Properties

Label 1386.2.k.e.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.e.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} +1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} -9.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{38} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} -5.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-5.50000 - 9.52628i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.00000 - 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(-3.00000 + 5.19615i) q^{82} +6.00000 q^{83} +(2.00000 - 3.46410i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-9.00000 + 15.5885i) q^{89} +(0.500000 + 2.59808i) q^{91} +6.00000 q^{92} +(-3.00000 - 5.19615i) q^{94} -13.0000 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - q^{7} + 2q^{8} - q^{11} - 2q^{13} + 5q^{14} - q^{16} - 6q^{17} - 2q^{19} + 2q^{22} - 6q^{23} + 5q^{25} + q^{26} - 4q^{28} - 18q^{29} + 4q^{31} - q^{32} + 12q^{34} - 2q^{37} - 2q^{38} + 12q^{41} - 8q^{43} - q^{44} - 6q^{46} - 6q^{47} - 13q^{49} - 10q^{50} + q^{52} - q^{56} + 9q^{58} - 3q^{59} - 11q^{61} - 8q^{62} + 2q^{64} - 11q^{67} - 6q^{68} - 2q^{73} - 2q^{74} + 4q^{76} - 4q^{77} - 5q^{79} - 6q^{82} + 12q^{83} + 4q^{86} - q^{88} - 18q^{89} + q^{91} + 12q^{92} - 6q^{94} - 26q^{97} + 2q^{98} + O(q^{100}) \)

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
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −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 \(0.544284\pi\)
\(14\) 2.50000 + 0.866025i 0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) 0 0
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 0 0
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) 0 0
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.00000 + 5.19615i −0.331295 + 0.573819i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −9.00000 + 15.5885i −0.953998 + 1.65237i −0.217354 + 0.976093i \(0.569742\pi\)
−0.736644 + 0.676280i \(0.763591\pi\)
\(90\) 0 0
\(91\) 0.500000 + 2.59808i 0.0524142 + 0.272352i
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −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
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 0 0
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 0 0
\(109\) −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i \(-0.197202\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.50000 + 7.79423i 0.417815 + 0.723676i
\(117\) 0 0
\(118\) 3.00000 0.276172
\(119\) −12.0000 + 10.3923i −1.10004 + 0.952661i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −5.50000 9.52628i −0.497947 0.862469i
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 0 0
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) 0 0
\(133\) 5.00000 + 1.73205i 0.433555 + 0.150188i
\(134\) 11.0000 0.950255
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −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 \(0.389818\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.500000 + 0.866025i 0.0418121 + 0.0724207i
\(144\) 0 0
\(145\) 0 0
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) 0 0
\(154\) −0.500000 2.59808i −0.0402911 0.209359i
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −2.50000 4.33013i −0.198889 0.344486i
\(159\) 0 0
\(160\) 0 0
\(161\) 15.0000 + 5.19615i 1.18217 + 0.409514i
\(162\) 0 0
\(163\) −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i \(0.398564\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) 0 0
\(175\) 10.0000 8.66025i 0.755929 0.654654i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −9.00000 15.5885i −0.674579 1.16840i
\(179\) −7.50000 12.9904i −0.560576 0.970947i −0.997446 0.0714220i \(-0.977246\pi\)
0.436870 0.899525i \(-0.356087\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −2.50000 0.866025i −0.185312 0.0641941i
\(183\) 0 0
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) 0 0
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 6.50000 11.2583i 0.466673 0.808301i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) 2.50000 + 4.33013i 0.176777 + 0.306186i
\(201\) 0 0
\(202\) 15.0000 1.05540
\(203\) 4.50000 + 23.3827i 0.315838 + 1.64114i
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 + 13.8564i 0.557386 + 0.965422i
\(207\) 0 0
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 0 0
\(216\) 0 0
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) 0 0
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) 0 0
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 0 0
\(226\) 4.50000 7.79423i 0.299336 0.518464i
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) 0 0
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) 0 0
\(238\) −3.00000 15.5885i −0.194461 1.01045i
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 0 0
\(241\) −13.0000 22.5167i −0.837404 1.45043i −0.892058 0.451920i \(-0.850739\pi\)
0.0546547 0.998505i \(-0.482594\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 0 0
\(244\) 11.0000 0.704203
\(245\) 0 0
\(246\) 0 0
\(247\) 1.00000 1.73205i 0.0636285 0.110208i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 3.50000 6.06218i 0.219610 0.380375i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) 0 0
\(259\) 5.00000 + 1.73205i 0.310685 + 0.107624i
\(260\) 0 0
\(261\) 0 0
\(262\) 9.00000 + 15.5885i 0.556022 + 0.963058i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.00000 + 3.46410i −0.245256 + 0.212398i
\(267\) 0 0
\(268\) −5.50000 + 9.52628i −0.335966 + 0.581910i
\(269\) 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
\(271\) −14.5000 + 25.1147i −0.880812 + 1.52561i −0.0303728 + 0.999539i \(0.509669\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 9.00000 0.543710
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) 0 0
\(277\) −14.5000 25.1147i −0.871221 1.50900i −0.860735 0.509053i \(-0.829996\pi\)
−0.0104855 0.999945i \(-0.503338\pi\)
\(278\) −4.00000 + 6.92820i −0.239904 + 0.415526i
\(279\) 0 0
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i \(-0.0706075\pi\)
−0.678280 + 0.734804i \(0.737274\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −1.00000 −0.0591312
\(287\) −3.00000 15.5885i −0.177084 0.920158i
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.00000 + 1.73205i −0.0581238 + 0.100673i
\(297\) 0 0
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) 2.00000 + 10.3923i 0.115278 + 0.599002i
\(302\) −19.0000 −1.09333
\(303\) 0 0
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 2.50000 + 0.866025i 0.142451 + 0.0493464i
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 0 0
\(313\) −8.50000 + 14.7224i −0.480448 + 0.832161i −0.999748 0.0224310i \(-0.992859\pi\)
0.519300 + 0.854592i \(0.326193\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 5.00000 0.281272
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) 0 0
\(322\) −12.0000 + 10.3923i −0.668734 + 0.579141i
\(323\) 12.0000 0.667698
\(324\) 0 0
\(325\) −2.50000 4.33013i −0.138675 0.240192i
\(326\) −8.50000 14.7224i −0.470771 0.815400i
\(327\) 0 0
\(328\) 6.00000 0.331295
\(329\) 15.0000 + 5.19615i 0.826977 + 0.286473i
\(330\) 0 0
\(331\) −17.5000 + 30.3109i −0.961887 + 1.66604i −0.244131 + 0.969742i \(0.578503\pi\)
−0.717756 + 0.696295i \(0.754831\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 0 0
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) 0 0
\(341\) 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
\(346\) −10.5000 18.1865i −0.564483 0.977714i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 2.50000 + 12.9904i 0.133631 + 0.694365i
\(351\) 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
\(355\) 0 0
\(356\) 18.0000 0.953998
\(357\) 0 0
\(358\) 15.0000 0.792775
\(359\) −1.50000 + 2.59808i −0.0791670 + 0.137121i −0.902891 0.429870i \(-0.858559\pi\)
0.823724 + 0.566991i \(0.191893\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −1.00000 + 1.73205i −0.0525588 + 0.0910346i
\(363\) 0 0
\(364\) 2.00000 1.73205i 0.104828 0.0907841i
\(365\) 0 0
\(366\) 0 0
\(367\) 5.00000 + 8.66025i 0.260998 + 0.452062i 0.966507 0.256639i \(-0.0826151\pi\)
−0.705509 + 0.708700i \(0.749282\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 15.5000 26.8468i 0.802560 1.39007i −0.115367 0.993323i \(-0.536804\pi\)
0.917926 0.396751i \(-0.129862\pi\)
\(374\) −3.00000 5.19615i −0.155126 0.268687i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 3.00000 + 5.19615i 0.153493 + 0.265858i
\(383\) −18.0000 + 31.1769i −0.919757 + 1.59307i −0.119974 + 0.992777i \(0.538281\pi\)
−0.799783 + 0.600289i \(0.795052\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) 6.50000 + 11.2583i 0.329988 + 0.571555i
\(389\) 6.00000 + 10.3923i 0.304212 + 0.526911i 0.977086 0.212847i \(-0.0682735\pi\)
−0.672874 + 0.739758i \(0.734940\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) −6.50000 + 2.59808i −0.328300 + 0.131223i
\(393\) 0 0
\(394\) −1.50000 + 2.59808i −0.0755689 + 0.130889i
\(395\) 0 0
\(396\) 0 0
\(397\) 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i \(-0.647170\pi\)
0.998125 0.0612128i \(-0.0194968\pi\)
\(398\) 14.0000 0.701757
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −16.5000 + 28.5788i −0.823971 + 1.42716i 0.0787327 + 0.996896i \(0.474913\pi\)
−0.902703 + 0.430263i \(0.858421\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) −7.50000 + 12.9904i −0.373139 + 0.646296i
\(405\) 0 0
\(406\) −22.5000 7.79423i −1.11666 0.386821i
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i \(-0.135136\pi\)
−0.812333 + 0.583193i \(0.801803\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −16.0000 −0.788263
\(413\) −6.00000 + 5.19615i −0.295241 + 0.255686i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) −1.00000 + 1.73205i −0.0489116 + 0.0847174i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 5.00000 8.66025i 0.243396 0.421575i
\(423\) 0 0
\(424\) 0 0
\(425\) 15.0000 25.9808i 0.727607 1.26025i
\(426\) 0 0
\(427\) 27.5000 + 9.52628i 1.33082 + 0.461009i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −1.50000 2.59808i −0.0722525 0.125145i 0.827636 0.561266i \(-0.189685\pi\)
−0.899888 + 0.436121i \(0.856352\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 2.00000 + 10.3923i 0.0960031 + 0.498847i
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) −6.00000 10.3923i −0.287019 0.497131i
\(438\) 0 0
\(439\) 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i \(-0.825737\pi\)
0.877711 + 0.479191i \(0.159070\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −13.0000 + 22.5167i −0.615568 + 1.06619i
\(447\) 0 0
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) 4.50000 + 7.79423i 0.211662 + 0.366610i
\(453\) 0 0
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) 0 0
\(457\) 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) 8.00000 + 13.8564i 0.373815 + 0.647467i
\(459\) 0 0
\(460\) 0 0
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 0 0
\(469\) −22.0000 + 19.0526i −1.01587 + 0.879765i
\(470\) 0 0
\(471\) 0 0
\(472\) −1.50000 2.59808i −0.0690431 0.119586i
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) 0 0
\(475\) −10.0000 −0.458831
\(476\) 15.0000 + 5.19615i 0.687524 + 0.238165i
\(477\) 0 0
\(478\) −4.50000 + 7.79423i −0.205825 + 0.356500i
\(479\) 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i \(-0.0553307\pi\)
−0.642246 + 0.766498i \(0.721997\pi\)
\(480\) 0 0
\(481\) 1.00000 1.73205i 0.0455961 0.0789747i
\(482\) 26.0000 1.18427
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 0 0
\(487\) −10.0000 17.3205i −0.453143 0.784867i 0.545436 0.838152i \(-0.316364\pi\)
−0.998579 + 0.0532853i \(0.983031\pi\)
\(488\) −5.50000 + 9.52628i −0.248973 + 0.431234i
\(489\) 0 0
\(490\) 0 0
\(491\) −42.0000 −1.89543 −0.947717 0.319113i \(-0.896615\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) 0 0
\(493\) 27.0000 + 46.7654i 1.21602 + 2.10621i
\(494\) 1.00000 + 1.73205i 0.0449921 + 0.0779287i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 20.0000 34.6410i 0.895323 1.55074i 0.0619186 0.998081i \(-0.480278\pi\)
0.833404 0.552664i \(-0.186389\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −6.00000 + 10.3923i −0.267793 + 0.463831i
\(503\) 33.0000 1.47140 0.735699 0.677309i \(-0.236854\pi\)
0.735699 + 0.677309i \(0.236854\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −3.00000 + 5.19615i −0.133366 + 0.230997i
\(507\) 0 0
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i \(-0.875786\pi\)
0.791849 + 0.610718i \(0.209119\pi\)
\(510\) 0 0
\(511\) −4.00000 + 3.46410i −0.176950 + 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 1.50000 + 2.59808i 0.0661622 + 0.114596i
\(515\) 0 0
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) −4.00000 + 3.46410i −0.175750 + 0.152204i
\(519\) 0 0
\(520\) 0 0
\(521\) −21.0000 36.3731i −0.920027 1.59353i −0.799370 0.600839i \(-0.794833\pi\)
−0.120656 0.992694i \(-0.538500\pi\)
\(522\) 0 0
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) 9.00000 0.392419
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) −1.00000 5.19615i −0.0433555 0.225282i
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) 0 0
\(536\) −5.50000 9.52628i −0.237564 0.411473i
\(537\) 0 0
\(538\) −12.0000 −0.517357
\(539\) 5.50000 + 4.33013i 0.236902 + 0.186512i
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) −14.5000 25.1147i −0.622828 1.07877i
\(543\) 0 0
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −4.50000 + 7.79423i −0.192230 + 0.332953i
\(549\) 0 0
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) 9.00000 15.5885i 0.383413 0.664091i
\(552\) 0 0
\(553\) 12.5000 + 4.33013i 0.531554 + 0.184136i
\(554\) 29.0000 1.23209
\(555\) 0 0
\(556\) −4.00000 6.92820i −0.169638 0.293821i
\(557\) −9.00000 15.5885i −0.381342 0.660504i 0.609912 0.792469i \(-0.291205\pi\)
−0.991254 + 0.131965i \(0.957871\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) 9.00000 15.5885i 0.379642 0.657559i
\(563\) −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i \(-0.290503\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −10.0000 −0.420331
\(567\) 0 0
\(568\) 0 0
\(569\) −18.0000 + 31.1769i −0.754599 + 1.30700i 0.190974 + 0.981595i \(0.438835\pi\)
−0.945573 + 0.325409i \(0.894498\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 0.500000 0.866025i 0.0209061 0.0362103i
\(573\) 0 0
\(574\) 15.0000 + 5.19615i 0.626088 + 0.216883i
\(575\) −30.0000 −1.25109
\(576\) 0 0
\(577\) 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i \(-0.120121\pi\)
−0.783930 + 0.620850i \(0.786788\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) 0 0
\(580\) 0 0
\(581\) −3.00000 15.5885i −0.124461 0.646718i
\(582\) 0 0
\(583\) 0 0
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) 0 0
\(586\) −15.0000 + 25.9808i −0.619644 + 1.07326i
\(587\) −9.00000 −0.371470 −0.185735 0.982600i \(-0.559467\pi\)
−0.185735 + 0.982600i \(0.559467\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i \(-0.568551\pi\)
0.952869 0.303383i \(-0.0981160\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) 3.00000 + 5.19615i 0.122679 + 0.212486i
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −10.0000 3.46410i −0.407570 0.141186i
\(603\) 0 0
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) 0 0
\(606\) 0 0
\(607\) 20.0000 34.6410i 0.811775 1.40604i −0.0998457 0.995003i \(-0.531835\pi\)
0.911621 0.411033i \(-0.134832\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) 3.00000 5.19615i 0.121367 0.210214i
\(612\) 0 0
\(613\) 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i \(-0.101939\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(614\) −10.0000 + 17.3205i −0.403567 + 0.698999i
\(615\) 0 0
\(616\) −2.00000 + 1.73205i −0.0805823 + 0.0697863i
\(617\) −21.0000 −0.845428 −0.422714 0.906263i \(-0.638923\pi\)
−0.422714 + 0.906263i \(0.638923\pi\)
\(618\) 0 0
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) 45.0000 + 15.5885i 1.80289 + 0.624538i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −8.50000 14.7224i −0.339728 0.588427i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −2.50000 + 4.33013i −0.0994447 + 0.172243i
\(633\) 0 0
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 0 0
\(636\) 0 0
\(637\) 6.50000 2.59808i 0.257539 0.102940i
\(638\) −9.00000 −0.356313
\(639\) 0 0
\(640\) 0 0
\(641\) 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
\(643\) 5.00000 0.197181 0.0985904 0.995128i \(-0.468567\pi\)
0.0985904 + 0.995128i \(0.468567\pi\)
\(644\) −3.00000 15.5885i −0.118217 0.614271i
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) −6.00000 10.3923i −0.235884 0.408564i 0.723645 0.690172i \(-0.242465\pi\)
−0.959529 + 0.281609i \(0.909132\pi\)
\(648\) 0 0
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) 5.00000 0.196116
\(651\) 0 0
\(652\) 17.0000 0.665771
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 0 0
\(658\) −12.0000 + 10.3923i −0.467809 + 0.405134i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) −17.5000 30.3109i −0.680157 1.17807i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) 1.50000 + 2.59808i 0.0580367 + 0.100523i
\(669\) 0 0
\(670\) 0 0
\(671\) 11.0000 0.424650
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) −7.00000 + 12.1244i −0.269630 + 0.467013i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) 0 0
\(679\) 6.50000 + 33.7750i 0.249447 + 1.29617i
\(680\) 0 0
\(681\) 0 0
\(682\) 2.00000 + 3.46410i 0.0765840 + 0.132647i
\(683\) −10.5000 18.1865i −0.401771 0.695888i 0.592168 0.805814i \(-0.298272\pi\)
−0.993940 + 0.109926i \(0.964939\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 0 0
\(690\) 0 0
\(691\) −5.50000 + 9.52628i −0.209230 + 0.362397i −0.951472 0.307735i \(-0.900429\pi\)
0.742242 + 0.670132i \(0.233762\pi\)
\(692\) 21.0000 0.798300
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) −1.00000 + 1.73205i −0.0378506 + 0.0655591i
\(699\) 0 0
\(700\) −12.5000 4.33013i −0.472456 0.163663i
\(701\) −39.0000 −1.47301 −0.736505 0.676432i \(-0.763525\pi\)
−0.736505 + 0.676432i \(0.763525\pi\)
\(702\) 0 0
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) −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
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −9.00000 + 15.5885i −0.337289 + 0.584202i
\(713\) −24.0000 −0.898807
\(714\) 0 0
\(715\) 0 0
\(716\) −7.50000 + 12.9904i −0.280288 + 0.485473i
\(717\) 0 0
\(718\) −1.50000 2.59808i −0.0559795 0.0969593i
\(719\) −21.0000 + 36.3731i −0.783168 + 1.35649i 0.146920 + 0.989148i \(0.453064\pi\)
−0.930087 + 0.367338i \(0.880269\pi\)
\(720\) 0 0
\(721\) −40.0000 13.8564i −1.48968 0.516040i
\(722\) −15.0000 −0.558242
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) −22.5000 38.9711i −0.835629 1.44735i
\(726\) 0 0
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 0.500000 + 2.59808i 0.0185312 + 0.0962911i
\(729\) 0 0
\(730\) 0 0
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) 0 0
\(733\) 12.5000 21.6506i 0.461698 0.799684i −0.537348 0.843361i \(-0.680574\pi\)
0.999046 + 0.0436764i \(0.0139070\pi\)
\(734\) −10.0000 −0.369107
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) −5.50000 + 9.52628i −0.202595 + 0.350905i
\(738\) 0 0
\(739\) −25.0000 43.3013i −0.919640 1.59286i −0.799962 0.600050i \(-0.795147\pi\)
−0.119677 0.992813i \(-0.538186\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 15.5000 + 26.8468i 0.567495 + 0.982931i
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) −30.0000 10.3923i −1.09618 0.379727i
\(750\) 0 0
\(751\) 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i \(-0.810082\pi\)
0.900207 + 0.435463i \(0.143415\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 0 0
\(754\) −4.50000 + 7.79423i −0.163880 + 0.283849i
\(755\) 0 0
\(756\) 0 0
\(757\) −46.0000 −1.67190 −0.835949 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) −11.5000 + 19.9186i −0.417699 + 0.723476i
\(759\) 0 0
\(760\) 0 0
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) 0 0
\(763\) −4.00000 + 3.46410i −0.144810 + 0.125409i
\(764\) −6.00000 −0.217072
\(765\) 0 0
\(766\) −18.0000 31.1769i −0.650366 1.12647i
\(767\) 1.50000 + 2.59808i 0.0541619 + 0.0938111i
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 12.0000 + 20.7846i 0.431610 + 0.747570i 0.997012 0.0772449i \(-0.0246123\pi\)
−0.565402 + 0.824815i \(0.691279\pi\)
\(774\) 0 0
\(775\) −10.0000 + 17.3205i −0.359211 + 0.622171i
\(776\) −13.0000 −0.466673
\(777\) 0 0
\(778\) −12.0000 −0.430221
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 0 0
\(781\) 0 0
\(782\) −18.0000 + 31.1769i −0.643679 + 1.11488i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 0 0
\(786\) 0 0
\(787\) −7.00000 12.1244i −0.249523 0.432187i 0.713871 0.700278i \(-0.246941\pi\)
−0.963394 + 0.268091i \(0.913607\pi\)
\(788\) −1.50000 2.59808i −0.0534353 0.0925526i
\(789\) 0 0
\(790\) 0 0
\(791\) 4.50000 + 23.3827i 0.160002 + 0.831393i
\(792\) 0 0
\(793\) 5.50000 9.52628i 0.195311 0.338288i
\(794\) 11.0000 + 19.0526i 0.390375 + 0.676150i
\(795\) 0 0