Properties

Label 405.2.e.c.271.1
Level $405$
Weight $2$
Character 405.271
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 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.2.e.c.136.1

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

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

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 \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) −3.00000 −1.06066
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 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 \(-0.226120\pi\)
−0.943811 + 0.330487i \(0.892787\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −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 −0.150567 0.988600i \(-0.548110\pi\)
0.931436 0.363905i \(-0.118557\pi\)
\(42\) 0 0
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 0 0
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 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 \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 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 \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 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 0.222571 + 0.974916i \(0.428555\pi\)
−0.955588 + 0.294706i \(0.904778\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 1.00000 0.111803
\(81\) 0 0
\(82\) −10.0000 −1.10432
\(83\) 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 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 \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 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 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) −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 \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) −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 \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 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 \(-0.803345\pi\)
0.909221 + 0.416314i \(0.136678\pi\)
\(114\) 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 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 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 \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 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 0.0751583 0.997172i \(-0.476054\pi\)
0.825997 0.563675i \(-0.190613\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) −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 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 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 −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 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 \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 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 0.995610 + 0.0935936i \(0.0298354\pi\)
−0.416751 + 0.909021i \(0.636831\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −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 \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 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 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 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 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2.00000 −0.133038
\(227\) −10.0000 17.3205i −0.663723 1.14960i −0.979630 0.200812i \(-0.935642\pi\)
0.315906 0.948790i \(-0.397691\pi\)
\(228\) 0 0
\(229\) −3.00000 + 5.19615i −0.198246 + 0.343371i −0.947960 0.318390i \(-0.896858\pi\)
0.749714 + 0.661762i \(0.230191\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 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 0.482317 + 0.875997i \(0.339795\pi\)
−0.999794 + 0.0202996i \(0.993538\pi\)
\(240\) 0 0
\(241\) 7.00000 + 12.1244i 0.450910 + 0.780998i 0.998443 0.0557856i \(-0.0177663\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 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 \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 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 −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 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 \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) 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 \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 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 0.761714 0.647913i \(-0.224358\pi\)
−0.941966 + 0.335707i \(0.891025\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) 0 0
\(281\) −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i \(-0.223942\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(282\) 0 0
\(283\) 6.00000 10.3923i 0.356663 0.617758i −0.630738 0.775996i \(-0.717248\pi\)
0.987401 + 0.158237i \(0.0505811\pi\)
\(284\) 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 \(-0.777256\pi\)
0.940252 + 0.340480i \(0.110589\pi\)
\(294\) 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 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) −13.0000 22.5167i −0.734803 1.27272i −0.954810 0.297218i \(-0.903941\pi\)
0.220006 0.975499i \(-0.429392\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 0 0
\(317\) −1.00000 1.73205i −0.0561656 0.0972817i 0.836576 0.547852i \(-0.184554\pi\)
−0.892741 + 0.450570i \(0.851221\pi\)
\(318\) 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 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) 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 −0.609936 0.792451i \(-0.708805\pi\)
0.991250 + 0.131995i \(0.0421382\pi\)
\(338\) 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 0.195507 + 0.980702i \(0.437365\pi\)
−0.947067 + 0.321037i \(0.895969\pi\)
\(348\) 0 0
\(349\) 1.00000 + 1.73205i 0.0535288 + 0.0927146i 0.891548 0.452926i \(-0.149620\pi\)
−0.838019 + 0.545640i \(0.816286\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 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 \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 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 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) 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 −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) 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 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) 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 \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 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 \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 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 0.341994 + 0.939702i \(0.388898\pi\)
−0.984803 + 0.173675i \(0.944436\pi\)
\(410\) −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 \(-0.802183\pi\)
0.910735 + 0.412991i \(0.135516\pi\)
\(420\) 0 0
\(421\) 13.0000 + 22.5167i 0.633581 + 1.09739i 0.986814 + 0.161859i \(0.0517491\pi\)
−0.353233 + 0.935536i \(0.614918\pi\)
\(422\) 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 −0.735399 0.677634i \(-0.763005\pi\)
−0.219149 0.975691i \(-0.570328\pi\)
\(440\) 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 \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 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 \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 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 0.725059 0.688686i \(-0.241812\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 6.00000 0.280362
\(459\) 0 0
\(460\) 0 0
\(461\) −9.00000 15.5885i −0.419172 0.726027i 0.576685 0.816967i \(-0.304346\pi\)
−0.995856 + 0.0909401i \(0.971013\pi\)
\(462\) 0 0
\(463\) −12.0000 + 20.7846i −0.557687 + 0.965943i 0.440002 + 0.897997i \(0.354978\pi\)
−0.997689 + 0.0679458i \(0.978356\pi\)
\(464\) 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 \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 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 −0.355370 0.934726i \(-0.615645\pi\)
0.987181 0.159603i \(-0.0510215\pi\)
\(492\) 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 −0.907314 0.420455i \(-0.861871\pi\)
0.817781 + 0.575529i \(0.195204\pi\)
\(500\) −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 \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 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 0.192599 + 0.981278i \(0.438308\pi\)
−0.946111 + 0.323843i \(0.895025\pi\)
\(510\) 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 \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 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 0.996657 0.0817056i \(-0.0260367\pi\)
−0.569087 + 0.822277i \(0.692703\pi\)
\(548\) −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 \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 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 \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) 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 \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) −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 \(-0.246324\pi\)
−0.962872 + 0.269957i \(0.912990\pi\)
\(588\) 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 \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) 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 \(-0.885591\pi\)
0.772663 + 0.634816i \(0.218924\pi\)
\(600\) 0 0
\(601\) −13.0000 22.5167i −0.530281 0.918474i −0.999376 0.0353259i \(-0.988753\pi\)
0.469095 0.883148i \(-0.344580\pi\)
\(602\) 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 −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) −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 \(-0.871871\pi\)
0.799298 + 0.600935i \(0.205205\pi\)
\(618\) 0 0
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) 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 −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 0 0
\(643\) 18.0000 31.1769i 0.709851 1.22950i −0.255062 0.966925i \(-0.582096\pi\)
0.964912 0.262573i \(-0.0845709\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.00000 + 6.92820i 0.157378 + 0.272587i
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) 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 0.0726446 0.997358i \(-0.476856\pi\)
0.827415 0.561591i \(-0.189811\pi\)
\(654\) 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 \(-0.0392990\pi\)
−0.602844 + 0.797859i \(0.705966\pi\)
\(660\) 0 0
\(661\) −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) −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 0.995685 + 0.0927975i \(0.0295809\pi\)
−0.417477 + 0.908687i \(0.637086\pi\)
\(674\) −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 \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) 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 \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 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 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) −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 \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 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 0.999908 0.0135434i \(-0.00431112\pi\)
−0.511683 + 0.859174i \(0.670978\pi\)
\(710\) −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 \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) 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 0.975380 0.220532i \(-0.0707793\pi\)
−0.678676 + 0.734438i \(0.737446\pi\)
\(728\) 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 −0.965854 0.259087i \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) 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 \(-0.928151\pi\)
0.681141 + 0.732152i \(0.261484\pi\)
\(744\) 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 −0.974265 0.225407i \(-0.927629\pi\)
0.682341 + 0.731034i \(0.260962\pi\)
\(752\) −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 \(-0.868018\pi\)
0.806514 + 0.591215i \(0.201351\pi\)
\(762\) 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 −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.00000 + 1.73205i 0.0359908 + 0.0623379i
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 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 −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) −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
\(796\) −4.00000 +