Properties

Label 405.2.e.f.136.1
Level $405$
Weight $2$
Character 405.136
Analytic conductor $3.234$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
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 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.2.e.f.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{8} -1.00000 q^{10} +(2.00000 - 3.46410i) q^{11} +(1.00000 + 1.73205i) q^{13} +(0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +4.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} +(1.00000 - 1.73205i) q^{29} +(2.50000 + 4.33013i) q^{32} +(1.00000 - 1.73205i) q^{34} -10.0000 q^{37} +(2.00000 - 3.46410i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-5.00000 - 8.66025i) q^{41} +(-2.00000 + 3.46410i) q^{43} +4.00000 q^{44} +(-4.00000 + 6.92820i) q^{47} +(3.50000 + 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} -10.0000 q^{53} -4.00000 q^{55} +(-1.00000 - 1.73205i) q^{58} +(2.00000 + 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +7.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-6.00000 - 10.3923i) q^{67} +(1.00000 + 1.73205i) q^{68} -8.00000 q^{71} +10.0000 q^{73} +(-5.00000 + 8.66025i) q^{74} +(2.00000 + 3.46410i) q^{76} -1.00000 q^{80} -10.0000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-1.00000 - 1.73205i) q^{85} +(2.00000 + 3.46410i) q^{86} +(6.00000 - 10.3923i) q^{88} -6.00000 q^{89} +(4.00000 + 6.92820i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(-1.00000 + 1.73205i) q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{4} - q^{5} + 6q^{8} + O(q^{10}) \) \( 2q + q^{2} + q^{4} - q^{5} + 6q^{8} - 2q^{10} + 4q^{11} + 2q^{13} + q^{16} + 4q^{17} + 8q^{19} + q^{20} - 4q^{22} - q^{25} + 4q^{26} + 2q^{29} + 5q^{32} + 2q^{34} - 20q^{37} + 4q^{38} - 3q^{40} - 10q^{41} - 4q^{43} + 8q^{44} - 8q^{47} + 7q^{49} + q^{50} - 2q^{52} - 20q^{53} - 8q^{55} - 2q^{58} + 4q^{59} + 2q^{61} + 14q^{64} + 2q^{65} - 12q^{67} + 2q^{68} - 16q^{71} + 20q^{73} - 10q^{74} + 4q^{76} - 2q^{80} - 20q^{82} - 12q^{83} - 2q^{85} + 4q^{86} + 12q^{88} - 12q^{89} + 8q^{94} - 4q^{95} - 2q^{97} + 14q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i −0.633316 0.773893i \(-0.718307\pi\)
0.986869 + 0.161521i \(0.0516399\pi\)
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 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
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 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
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 0 0
\(29\) 1.00000 1.73205i 0.185695 0.321634i −0.758115 0.652121i \(-0.773880\pi\)
0.943811 + 0.330487i \(0.107213\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 2.50000 + 4.33013i 0.441942 + 0.765466i
\(33\) 0 0
\(34\) 1.00000 1.73205i 0.171499 0.297044i
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) −5.00000 8.66025i −0.780869 1.35250i −0.931436 0.363905i \(-0.881443\pi\)
0.150567 0.988600i \(-0.451890\pi\)
\(42\) 0 0
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 0 0
\(47\) −4.00000 + 6.92820i −0.583460 + 1.01058i 0.411606 + 0.911362i \(0.364968\pi\)
−0.995066 + 0.0992202i \(0.968365\pi\)
\(48\) 0 0
\(49\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 1.73205i −0.131306 0.227429i
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 0 0
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) −5.00000 + 8.66025i −0.581238 + 1.00673i
\(75\) 0 0
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) −10.0000 −1.10432
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 0 0
\(85\) −1.00000 1.73205i −0.108465 0.187867i
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 0 0
\(88\) 6.00000 10.3923i 0.639602 1.10782i
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 4.00000 + 6.92820i 0.412568 + 0.714590i
\(95\) −2.00000 3.46410i −0.205196 0.355409i
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 7.00000 0.707107
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) 8.00000 + 13.8564i 0.788263 + 1.36531i 0.927030 + 0.374987i \(0.122353\pi\)
−0.138767 + 0.990325i \(0.544314\pi\)
\(104\) 3.00000 + 5.19615i 0.294174 + 0.509525i
\(105\) 0 0
\(106\) −5.00000 + 8.66025i −0.485643 + 0.841158i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −2.00000 + 3.46410i −0.190693 + 0.330289i
\(111\) 0 0
\(112\) 0 0
\(113\) −1.00000 1.73205i −0.0940721 0.162938i 0.815149 0.579252i \(-0.196655\pi\)
−0.909221 + 0.416314i \(0.863322\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2.00000 0.185695
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) −1.00000 1.73205i −0.0905357 0.156813i
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −1.50000 + 2.59808i −0.132583 + 0.229640i
\(129\) 0 0
\(130\) −1.00000 1.73205i −0.0877058 0.151911i
\(131\) 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.00000 + 6.92820i −0.335673 + 0.581402i
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −2.00000 −0.166091
\(146\) 5.00000 8.66025i 0.413803 0.716728i
\(147\) 0 0
\(148\) −5.00000 8.66025i −0.410997 0.711868i
\(149\) −11.0000 19.0526i −0.901155 1.56085i −0.825997 0.563675i \(-0.809387\pi\)
−0.0751583 0.997172i \(-0.523946\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 12.0000 0.973329
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 2.50000 4.33013i 0.197642 0.342327i
\(161\) 0 0
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 5.00000 8.66025i 0.390434 0.676252i
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) −2.00000 −0.153393
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.00000 3.46410i −0.150756 0.261116i
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 20.0000 1.49487 0.747435 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.00000 + 8.66025i 0.367607 + 0.636715i
\(186\) 0 0
\(187\) 4.00000 6.92820i 0.292509 0.506640i
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −8.00000 + 13.8564i −0.578860 + 1.00261i 0.416751 + 0.909021i \(0.363169\pi\)
−0.995610 + 0.0935936i \(0.970165\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 0 0
\(196\) −3.50000 + 6.06218i −0.250000 + 0.433013i
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) −1.50000 + 2.59808i −0.106066 + 0.183712i
\(201\) 0 0
\(202\) 3.00000 + 5.19615i 0.211079 + 0.365600i
\(203\) 0 0
\(204\) 0 0
\(205\) −5.00000 + 8.66025i −0.349215 + 0.604858i
\(206\) 16.0000 1.11477
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 8.00000 13.8564i 0.553372 0.958468i
\(210\) 0 0
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) −5.00000 8.66025i −0.343401 0.594789i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 0 0
\(218\) 7.00000 12.1244i 0.474100 0.821165i
\(219\) 0 0
\(220\) −2.00000 3.46410i −0.134840 0.233550i
\(221\) 2.00000 + 3.46410i 0.134535 + 0.233021i
\(222\) 0 0
\(223\) −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2.00000 −0.133038
\(227\) 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
\(229\) −3.00000 5.19615i −0.198246 0.343371i 0.749714 0.661762i \(-0.230191\pi\)
−0.947960 + 0.318390i \(0.896858\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) −2.00000 + 3.46410i −0.130189 + 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) 8.00000 + 13.8564i 0.517477 + 0.896296i 0.999794 + 0.0202996i \(0.00646202\pi\)
−0.482317 + 0.875997i \(0.660205\pi\)
\(240\) 0 0
\(241\) 7.00000 12.1244i 0.450910 0.780998i −0.547533 0.836784i \(-0.684433\pi\)
0.998443 + 0.0557856i \(0.0177663\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 3.50000 6.06218i 0.223607 0.387298i
\(246\) 0 0
\(247\) 4.00000 + 6.92820i 0.254514 + 0.440831i
\(248\) 0 0
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −4.00000 + 6.92820i −0.250982 + 0.434714i
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) 0 0
\(265\) 5.00000 + 8.66025i 0.307148 + 0.531995i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 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
\(277\) −3.00000 + 5.19615i −0.180253 + 0.312207i −0.941966 0.335707i \(-0.891025\pi\)
0.761714 + 0.647913i \(0.224358\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) 0 0
\(281\) 3.00000 5.19615i 0.178965 0.309976i −0.762561 0.646916i \(-0.776058\pi\)
0.941526 + 0.336939i \(0.109392\pi\)
\(282\) 0 0
\(283\) 6.00000 + 10.3923i 0.356663 + 0.617758i 0.987401 0.158237i \(-0.0505811\pi\)
−0.630738 + 0.775996i \(0.717248\pi\)
\(284\) −4.00000 6.92820i −0.237356 0.411113i
\(285\) 0 0
\(286\) 4.00000 6.92820i 0.236525 0.409673i
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) −1.00000 + 1.73205i −0.0587220 + 0.101710i
\(291\) 0 0
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) −3.00000 5.19615i −0.175262 0.303562i 0.764990 0.644042i \(-0.222744\pi\)
−0.940252 + 0.340480i \(0.889411\pi\)
\(294\) 0 0
\(295\) 2.00000 3.46410i 0.116445 0.201688i
\(296\) −30.0000 −1.74371
\(297\) 0 0
\(298\) −22.0000 −1.27443
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −4.00000 6.92820i −0.230174 0.398673i
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) −2.00000 −0.114520
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 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
\(313\) −13.0000 + 22.5167i −0.734803 + 1.27272i 0.220006 + 0.975499i \(0.429392\pi\)
−0.954810 + 0.297218i \(0.903941\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 0 0
\(317\) 1.00000 1.73205i 0.0561656 0.0972817i −0.836576 0.547852i \(-0.815446\pi\)
0.892741 + 0.450570i \(0.148779\pi\)
\(318\) 0 0
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) −3.50000 6.06218i −0.195656 0.338886i
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) −2.00000 −0.110940
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) 0 0
\(328\) −15.0000 25.9808i −0.828236 1.43455i
\(329\) 0 0
\(330\) 0 0
\(331\) −6.00000 + 10.3923i −0.329790 + 0.571213i −0.982470 0.186421i \(-0.940311\pi\)
0.652680 + 0.757634i \(0.273645\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 0 0
\(335\) −6.00000 + 10.3923i −0.327815 + 0.567792i
\(336\) 0 0
\(337\) 7.00000 + 12.1244i 0.381314 + 0.660456i 0.991250 0.131995i \(-0.0421382\pi\)
−0.609936 + 0.792451i \(0.708805\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 0 0
\(340\) 1.00000 1.73205i 0.0542326 0.0939336i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −6.00000 + 10.3923i −0.323498 + 0.560316i
\(345\) 0 0
\(346\) −9.00000 15.5885i −0.483843 0.838041i
\(347\) 14.0000 + 24.2487i 0.751559 + 1.30174i 0.947067 + 0.321037i \(0.104031\pi\)
−0.195507 + 0.980702i \(0.562635\pi\)
\(348\) 0 0
\(349\) 1.00000 1.73205i 0.0535288 0.0927146i −0.838019 0.545640i \(-0.816286\pi\)
0.891548 + 0.452926i \(0.149620\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 0 0
\(355\) 4.00000 + 6.92820i 0.212298 + 0.367711i
\(356\) −3.00000 5.19615i −0.159000 0.275396i
\(357\) 0 0
\(358\) 10.0000 17.3205i 0.528516 0.915417i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −5.00000 + 8.66025i −0.262794 + 0.455173i
\(363\) 0 0
\(364\) 0 0
\(365\) −5.00000 8.66025i −0.261712 0.453298i
\(366\) 0 0
\(367\) 12.0000 20.7846i 0.626395 1.08495i −0.361874 0.932227i \(-0.617863\pi\)
0.988269 0.152721i \(-0.0488036\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 10.0000 0.519875
\(371\) 0 0
\(372\) 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
\(376\) −12.0000 + 20.7846i −0.618853 + 1.07188i
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 2.00000 3.46410i 0.102598 0.177705i
\(381\) 0 0
\(382\) 8.00000 + 13.8564i 0.409316 + 0.708955i
\(383\) 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 10.5000 + 18.1865i 0.530330 + 0.918559i
\(393\) 0 0
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 0 0
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) −4.00000 + 6.92820i −0.200502 + 0.347279i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) −20.0000 + 34.6410i −0.991363 + 1.71709i
\(408\) 0 0
\(409\) −13.0000 22.5167i −0.642809 1.11338i −0.984803 0.173675i \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) 5.00000 + 8.66025i 0.246932 + 0.427699i
\(411\) 0 0
\(412\) −8.00000 + 13.8564i −0.394132 + 0.682656i
\(413\) 0 0
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) −5.00000 + 8.66025i −0.245145 + 0.424604i
\(417\) 0 0
\(418\) −8.00000 13.8564i −0.391293 0.677739i
\(419\) −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
\(421\) 13.0000 22.5167i 0.633581 1.09739i −0.353233 0.935536i \(-0.614918\pi\)
0.986814 0.161859i \(-0.0517491\pi\)
\(422\) −20.0000 −0.973585
\(423\) 0 0
\(424\) −30.0000 −1.45693
\(425\) −1.00000 + 1.73205i −0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.00000 10.3923i −0.290021 0.502331i
\(429\) 0 0
\(430\) 2.00000 3.46410i 0.0964486 0.167054i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.00000 + 12.1244i 0.335239 + 0.580651i
\(437\) 0 0
\(438\) 0 0
\(439\) −20.0000 + 34.6410i −0.954548 + 1.65333i −0.219149 + 0.975691i \(0.570328\pi\)
−0.735399 + 0.677634i \(0.763005\pi\)
\(440\) −12.0000 −0.572078
\(441\) 0 0
\(442\) 4.00000 0.190261
\(443\) 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
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 0 0
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) −40.0000 −1.88353
\(452\) 1.00000 1.73205i 0.0470360 0.0814688i
\(453\) 0 0
\(454\) −10.0000 17.3205i −0.469323 0.812892i
\(455\) 0 0
\(456\) 0 0
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) −6.00000 −0.280362
\(459\) 0 0
\(460\) 0 0
\(461\) 9.00000 15.5885i 0.419172 0.726027i −0.576685 0.816967i \(-0.695654\pi\)
0.995856 + 0.0909401i \(0.0289872\pi\)
\(462\) 0 0
\(463\) −12.0000 20.7846i −0.557687 0.965943i −0.997689 0.0679458i \(-0.978356\pi\)
0.440002 0.897997i \(-0.354978\pi\)
\(464\) −1.00000 1.73205i −0.0464238 0.0804084i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 28.0000 1.29569 0.647843 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 4.00000 6.92820i 0.184506 0.319574i
\(471\) 0 0
\(472\) 6.00000 + 10.3923i 0.276172 + 0.478345i
\(473\) 8.00000 + 13.8564i 0.367840 + 0.637118i
\(474\) 0 0
\(475\) −2.00000 + 3.46410i −0.0917663 + 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) 16.0000 0.731823
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) −10.0000 17.3205i −0.455961 0.789747i
\(482\) −7.00000 12.1244i −0.318841 0.552249i
\(483\) 0 0
\(484\) 2.50000 4.33013i 0.113636 0.196824i
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 3.00000 5.19615i 0.135804 0.235219i
\(489\) 0 0
\(490\) −3.50000 6.06218i −0.158114 0.273861i
\(491\) −14.0000 24.2487i −0.631811 1.09433i −0.987181 0.159603i \(-0.948978\pi\)
0.355370 0.934726i \(-0.384355\pi\)
\(492\) 0 0
\(493\) 2.00000 3.46410i 0.0900755 0.156015i
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i \(-0.195204\pi\)
−0.907314 + 0.420455i \(0.861871\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) −32.0000 −1.42681 −0.713405 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) 0 0
\(508\) −4.00000 6.92820i −0.177471 0.307389i
\(509\) 17.0000 + 29.4449i 0.753512 + 1.30512i 0.946111 + 0.323843i \(0.104975\pi\)
−0.192599 + 0.981278i \(0.561692\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) −18.0000 −0.793946
\(515\) 8.00000 13.8564i 0.352522 0.610586i
\(516\) 0 0
\(517\) 16.0000 + 27.7128i 0.703679 + 1.21881i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) −6.00000 + 10.3923i −0.262111 + 0.453990i
\(525\) 0 0
\(526\) 8.00000 + 13.8564i 0.348817 + 0.604168i
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 10.0000 0.434372
\(531\) 0 0
\(532\) 0 0
\(533\) 10.0000 17.3205i 0.433148 0.750234i
\(534\) 0 0
\(535\) 6.00000 + 10.3923i 0.259403 + 0.449299i
\(536\) −18.0000 31.1769i −0.777482 1.34664i
\(537\) 0 0
\(538\) 7.00000 12.1244i 0.301791 0.522718i
\(539\) 28.0000 1.20605
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) 5.00000 + 8.66025i 0.214373 + 0.371305i
\(545\) −7.00000 12.1244i −0.299847 0.519350i
\(546\) 0 0
\(547\) 10.0000 17.3205i 0.427569 0.740571i −0.569087 0.822277i \(-0.692703\pi\)
0.996657 + 0.0817056i \(0.0260367\pi\)
\(548\) 6.00000 0.256307
\(549\) 0 0
\(550\) 4.00000 0.170561
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) 3.00000 + 5.19615i 0.127458 + 0.220763i
\(555\) 0 0
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) 0 0
\(565\) −1.00000 + 1.73205i −0.0420703 + 0.0728679i
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) −24.0000 −1.00702
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) 4.00000 + 6.92820i 0.167248 + 0.289683i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −6.50000 + 11.2583i −0.270364 + 0.468285i
\(579\) 0 0
\(580\) −1.00000 1.73205i −0.0415227 0.0719195i
\(581\) 0 0
\(582\) 0 0
\(583\) −20.0000 + 34.6410i −0.828315 + 1.43468i
\(584\) 30.0000 1.24141
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −2.00000 3.46410i −0.0823387 0.142615i
\(591\) 0 0
\(592\) −5.00000 + 8.66025i −0.205499 + 0.355934i
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11.0000 19.0526i 0.450578 0.780423i
\(597\) 0 0
\(598\) 0 0
\(599\) 4.00000 + 6.92820i 0.163436 + 0.283079i 0.936099 0.351738i \(-0.114409\pi\)
−0.772663 + 0.634816i \(0.781076\pi\)
\(600\) 0 0
\(601\) −13.0000 + 22.5167i −0.530281 + 0.918474i 0.469095 + 0.883148i \(0.344580\pi\)
−0.999376 + 0.0353259i \(0.988753\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) −2.50000 + 4.33013i −0.101639 + 0.176045i
\(606\) 0 0
\(607\) 4.00000 + 6.92820i 0.162355 + 0.281207i 0.935713 0.352763i \(-0.114758\pi\)
−0.773358 + 0.633970i \(0.781424\pi\)
\(608\) 10.0000 + 17.3205i 0.405554 + 0.702439i
\(609\) 0 0
\(610\) −1.00000 + 1.73205i −0.0404888 + 0.0701287i
\(611\) −16.0000 −0.647291
\(612\) 0 0
\(613\) 22.0000 0.888572 0.444286 0.895885i \(-0.353457\pi\)
0.444286 + 0.895885i \(0.353457\pi\)
\(614\) 14.0000 24.2487i 0.564994 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) 3.00000 + 5.19615i 0.120775 + 0.209189i 0.920074 0.391745i \(-0.128129\pi\)
−0.799298 + 0.600935i \(0.794795\pi\)
\(618\) 0 0
\(619\) 2.00000 3.46410i 0.0803868 0.139234i −0.823029 0.567999i \(-0.807718\pi\)
0.903416 + 0.428765i \(0.141051\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 13.0000 + 22.5167i 0.519584 + 0.899947i
\(627\) 0 0
\(628\) 7.00000 12.1244i 0.279330 0.483814i
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −1.00000 1.73205i −0.0397151 0.0687885i
\(635\) 4.00000 + 6.92820i 0.158735 + 0.274937i
\(636\) 0 0
\(637\) −7.00000 + 12.1244i −0.277350 + 0.480384i
\(638\) −8.00000 −0.316723
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 0 0
\(643\) 18.0000 + 31.1769i 0.709851 + 1.22950i 0.964912 + 0.262573i \(0.0845709\pi\)
−0.255062 + 0.966925i \(0.582096\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.00000 6.92820i 0.157378 0.272587i
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 0 0
\(649\) 16.0000 0.628055
\(650\) −1.00000 + 1.73205i −0.0392232 + 0.0679366i
\(651\) 0 0
\(652\) −2.00000 3.46410i −0.0783260 0.135665i
\(653\) −23.0000 39.8372i −0.900060 1.55895i −0.827415 0.561591i \(-0.810189\pi\)
−0.0726446 0.997358i \(-0.523144\pi\)
\(654\) 0 0
\(655\) 6.00000 10.3923i 0.234439 0.406061i
\(656\) −10.0000 −0.390434
\(657\) 0 0
\(658\) 0 0
\(659\) −10.0000 + 17.3205i −0.389545 + 0.674711i −0.992388 0.123148i \(-0.960701\pi\)
0.602844 + 0.797859i \(0.294034\pi\)
\(660\) 0 0
\(661\) −11.0000 19.0526i −0.427850 0.741059i 0.568831 0.822454i \(-0.307396\pi\)
−0.996682 + 0.0813955i \(0.974062\pi\)
\(662\) 6.00000 + 10.3923i 0.233197 + 0.403908i
\(663\) 0 0
\(664\) −18.0000 + 31.1769i −0.698535 + 1.20990i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 6.00000 + 10.3923i 0.231800 + 0.401490i
\(671\) −4.00000 6.92820i −0.154418 0.267460i
\(672\) 0 0
\(673\) 15.0000 25.9808i 0.578208 1.00148i −0.417477 0.908687i \(-0.637086\pi\)
0.995685 0.0927975i \(-0.0295809\pi\)
\(674\) 14.0000 0.539260
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) −3.00000 + 5.19615i −0.115299 + 0.199704i −0.917899 0.396813i \(-0.870116\pi\)
0.802600 + 0.596518i \(0.203449\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.00000 5.19615i −0.115045 0.199263i
\(681\) 0 0
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 0 0
\(687\) 0 0
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −10.0000 17.3205i −0.380970 0.659859i
\(690\) 0 0
\(691\) 22.0000 38.1051i 0.836919 1.44959i −0.0555386 0.998457i \(-0.517688\pi\)
0.892458 0.451130i \(-0.148979\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) 0 0
\(697\) −10.0000 17.3205i −0.378777 0.656061i
\(698\) −1.00000 1.73205i −0.0378506 0.0655591i
\(699\) 0 0
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) −40.0000 −1.50863
\(704\) 14.0000 24.2487i 0.527645 0.913908i
\(705\) 0 0
\(706\) 9.00000 + 15.5885i 0.338719 + 0.586679i
\(707\) 0 0
\(708\) 0 0
\(709\) 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i \(-0.670978\pi\)
0.999908 + 0.0135434i \(0.00431112\pi\)
\(710\) 8.00000 0.300235
\(711\) 0 0
\(712\) −18.0000 −0.674579
\(713\) 0 0
\(714\) 0 0
\(715\) −4.00000 6.92820i −0.149592 0.259100i
\(716\) 10.0000 + 17.3205i 0.373718 + 0.647298i
\(717\) 0 0
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.50000 + 2.59808i −0.0558242 + 0.0966904i
\(723\) 0 0
\(724\) −5.00000 8.66025i −0.185824 0.321856i
\(725\) 1.00000 + 1.73205i 0.0371391 + 0.0643268i
\(726\) 0 0
\(727\) 8.00000 13.8564i 0.296704 0.513906i −0.678676 0.734438i \(-0.737446\pi\)
0.975380 + 0.220532i \(0.0707793\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −10.0000 −0.370117
\(731\) −4.00000 + 6.92820i −0.147945 + 0.256249i
\(732\) 0 0
\(733\) −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) −12.0000 20.7846i −0.442928 0.767174i
\(735\) 0 0
\(736\) 0 0
\(737\) −48.0000 −1.76810
\(738\) 0 0
\(739\) −44.0000 −1.61857 −0.809283 0.587419i \(-0.800144\pi\)
−0.809283 + 0.587419i \(0.800144\pi\)
\(740\) −5.00000 + 8.66025i −0.183804 + 0.318357i
\(741\) 0 0
\(742\) 0 0
\(743\) 8.00000 + 13.8564i 0.293492 + 0.508342i 0.974633 0.223810i \(-0.0718494\pi\)
−0.681141 + 0.732152i \(0.738516\pi\)
\(744\) 0 0
\(745\) −11.0000 + 19.0526i −0.403009 + 0.698032i
\(746\) 26.0000 0.951928
\(747\) 0 0
\(748\) 8.00000 0.292509
\(749\) 0 0
\(750\) 0 0
\(751\) −8.00000 13.8564i −0.291924 0.505627i 0.682341 0.731034i \(-0.260962\pi\)
−0.974265 + 0.225407i \(0.927629\pi\)
\(752\) 4.00000 + 6.92820i 0.145865 + 0.252646i
\(753\) 0 0
\(754\) 2.00000 3.46410i 0.0728357 0.126155i
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 0 0
\(760\) −6.00000 10.3923i −0.217643 0.376969i
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) −4.00000 + 6.92820i −0.144432 + 0.250163i
\(768\) 0 0
\(769\) −1.00000 1.73205i −0.0360609 0.0624593i 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.00000 1.73205i 0.0359908 0.0623379i
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −3.00000 + 5.19615i −0.107694 + 0.186531i
\(777\) 0 0
\(778\) 3.00000 + 5.19615i 0.107555 + 0.186291i
\(779\) −20.0000 34.6410i −0.716574 1.24114i
\(780\) 0 0
\(781\) −16.0000 + 27.7128i −0.572525 + 0.991642i
\(782\) 0 0
\(783\) 0 0
\(784\) 7.00000 0.250000
\(785\) −7.00000 + 12.1244i −0.249841 + 0.432737i
\(786\) 0 0
\(787\) −14.0000 24.2487i −0.499046 0.864373i 0.500953 0.865474i \(-0.332983\pi\)
−0.999999 + 0.00110111i \(0.999650\pi\)
\(788\) 3.00000 + 5.19615i 0.106871 + 0.185105i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 4.00000 0.142044
\(794\) −1.00000 + 1.73205i −0.0354887 + 0.0614682i
\(795\) 0 0