} + 2q^{22} - 2q^{23} - 11q^{25} + q^{26} + 4q^{28} - 2q^{29} - 4q^{31} - q^{32} - 4q^{34} + 4q^{35} + 2q^{37} - 6q^{38} - 4q^{40} + 4q^{41} + 8q^{43} - q^{44} - 2q^{46} + 2q^{47} + 11q^{49} + 22q^{50} + q^{52} - 12q^{53} + 8q^{55} - 5q^{56} + q^{58} + 9q^{59} + 5q^{61} + 8q^{62} + 2q^{64} + 4q^{65} + 9q^{67} + 2q^{68} + 16q^{70} - 8q^{71} + 2q^{73} + 2q^{74} + 12q^{76} + 4q^{77} + 15q^{79} - 4q^{80} - 2q^{82} + 12q^{83} - 16q^{85} - 4q^{86} - q^{88} + 6q^{89} + 5q^{91} + 4q^{92} + 2q^{94} - 24q^{95} - 10q^{97} + 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.00000 + 3.46410i −0.894427 + 1.54919i −0.0599153 + 0.998203i \(0.519083\pi\)
−0.834512 + 0.550990i \(0.814250\pi\)
\(6\) 0 0
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −2.00000 3.46410i −0.632456 1.09545i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0.500000 2.59808i 0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) 4.00000 0.894427
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i \(-0.900196\pi\)
0.742732 + 0.669588i \(0.233529\pi\)
\(24\) 0 0
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) 0 0
\(28\) 2.00000 + 1.73205i 0.377964 + 0.327327i
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 2.00000 10.3923i 0.338062 1.75662i
\(36\) 0 0
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) −3.00000 5.19615i −0.486664 0.842927i
\(39\) 0 0
\(40\) −2.00000 + 3.46410i −0.316228 + 0.547723i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −1.00000 1.73205i −0.147442 0.255377i
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 11.0000 1.55563
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i \(-0.858312\pi\)
0.0783936 0.996922i \(-0.475021\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) 0 0
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) 4.50000 + 7.79423i 0.585850 + 1.01472i 0.994769 + 0.102151i \(0.0325726\pi\)
−0.408919 + 0.912571i \(0.634094\pi\)
\(60\) 0 0
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 3.46410i 0.248069 0.429669i
\(66\) 0 0
\(67\) 4.50000 + 7.79423i 0.549762 + 0.952217i 0.998290 + 0.0584478i \(0.0186151\pi\)
−0.448528 + 0.893769i \(0.648052\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0 0
\(70\) 8.00000 + 6.92820i 0.956183 + 0.828079i
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 0 0
\(76\) 6.00000 0.688247
\(77\) 2.00000 + 1.73205i 0.227921 + 0.197386i
\(78\) 0 0
\(79\) 7.50000 12.9904i 0.843816 1.46153i −0.0428296 0.999082i \(-0.513637\pi\)
0.886646 0.462450i \(-0.153029\pi\)
\(80\) −2.00000 3.46410i −0.223607 0.387298i
\(81\) 0 0
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) −8.00000 −0.867722
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 2.50000 0.866025i 0.262071 0.0907841i
\(92\) 2.00000 0.208514
\(93\) 0 0
\(94\) 1.00000 + 1.73205i 0.103142 + 0.178647i
\(95\) −12.0000 20.7846i −1.23117 2.13246i
\(96\) 0 0
\(97\) −5.00000 −0.507673 −0.253837 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 1.00000 + 6.92820i 0.101015 + 0.699854i
\(99\) 0 0
\(100\) −5.50000 + 9.52628i −0.550000 + 0.952628i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) −6.00000 + 10.3923i −0.591198 + 1.02398i 0.402874 + 0.915255i \(0.368011\pi\)
−0.994071 + 0.108729i \(0.965322\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) 4.00000 6.92820i 0.386695 0.669775i −0.605308 0.795991i \(-0.706950\pi\)
0.992003 + 0.126217i \(0.0402834\pi\)
\(108\) 0 0
\(109\) −5.00000 8.66025i −0.478913 0.829502i 0.520794 0.853682i \(-0.325636\pi\)
−0.999708 + 0.0241802i \(0.992302\pi\)
\(110\) −2.00000 + 3.46410i −0.190693 + 0.330289i
\(111\) 0 0
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) −17.0000 −1.59923 −0.799613 0.600516i \(-0.794962\pi\)
−0.799613 + 0.600516i \(0.794962\pi\)
\(114\) 0 0
\(115\) −4.00000 6.92820i −0.373002 0.646058i
\(116\) 0.500000 + 0.866025i 0.0464238 + 0.0804084i
\(117\) 0 0
\(118\) −9.00000 −0.828517
\(119\) −4.00000 3.46410i −0.366679 0.317554i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 2.50000 + 4.33013i 0.226339 + 0.392031i
\(123\) 0 0
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 0 0
\(133\) 3.00000 15.5885i 0.260133 1.35169i
\(134\) −9.00000 −0.777482
\(135\) 0 0
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i \(-0.292279\pi\)
−0.991694 + 0.128618i \(0.958946\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) −10.0000 + 3.46410i −0.845154 + 0.292770i
\(141\) 0 0
\(142\) 2.00000 3.46410i 0.167836 0.290701i
\(143\) 0.500000 + 0.866025i 0.0418121 + 0.0724207i
\(144\) 0 0
\(145\) 2.00000 3.46410i 0.166091 0.287678i
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i \(-0.967671\pi\)
0.585231 + 0.810867i \(0.301004\pi\)
\(150\) 0 0
\(151\) −4.50000 7.79423i −0.366205 0.634285i 0.622764 0.782410i \(-0.286010\pi\)
−0.988969 + 0.148124i \(0.952676\pi\)
\(152\) −3.00000 + 5.19615i −0.243332 + 0.421464i
\(153\) 0 0
\(154\) −2.50000 + 0.866025i −0.201456 + 0.0697863i
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) −2.00000 3.46410i −0.159617 0.276465i 0.775113 0.631822i \(-0.217693\pi\)
−0.934731 + 0.355357i \(0.884359\pi\)
\(158\) 7.50000 + 12.9904i 0.596668 + 1.03346i
\(159\) 0 0
\(160\) 4.00000 0.316228
\(161\) 1.00000 5.19615i 0.0788110 0.409514i
\(162\) 0 0
\(163\) −6.50000 + 11.2583i −0.509119 + 0.881820i 0.490825 + 0.871258i \(0.336695\pi\)
−0.999944 + 0.0105623i \(0.996638\pi\)
\(164\) −1.00000 1.73205i −0.0780869 0.135250i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 17.0000 1.31550 0.657750 0.753237i \(-0.271508\pi\)
0.657750 + 0.753237i \(0.271508\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 4.00000 6.92820i 0.306786 0.531369i
\(171\) 0 0
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) −2.50000 + 4.33013i −0.190071 + 0.329213i −0.945274 0.326278i \(-0.894205\pi\)
0.755202 + 0.655492i \(0.227539\pi\)
\(174\) 0 0
\(175\) 22.0000 + 19.0526i 1.66304 + 1.44024i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) 6.50000 + 11.2583i 0.485833 + 0.841487i 0.999867 0.0162823i \(-0.00518305\pi\)
−0.514035 + 0.857769i \(0.671850\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −0.500000 + 2.59808i −0.0370625 + 0.192582i
\(183\) 0 0
\(184\) −1.00000 + 1.73205i −0.0737210 + 0.127688i
\(185\) 4.00000 + 6.92820i 0.294086 + 0.509372i
\(186\) 0 0
\(187\) 1.00000 1.73205i 0.0731272 0.126660i
\(188\) −2.00000 −0.145865
\(189\) 0 0
\(190\) 24.0000 1.74114
\(191\) 7.00000 12.1244i 0.506502 0.877288i −0.493469 0.869763i \(-0.664272\pi\)
0.999972 0.00752447i \(-0.00239513\pi\)
\(192\) 0 0
\(193\) 11.0000 + 19.0526i 0.791797 + 1.37143i 0.924853 + 0.380325i \(0.124188\pi\)
−0.133056 + 0.991109i \(0.542479\pi\)
\(194\) 2.50000 4.33013i 0.179490 0.310885i
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) −5.50000 9.52628i −0.388909 0.673610i
\(201\) 0 0
\(202\) 15.0000 1.05540
\(203\) 2.50000 0.866025i 0.175466 0.0607831i
\(204\) 0 0
\(205\) −4.00000 + 6.92820i −0.279372 + 0.483887i
\(206\) −6.00000 10.3923i −0.418040 0.724066i
\(207\) 0 0
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) −6.00000 + 10.3923i −0.412082 + 0.713746i
\(213\) 0 0
\(214\) 4.00000 + 6.92820i 0.273434 + 0.473602i
\(215\) −8.00000 + 13.8564i −0.545595 + 0.944999i
\(216\) 0 0
\(217\) 8.00000 + 6.92820i 0.543075 + 0.470317i
\(218\) 10.0000 0.677285
\(219\) 0 0
\(220\) −2.00000 3.46410i −0.134840 0.233550i
\(221\) −1.00000 1.73205i −0.0672673 0.116510i
\(222\) 0 0
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 2.00000 + 1.73205i 0.133631 + 0.115728i
\(225\) 0 0
\(226\) 8.50000 14.7224i 0.565412 0.979322i
\(227\) 5.00000 + 8.66025i 0.331862 + 0.574801i 0.982877 0.184263i \(-0.0589899\pi\)
−0.651015 + 0.759065i \(0.725657\pi\)
\(228\) 0 0
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) −1.00000 −0.0656532
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 0 0
\(235\) 4.00000 + 6.92820i 0.260931 + 0.451946i
\(236\) 4.50000 7.79423i 0.292925 0.507361i
\(237\) 0 0
\(238\) 5.00000 1.73205i 0.324102 0.112272i
\(239\) −19.0000 −1.22901 −0.614504 0.788914i \(-0.710644\pi\)
−0.614504 + 0.788914i \(0.710644\pi\)
\(240\) 0 0
\(241\) −15.0000 25.9808i −0.966235 1.67357i −0.706260 0.707953i \(-0.749619\pi\)
−0.259975 0.965615i \(-0.583714\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 0 0
\(244\) −5.00000 −0.320092
\(245\) 4.00000 + 27.7128i 0.255551 + 1.77051i
\(246\) 0 0
\(247\) 3.00000 5.19615i 0.190885 0.330623i
\(248\) −2.00000 3.46410i −0.127000 0.219971i
\(249\) 0 0
\(250\) −12.0000 + 20.7846i −0.758947 + 1.31453i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 2.00000 0.125739
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.5000 + 18.1865i −0.654972 + 1.13444i 0.326929 + 0.945049i \(0.393986\pi\)
−0.981901 + 0.189396i \(0.939347\pi\)
\(258\) 0 0
\(259\) −1.00000 + 5.19615i −0.0621370 + 0.322873i
\(260\) −4.00000 −0.248069
\(261\) 0 0
\(262\) −9.00000 15.5885i −0.556022 0.963058i
\(263\) 1.50000 + 2.59808i 0.0924940 + 0.160204i 0.908560 0.417755i \(-0.137183\pi\)
−0.816066 + 0.577959i \(0.803849\pi\)
\(264\) 0 0
\(265\) 48.0000 2.94862
\(266\) 12.0000 + 10.3923i 0.735767 + 0.637193i
\(267\) 0 0
\(268\) 4.50000 7.79423i 0.274881 0.476108i
\(269\) 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) 0 0
\(271\) −12.5000 + 21.6506i −0.759321 + 1.31518i 0.183876 + 0.982949i \(0.441135\pi\)
−0.943197 + 0.332233i \(0.892198\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 9.00000 0.543710
\(275\) −5.50000 + 9.52628i −0.331662 + 0.574456i
\(276\) 0 0
\(277\) 1.50000 + 2.59808i 0.0901263 + 0.156103i 0.907564 0.419914i \(-0.137940\pi\)
−0.817438 + 0.576017i \(0.804606\pi\)
\(278\) −4.00000 + 6.92820i −0.239904 + 0.415526i
\(279\) 0 0
\(280\) 2.00000 10.3923i 0.119523 0.621059i
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) 3.00000 + 5.19615i 0.178331 + 0.308879i 0.941309 0.337546i \(-0.109597\pi\)
−0.762978 + 0.646425i \(0.776263\pi\)
\(284\) 2.00000 + 3.46410i 0.118678 + 0.205557i
\(285\) 0 0
\(286\) −1.00000 −0.0591312
\(287\) −5.00000 + 1.73205i −0.295141 + 0.102240i
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 2.00000 + 3.46410i 0.117444 + 0.203419i
\(291\) 0 0
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −36.0000 −2.09600
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 0 0
\(298\) −5.00000 8.66025i −0.289642 0.501675i
\(299\) 1.00000 1.73205i 0.0578315 0.100167i
\(300\) 0 0
\(301\) −10.0000 + 3.46410i −0.576390 + 0.199667i
\(302\) 9.00000 0.517892
\(303\) 0 0
\(304\) −3.00000 5.19615i −0.172062 0.298020i
\(305\) 10.0000 + 17.3205i 0.572598 + 0.991769i
\(306\) 0 0
\(307\) 32.0000 1.82634 0.913168 0.407583i \(-0.133628\pi\)
0.913168 + 0.407583i \(0.133628\pi\)
\(308\) 0.500000 2.59808i 0.0284901 0.148039i
\(309\) 0 0
\(310\) −8.00000 + 13.8564i −0.454369 + 0.786991i
\(311\) −14.0000 24.2487i −0.793867 1.37502i −0.923556 0.383464i \(-0.874731\pi\)
0.129689 0.991555i \(-0.458602\pi\)
\(312\) 0 0
\(313\) −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i \(-0.842331\pi\)
0.851549 + 0.524276i \(0.175664\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −15.0000 −0.843816
\(317\) −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i \(-0.942743\pi\)
0.646872 + 0.762598i \(0.276077\pi\)
\(318\) 0 0
\(319\) 0.500000 + 0.866025i 0.0279946 + 0.0484881i
\(320\) −2.00000 + 3.46410i −0.111803 + 0.193649i
\(321\) 0 0
\(322\) 4.00000 + 3.46410i 0.222911 + 0.193047i
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 5.50000 + 9.52628i 0.305085 + 0.528423i
\(326\) −6.50000 11.2583i −0.360002 0.623541i
\(327\) 0 0
\(328\) 2.00000 0.110432
\(329\) −1.00000 + 5.19615i −0.0551318 + 0.286473i
\(330\) 0 0
\(331\) −3.50000 + 6.06218i −0.192377 + 0.333207i −0.946038 0.324057i \(-0.894953\pi\)
0.753660 + 0.657264i \(0.228286\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 0 0
\(334\) −8.50000 + 14.7224i −0.465099 + 0.805576i
\(335\) −36.0000 −1.96689
\(336\) 0 0
\(337\) −30.0000 −1.63420 −0.817102 0.576493i \(-0.804421\pi\)
−0.817102 + 0.576493i \(0.804421\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) 4.00000 + 6.92820i 0.216930 + 0.375735i
\(341\) −2.00000 + 3.46410i −0.108306 + 0.187592i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) −2.50000 4.33013i −0.134401 0.232789i
\(347\) −14.0000 24.2487i −0.751559 1.30174i −0.947067 0.321037i \(-0.895969\pi\)
0.195507 0.980702i \(-0.437365\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −27.5000 + 9.52628i −1.46994 + 0.509201i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) 0 0
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −13.0000 −0.687071
\(359\) −15.5000 + 26.8468i −0.818059 + 1.41692i 0.0890519 + 0.996027i \(0.471616\pi\)
−0.907111 + 0.420892i \(0.861717\pi\)
\(360\) 0 0
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 11.0000 19.0526i 0.578147 1.00138i
\(363\) 0 0
\(364\) −2.00000 1.73205i −0.104828 0.0907841i
\(365\) −8.00000 −0.418739
\(366\) 0 0
\(367\) 7.00000 + 12.1244i 0.365397 + 0.632886i 0.988840 0.148983i \(-0.0475999\pi\)
−0.623443 + 0.781869i \(0.714267\pi\)
\(368\) −1.00000 1.73205i −0.0521286 0.0902894i
\(369\) 0 0
\(370\) −8.00000 −0.415900
\(371\) 24.0000 + 20.7846i 1.24602 + 1.07908i
\(372\) 0 0
\(373\) 3.50000 6.06218i 0.181223 0.313888i −0.761074 0.648665i \(-0.775328\pi\)
0.942297 + 0.334777i \(0.108661\pi\)
\(374\) 1.00000 + 1.73205i 0.0517088 + 0.0895622i
\(375\) 0 0
\(376\) 1.00000 1.73205i 0.0515711 0.0893237i
\(377\) 1.00000 0.0515026
\(378\) 0 0
\(379\) −29.0000 −1.48963 −0.744815 0.667271i \(-0.767462\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) −12.0000 + 20.7846i −0.615587 + 1.06623i
\(381\) 0 0
\(382\) 7.00000 + 12.1244i 0.358151 + 0.620336i
\(383\) 4.00000 6.92820i 0.204390 0.354015i −0.745548 0.666452i \(-0.767812\pi\)
0.949938 + 0.312437i \(0.101145\pi\)
\(384\) 0 0
\(385\) −10.0000 + 3.46410i −0.509647 + 0.176547i
\(386\) −22.0000 −1.11977
\(387\) 0 0
\(388\) 2.50000 + 4.33013i 0.126918 + 0.219829i
\(389\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 5.50000 4.33013i 0.277792 0.218704i
\(393\) 0 0
\(394\) −1.50000 + 2.59808i −0.0755689 + 0.130889i
\(395\) 30.0000 + 51.9615i 1.50946 + 2.61447i
\(396\) 0 0
\(397\) 15.0000 25.9808i 0.752828 1.30394i −0.193618 0.981077i \(-0.562022\pi\)
0.946447 0.322860i \(-0.104644\pi\)
\(398\) 10.0000 0.501255
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) 7.50000 12.9904i 0.374532 0.648709i −0.615725 0.787961i \(-0.711137\pi\)
0.990257 + 0.139253i \(0.0444700\pi\)
\(402\) 0 0
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) −7.50000 + 12.9904i −0.373139 + 0.646296i
\(405\) 0 0
\(406\) −0.500000 + 2.59808i −0.0248146 + 0.128940i
\(407\) −2.00000 −0.0991363
\(408\) 0 0
\(409\) 16.0000 + 27.7128i 0.791149 + 1.37031i 0.925256 + 0.379344i \(0.123850\pi\)
−0.134107 + 0.990967i \(0.542817\pi\)
\(410\) −4.00000 6.92820i −0.197546 0.342160i
\(411\) 0 0
\(412\) 12.0000 0.591198
\(413\) −18.0000 15.5885i −0.885722 0.767058i
\(414\) 0 0
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) −3.00000 + 5.19615i −0.146735 + 0.254152i
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 7.00000 12.1244i 0.340755 0.590204i
\(423\) 0 0
\(424\) −6.00000 10.3923i −0.291386 0.504695i
\(425\) 11.0000 19.0526i 0.533578 0.924185i
\(426\) 0 0
\(427\) −2.50000 + 12.9904i −0.120983 + 0.628649i
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) −8.00000 13.8564i −0.385794 0.668215i
\(431\) 0.500000 + 0.866025i 0.0240842 + 0.0417150i 0.877816 0.478997i \(-0.159000\pi\)
−0.853732 + 0.520712i \(0.825666\pi\)
\(432\) 0 0
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) −10.0000 + 3.46410i −0.480015 + 0.166282i
\(435\) 0 0
\(436\) −5.00000 + 8.66025i −0.239457 + 0.414751i
\(437\) −6.00000 10.3923i −0.287019 0.497131i
\(438\) 0 0
\(439\) 2.50000 4.33013i 0.119318 0.206666i −0.800179 0.599761i \(-0.795262\pi\)
0.919498 + 0.393095i \(0.128596\pi\)
\(440\) 4.00000 0.190693
\(441\) 0 0
\(442\) 2.00000 0.0951303
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 0 0
\(445\) 12.0000 + 20.7846i 0.568855 + 0.985285i
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) 0 0
\(448\) −2.50000 + 0.866025i −0.118114 + 0.0409159i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −1.00000 1.73205i −0.0470882 0.0815591i
\(452\) 8.50000 + 14.7224i 0.399806 + 0.692485i
\(453\) 0 0
\(454\) −10.0000 −0.469323
\(455\) −2.00000 + 10.3923i −0.0937614 + 0.487199i
\(456\) 0 0
\(457\) −1.00000 + 1.73205i −0.0467780 + 0.0810219i −0.888466 0.458942i \(-0.848229\pi\)
0.841688 + 0.539964i \(0.181562\pi\)
\(458\) 8.00000 + 13.8564i 0.373815 + 0.647467i
\(459\) 0 0
\(460\) −4.00000 + 6.92820i −0.186501 + 0.323029i
\(461\) 3.00000 0.139724 0.0698620 0.997557i \(-0.477744\pi\)
0.0698620 + 0.997557i \(0.477744\pi\)
\(462\) 0 0
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 0.500000 0.866025i 0.0232119 0.0402042i
\(465\) 0 0
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) 0 0
\(469\) −18.0000 15.5885i −0.831163 0.719808i
\(470\) −8.00000 −0.369012
\(471\) 0 0
\(472\) 4.50000 + 7.79423i 0.207129 + 0.358758i
\(473\) −2.00000 3.46410i −0.0919601 0.159280i
\(474\) 0 0
\(475\) 66.0000 3.02829
\(476\) −1.00000 + 5.19615i −0.0458349 + 0.238165i
\(477\) 0 0
\(478\) 9.50000 16.4545i 0.434520 0.752611i
\(479\) −18.5000 32.0429i −0.845287 1.46408i −0.885372 0.464883i \(-0.846096\pi\)
0.0400855 0.999196i \(-0.487237\pi\)
\(480\) 0 0
\(481\) −1.00000 + 1.73205i −0.0455961 + 0.0789747i
\(482\) 30.0000 1.36646
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 10.0000 17.3205i 0.454077 0.786484i
\(486\) 0 0
\(487\) 2.00000 + 3.46410i 0.0906287 + 0.156973i 0.907776 0.419456i \(-0.137779\pi\)
−0.817147 + 0.576429i \(0.804446\pi\)
\(488\) 2.50000 4.33013i 0.113170 0.196016i
\(489\) 0 0
\(490\) −26.0000 10.3923i −1.17456 0.469476i
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 0 0
\(493\) −1.00000 1.73205i −0.0450377 0.0780076i
\(494\) 3.00000 + 5.19615i 0.134976 + 0.233786i
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 10.0000 3.46410i 0.448561 0.155386i
\(498\) 0 0
\(499\) 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) −12.0000 20.7846i −0.536656 0.929516i
\(501\) 0 0
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) 60.0000 2.66996
\(506\) −1.00000 + 1.73205i −0.0444554 + 0.0769991i
\(507\) 0 0
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) 1.00000 1.73205i 0.0443242 0.0767718i −0.843012 0.537895i \(-0.819220\pi\)
0.887336 + 0.461123i \(0.152553\pi\)
\(510\) 0 0
\(511\) −4.00000 3.46410i −0.176950 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −10.5000 18.1865i −0.463135 0.802174i
\(515\) −24.0000 41.5692i −1.05757 1.83176i
\(516\) 0 0
\(517\) −2.00000 −0.0879599
\(518\) −4.00000 3.46410i −0.175750 0.152204i
\(519\) 0 0
\(520\) 2.00000 3.46410i 0.0877058 0.151911i
\(521\) −13.0000 22.5167i −0.569540 0.986473i −0.996611 0.0822547i \(-0.973788\pi\)
0.427071 0.904218i \(-0.359545\pi\)
\(522\) 0 0
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) 18.0000 0.786334
\(525\) 0 0
\(526\) −3.00000 −0.130806
\(527\) 4.00000 6.92820i 0.174243 0.301797i
\(528\) 0 0
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) −24.0000 + 41.5692i −1.04249 + 1.80565i
\(531\) 0 0
\(532\) −15.0000 + 5.19615i −0.650332 + 0.225282i
\(533\) −2.00000 −0.0866296
\(534\) 0 0
\(535\) 16.0000 + 27.7128i 0.691740 + 1.19813i
\(536\) 4.50000 + 7.79423i 0.194370 + 0.336659i
\(537\) 0 0
\(538\) −12.0000 −0.517357
\(539\) −6.50000 2.59808i −0.279975 0.111907i
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) −12.5000 21.6506i −0.536921 0.929974i
\(543\) 0 0
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 40.0000 1.71341
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −4.50000 + 7.79423i −0.192230 + 0.332953i
\(549\) 0 0
\(550\) −5.50000 9.52628i −0.234521 0.406202i
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 0 0
\(553\) −7.50000 + 38.9711i −0.318932 + 1.65722i
\(554\) −3.00000 −0.127458
\(555\) 0 0
\(556\) −4.00000 6.92820i −0.169638 0.293821i
\(557\) 19.0000 + 32.9090i 0.805056 + 1.39440i 0.916253 + 0.400599i \(0.131198\pi\)
−0.111198 + 0.993798i \(0.535469\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) 8.00000 + 6.92820i 0.338062 + 0.292770i
\(561\) 0 0
\(562\) −5.00000 + 8.66025i −0.210912 + 0.365311i
\(563\) 13.0000 + 22.5167i 0.547885 + 0.948964i 0.998419 + 0.0562051i \(0.0179001\pi\)
−0.450535 + 0.892759i \(0.648767\pi\)
\(564\) 0 0
\(565\) 34.0000 58.8897i 1.43039 2.47751i
\(566\) −6.00000 −0.252199
\(567\) 0 0
\(568\) −4.00000 −0.167836
\(569\) 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i \(-0.561165\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(570\) 0 0
\(571\) 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i \(-0.0292272\pi\)
−0.577301 + 0.816532i \(0.695894\pi\)
\(572\) 0.500000 0.866025i 0.0209061 0.0362103i
\(573\) 0 0
\(574\) 1.00000 5.19615i 0.0417392 0.216883i
\(575\) 22.0000 0.917463
\(576\) 0 0
\(577\) 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i \(-0.120121\pi\)
−0.783930 + 0.620850i \(0.786788\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 0 0
\(580\) −4.00000 −0.166091
\(581\) −15.0000 + 5.19615i −0.622305 + 0.215573i
\(582\) 0 0
\(583\) −6.00000 + 10.3923i −0.248495 + 0.430405i
\(584\) 1.00000 + 1.73205i 0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) −3.00000 + 5.19615i −0.123929 + 0.214651i
\(587\) 3.00000 0.123823 0.0619116 0.998082i \(-0.480280\pi\)
0.0619116 + 0.998082i \(0.480280\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) 18.0000 31.1769i 0.741048 1.28353i
\(591\) 0 0
\(592\) 1.00000 + 1.73205i 0.0410997 + 0.0711868i
\(593\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 0 0
\(595\) 20.0000 6.92820i 0.819920 0.284029i
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 1.00000 + 1.73205i 0.0408930 + 0.0708288i
\(599\) −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
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 2.00000 10.3923i 0.0815139 0.423559i
\(603\) 0 0
\(604\) −4.50000 + 7.79423i −0.183102 + 0.317143i
\(605\) −2.00000 3.46410i −0.0813116 0.140836i
\(606\) 0 0
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) 6.00000 0.243332
\(609\) 0 0
\(610\) −20.0000 −0.809776
\(611\) −1.00000 + 1.73205i −0.0404557 + 0.0700713i
\(612\) 0 0
\(613\) −11.0000 19.0526i −0.444286 0.769526i 0.553716 0.832705i \(-0.313209\pi\)
−0.998002 + 0.0631797i \(0.979876\pi\)
\(614\) −16.0000 + 27.7128i −0.645707 + 1.11840i
\(615\) 0 0
\(616\) 2.00000 + 1.73205i 0.0805823 + 0.0697863i
\(617\) 27.0000 1.08698 0.543490 0.839416i \(-0.317103\pi\)
0.543490 + 0.839416i \(0.317103\pi\)
\(618\) 0 0
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) −8.00000 13.8564i −0.321288 0.556487i
\(621\) 0 0
\(622\) 28.0000 1.12270
\(623\) −3.00000 + 15.5885i −0.120192 + 0.624538i
\(624\) 0 0
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) −0.500000 0.866025i −0.0199840 0.0346133i
\(627\) 0 0
\(628\) −2.00000 + 3.46410i −0.0798087 + 0.138233i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 7.50000 12.9904i 0.298334 0.516730i
\(633\) 0 0
\(634\) −6.00000 10.3923i −0.238290 0.412731i
\(635\) −10.0000 + 17.3205i −0.396838 + 0.687343i
\(636\) 0 0
\(637\) −5.50000 + 4.33013i −0.217918 + 0.171566i
\(638\) −1.00000 −0.0395904
\(639\) 0 0
\(640\) −2.00000 3.46410i −0.0790569 0.136931i
\(641\) 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i \(-0.109788\pi\)
−0.763367 + 0.645966i \(0.776455\pi\)
\(642\) 0 0
\(643\) 1.00000 0.0394362 0.0197181 0.999806i \(-0.493723\pi\)
0.0197181 + 0.999806i \(0.493723\pi\)
\(644\) −5.00000 + 1.73205i −0.197028 + 0.0682524i
\(645\) 0 0
\(646\) 6.00000 10.3923i 0.236067 0.408880i
\(647\) 12.0000 + 20.7846i 0.471769 + 0.817127i 0.999478 0.0322975i \(-0.0102824\pi\)
−0.527710 + 0.849425i \(0.676949\pi\)
\(648\) 0 0
\(649\) 4.50000 7.79423i 0.176640 0.305950i
\(650\) −11.0000 −0.431455
\(651\) 0 0
\(652\) 13.0000 0.509119
\(653\) 11.0000 19.0526i 0.430463 0.745584i −0.566450 0.824096i \(-0.691684\pi\)
0.996913 + 0.0785119i \(0.0250169\pi\)
\(654\) 0 0
\(655\) −36.0000 62.3538i −1.40664 2.43637i
\(656\) −1.00000 + 1.73205i −0.0390434 + 0.0676252i
\(657\) 0 0
\(658\) −4.00000 3.46410i −0.155936 0.135045i
\(659\) 32.0000 1.24654 0.623272 0.782006i \(-0.285803\pi\)
0.623272 + 0.782006i \(0.285803\pi\)
\(660\) 0 0
\(661\) 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) −3.50000 6.06218i −0.136031 0.235613i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 48.0000 + 41.5692i 1.86136 + 1.61199i
\(666\) 0 0
\(667\) 1.00000 1.73205i 0.0387202 0.0670653i
\(668\) −8.50000 14.7224i −0.328875 0.569628i
\(669\) 0 0
\(670\) 18.0000 31.1769i 0.695401 1.20447i
\(671\) −5.00000 −0.193023
\(672\) 0 0
\(673\) 16.0000 0.616755 0.308377 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) 15.0000 25.9808i 0.577778 1.00074i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 19.0000 32.9090i 0.730229 1.26479i −0.226556 0.973998i \(-0.572747\pi\)
0.956785 0.290796i \(-0.0939201\pi\)
\(678\) 0 0
\(679\) 12.5000 4.33013i 0.479706 0.166175i
\(680\) −8.00000 −0.306786
\(681\) 0 0
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) −16.5000 28.5788i −0.631355 1.09354i −0.987275 0.159022i \(-0.949166\pi\)
0.355920 0.934516i \(-0.384168\pi\)
\(684\) 0 0
\(685\) 36.0000 1.37549
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 0 0
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −7.50000 + 12.9904i −0.285313 + 0.494177i −0.972685 0.232128i \(-0.925431\pi\)
0.687372 + 0.726306i \(0.258764\pi\)
\(692\) 5.00000 0.190071
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) −16.0000 + 27.7128i −0.606915 + 1.05121i
\(696\) 0 0
\(697\) 2.00000 + 3.46410i 0.0757554 + 0.131212i
\(698\) −1.00000 + 1.73205i −0.0378506 + 0.0655591i
\(699\) 0 0
\(700\) 5.50000 28.5788i 0.207880 1.08018i
\(701\) −39.0000 −1.47301 −0.736505 0.676432i \(-0.763525\pi\)
−0.736505 + 0.676432i \(0.763525\pi\)
\(702\) 0 0
\(703\) 6.00000 + 10.3923i 0.226294 + 0.391953i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) 30.0000 + 25.9808i 1.12827 + 0.977107i
\(708\) 0 0
\(709\) −3.00000 + 5.19615i −0.112667 + 0.195146i −0.916845 0.399244i \(-0.869273\pi\)
0.804178 + 0.594389i \(0.202606\pi\)
\(710\) 8.00000 + 13.8564i 0.300235 + 0.520022i
\(711\) 0 0
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 8.00000 0.299602
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) 6.50000 11.2583i 0.242916 0.420744i
\(717\) 0 0
\(718\) −15.5000 26.8468i −0.578455 1.00191i
\(719\) −13.0000 + 22.5167i −0.484818 + 0.839730i −0.999848 0.0174426i \(-0.994448\pi\)
0.515030 + 0.857172i \(0.327781\pi\)
\(720\) 0 0
\(721\) 6.00000 31.1769i 0.223452 1.16109i
\(722\) 17.0000 0.632674
\(723\) 0 0
\(724\) 11.0000 + 19.0526i 0.408812 + 0.708083i
\(725\) 5.50000 + 9.52628i 0.204265 + 0.353797i
\(726\) 0 0
\(727\) −34.0000 −1.26099 −0.630495 0.776193i \(-0.717148\pi\)
−0.630495 + 0.776193i \(0.717148\pi\)
\(728\) 2.50000 0.866025i 0.0926562 0.0320970i
\(729\) 0 0
\(730\) 4.00000 6.92820i 0.148047 0.256424i
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 0 0
\(733\) 0.500000 0.866025i 0.0184679 0.0319874i −0.856644 0.515908i \(-0.827454\pi\)
0.875112 + 0.483921i \(0.160788\pi\)
\(734\) −14.0000 −0.516749
\(735\) 0 0
\(736\) 2.00000 0.0737210
\(737\) 4.50000 7.79423i 0.165760 0.287104i
\(738\) 0 0
\(739\) −9.00000 15.5885i −0.331070 0.573431i 0.651652 0.758518i \(-0.274076\pi\)
−0.982722 + 0.185088i \(0.940743\pi\)
\(740\) 4.00000 6.92820i 0.147043 0.254686i
\(741\) 0 0
\(742\) −30.0000 + 10.3923i −1.10133 + 0.381514i
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) −20.0000 34.6410i −0.732743 1.26915i
\(746\) 3.50000 + 6.06218i 0.128144 + 0.221952i
\(747\) 0 0
\(748\) −2.00000 −0.0731272
\(749\) −4.00000 + 20.7846i −0.146157 + 0.759453i
\(750\) 0 0
\(751\) 22.0000 38.1051i 0.802791 1.39048i −0.114981 0.993368i \(-0.536681\pi\)
0.917772 0.397108i \(-0.129986\pi\)
\(752\) 1.00000 + 1.73205i 0.0364662 + 0.0631614i
\(753\) 0 0
\(754\) −0.500000 + 0.866025i −0.0182089 + 0.0315388i
\(755\) 36.0000 1.31017
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 14.5000 25.1147i 0.526664 0.912208i
\(759\) 0 0
\(760\) −12.0000 20.7846i −0.435286 0.753937i
\(761\) 27.0000 46.7654i 0.978749 1.69524i 0.311787 0.950152i \(-0.399073\pi\)
0.666962 0.745091i \(-0.267594\pi\)
\(762\) 0 0
\(763\) 20.0000 + 17.3205i 0.724049 + 0.627044i
\(764\) −14.0000 −0.506502
\(765\) 0 0
\(766\) 4.00000 + 6.92820i 0.144526 + 0.250326i
\(767\) −4.50000 7.79423i −0.162486 0.281433i
\(768\) 0 0
\(769\) −38.0000 −1.37032 −0.685158 0.728395i \(-0.740267\pi\)
−0.685158 + 0.728395i \(0.740267\pi\)
\(770\) 2.00000 10.3923i 0.0720750 0.374513i
\(771\) 0 0
\(772\) 11.0000 19.0526i 0.395899 0.685717i
\(773\) −12.0000 20.7846i −0.431610 0.747570i 0.565402 0.824815i \(-0.308721\pi\)
−0.997012 + 0.0772449i \(0.975388\pi\)
\(774\) 0 0
\(775\) −22.0000 + 38.1051i −0.790263 + 1.36878i
\(776\) −5.00000 −0.179490
\(777\) 0 0
\(778\) 0 0
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) 2.00000 3.46410i 0.0715199 0.123876i
\(783\) 0 0
\(784\) 1.00000 + 6.92820i 0.0357143 + 0.247436i
\(785\) 16.0000 0.571064
\(786\) 0 0
\(787\) 11.0000 + 19.0526i 0.392108 + 0.679150i 0.992727 0.120384i \(-0.0384127\pi\)
−0.600620 + 0.799535i \(0.705079\pi\)
\(788\) −1.50000 2.59808i −0.0534353 0.0925526i
\(789\)