Properties

Label 735.2.i.d.226.1
Level $735$
Weight $2$
Character 735.226
Analytic conductor $5.869$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
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 226.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 735.226
Dual form 735.2.i.d.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.00000 + 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +4.00000 q^{22} +(-1.50000 - 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.50000 + 4.33013i) q^{32} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{34} -1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} -10.0000 q^{41} +4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.00000 - 6.92820i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{52} +(5.00000 + 8.66025i) q^{53} +(0.500000 - 0.866025i) q^{54} +4.00000 q^{55} -4.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-1.00000 + 1.73205i) q^{61} +7.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-1.00000 + 1.73205i) q^{68} -8.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(5.00000 + 8.66025i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-0.500000 + 0.866025i) q^{75} +4.00000 q^{76} -2.00000 q^{78} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} -12.0000 q^{83} +2.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(1.00000 + 1.73205i) q^{87} +(6.00000 + 10.3923i) q^{88} +(-3.00000 + 5.19615i) q^{89} +1.00000 q^{90} +(-4.00000 - 6.92820i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(2.50000 - 4.33013i) q^{96} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} + q^{4} + q^{5} - 2q^{6} + 6q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} + q^{4} + q^{5} - 2q^{6} + 6q^{8} - q^{9} - q^{10} + 4q^{11} + q^{12} + 4q^{13} - 2q^{15} + q^{16} + 2q^{17} + q^{18} + 4q^{19} + 2q^{20} + 8q^{22} - 3q^{24} - q^{25} + 2q^{26} + 2q^{27} - 4q^{29} - q^{30} + 5q^{32} + 4q^{33} + 4q^{34} - 2q^{36} + 10q^{37} - 4q^{38} - 2q^{39} + 3q^{40} - 20q^{41} + 8q^{43} - 4q^{44} + q^{45} + 8q^{47} - 2q^{48} - 2q^{50} + 2q^{51} + 2q^{52} + 10q^{53} + q^{54} + 8q^{55} - 8q^{57} - 2q^{58} - 4q^{59} - q^{60} - 2q^{61} + 14q^{64} + 2q^{65} - 4q^{66} - 12q^{67} - 2q^{68} - 16q^{71} - 3q^{72} + 10q^{73} - 10q^{74} - q^{75} + 8q^{76} - 4q^{78} - q^{80} - q^{81} - 10q^{82} - 24q^{83} + 4q^{85} + 4q^{86} + 2q^{87} + 12q^{88} - 6q^{89} + 2q^{90} - 8q^{94} - 4q^{95} + 5q^{96} - 4q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i −0.633316 0.773893i \(-0.718307\pi\)
0.986869 + 0.161521i \(0.0516399\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −1.50000 2.59808i −0.306186 0.530330i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 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
\(33\) 2.00000 3.46410i 0.348155 0.603023i
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 5.00000 8.66025i 0.821995 1.42374i −0.0821995 0.996616i \(-0.526194\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) −2.00000 3.46410i −0.324443 0.561951i
\(39\) −1.00000 1.73205i −0.160128 0.277350i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 0 0
\(47\) 4.00000 6.92820i 0.583460 1.01058i −0.411606 0.911362i \(-0.635032\pi\)
0.995066 0.0992202i \(-0.0316348\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) 1.00000 1.73205i 0.140028 0.242536i
\(52\) 1.00000 + 1.73205i 0.138675 + 0.240192i
\(53\) 5.00000 + 8.66025i 0.686803 + 1.18958i 0.972867 + 0.231367i \(0.0743197\pi\)
−0.286064 + 0.958211i \(0.592347\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) −1.00000 + 1.73205i −0.131306 + 0.227429i
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) −2.00000 3.46410i −0.246183 0.426401i
\(67\) −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 \(0.657448\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −5.00000 8.66025i −0.581238 1.00673i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −5.00000 + 8.66025i −0.552158 + 0.956365i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 1.00000 + 1.73205i 0.107211 + 0.185695i
\(88\) 6.00000 + 10.3923i 0.639602 + 1.10782i
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 1.00000 0.105409
\(91\) 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
\(96\) 2.50000 4.33013i 0.255155 0.441942i
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) −1.00000 1.73205i −0.0990148 0.171499i
\(103\) −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i \(0.455686\pi\)
−0.927030 + 0.374987i \(0.877647\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 2.00000 3.46410i 0.190693 0.330289i
\(111\) −10.0000 −0.949158
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −2.00000 + 3.46410i −0.187317 + 0.324443i
\(115\) 0 0
\(116\) −1.00000 1.73205i −0.0928477 0.160817i
\(117\) −1.00000 + 1.73205i −0.0924500 + 0.160128i
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) −3.00000 −0.273861
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 1.00000 + 1.73205i 0.0905357 + 0.156813i
\(123\) 5.00000 + 8.66025i 0.450835 + 0.780869i
\(124\) 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
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) −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 \(0.991023\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) −4.00000 + 6.92820i −0.335673 + 0.581402i
\(143\) 4.00000 + 6.92820i 0.334497 + 0.579365i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −1.00000 + 1.73205i −0.0830455 + 0.143839i
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) −11.0000 + 19.0526i −0.901155 + 1.56085i −0.0751583 + 0.997172i \(0.523946\pi\)
−0.825997 + 0.563675i \(0.809387\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 6.00000 10.3923i 0.486664 0.842927i
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 1.00000 1.73205i 0.0800641 0.138675i
\(157\) 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i \(0.0220180\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) 0 0
\(159\) 5.00000 8.66025i 0.396526 0.686803i
\(160\) 5.00000 0.395285
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) −5.00000 8.66025i −0.390434 0.676252i
\(165\) −2.00000 3.46410i −0.155700 0.269680i
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 1.00000 1.73205i 0.0766965 0.132842i
\(171\) 2.00000 + 3.46410i 0.152944 + 0.264906i
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 2.00000 0.151620
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) −2.00000 + 3.46410i −0.150329 + 0.260378i
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −10.0000 17.3205i −0.747435 1.29460i −0.949048 0.315130i \(-0.897952\pi\)
0.201613 0.979465i \(-0.435382\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 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 \(0.970165\pi\)
\(192\) −3.50000 6.06218i −0.252591 0.437500i
\(193\) −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
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −2.00000 + 3.46410i −0.142134 + 0.246183i
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) −5.00000 + 8.66025i −0.349215 + 0.604858i
\(206\) 8.00000 + 13.8564i 0.557386 + 0.965422i
\(207\) 0 0
\(208\) 1.00000 1.73205i 0.0693375 0.120096i
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −5.00000 + 8.66025i −0.343401 + 0.594789i
\(213\) 4.00000 + 6.92820i 0.274075 + 0.474713i
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) 2.00000 3.46410i 0.136399 0.236250i
\(216\) 3.00000 0.204124
\(217\) 0 0
\(218\) −14.0000 −0.948200
\(219\) 5.00000 8.66025i 0.337869 0.585206i
\(220\) 2.00000 + 3.46410i 0.134840 + 0.233550i
\(221\) 2.00000 + 3.46410i 0.134535 + 0.233021i
\(222\) −5.00000 + 8.66025i −0.335578 + 0.581238i
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 1.00000 1.73205i 0.0665190 0.115214i
\(227\) −10.0000 17.3205i −0.663723 1.14960i −0.979630 0.200812i \(-0.935642\pi\)
0.315906 0.948790i \(-0.397691\pi\)
\(228\) −2.00000 3.46410i −0.132453 0.229416i
\(229\) 3.00000 5.19615i 0.198246 0.343371i −0.749714 0.661762i \(-0.769809\pi\)
0.947960 + 0.318390i \(0.103142\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 1.00000 + 1.73205i 0.0653720 + 0.113228i
\(235\) −4.00000 6.92820i −0.260931 0.451946i
\(236\) 2.00000 3.46410i 0.130189 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 2.50000 + 4.33013i 0.160706 + 0.278351i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 10.0000 0.637577
\(247\) 4.00000 6.92820i 0.254514 0.440831i
\(248\) 0 0
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) −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
\(255\) −1.00000 1.73205i −0.0626224 0.108465i
\(256\) 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 \(-0.0230722\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 1.00000 1.73205i 0.0618984 0.107211i
\(262\) 6.00000 + 10.3923i 0.370681 + 0.642039i
\(263\) −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i \(-0.330877\pi\)
−0.999970 + 0.00771799i \(0.997543\pi\)
\(264\) 6.00000 10.3923i 0.369274 0.639602i
\(265\) 10.0000 0.614295
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) 7.00000 + 12.1244i 0.426798 + 0.739235i 0.996586 0.0825561i \(-0.0263084\pi\)
−0.569789 + 0.821791i \(0.692975\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 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 \(0.891025\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −4.00000 + 6.92820i −0.238197 + 0.412568i
\(283\) −6.00000 10.3923i −0.356663 0.617758i 0.630738 0.775996i \(-0.282752\pi\)
−0.987401 + 0.158237i \(0.949419\pi\)
\(284\) −4.00000 6.92820i −0.237356 0.411113i
\(285\) −2.00000 + 3.46410i −0.118470 + 0.205196i
\(286\) 8.00000 0.473050
\(287\) 0 0
\(288\) −5.00000 −0.294628
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 1.00000 + 1.73205i 0.0587220 + 0.101710i
\(291\) 1.00000 + 1.73205i 0.0586210 + 0.101535i
\(292\) −5.00000 + 8.66025i −0.292603 + 0.506803i
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 15.0000 25.9808i 0.871857 1.51010i
\(297\) 2.00000 + 3.46410i 0.116052 + 0.201008i
\(298\) 11.0000 + 19.0526i 0.637213 + 1.10369i
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) 8.00000 0.460348
\(303\) 3.00000 5.19615i 0.172345 0.298511i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) 1.00000 + 1.73205i 0.0572598 + 0.0991769i
\(306\) −1.00000 + 1.73205i −0.0571662 + 0.0990148i
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) −3.00000 5.19615i −0.169842 0.294174i
\(313\) 13.0000 22.5167i 0.734803 1.27272i −0.220006 0.975499i \(-0.570608\pi\)
0.954810 0.297218i \(-0.0960589\pi\)
\(314\) 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 \(0.148779\pi\)
\(318\) −5.00000 8.66025i −0.280386 0.485643i
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) 3.50000 6.06218i 0.195656 0.338886i
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) −2.00000 3.46410i −0.110770 0.191859i
\(327\) −7.00000 + 12.1244i −0.387101 + 0.670478i
\(328\) −30.0000 −1.65647
\(329\) 0 0
\(330\) −4.00000 −0.220193
\(331\) −6.00000 + 10.3923i −0.329790 + 0.571213i −0.982470 0.186421i \(-0.940311\pi\)
0.652680 + 0.757634i \(0.273645\pi\)
\(332\) −6.00000 10.3923i −0.329293 0.570352i
\(333\) 5.00000 + 8.66025i 0.273998 + 0.474579i
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) −1.00000 1.73205i −0.0543125 0.0940721i
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 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 \(0.562635\pi\)
\(348\) −1.00000 + 1.73205i −0.0536056 + 0.0928477i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) −10.0000 + 17.3205i −0.533002 + 0.923186i
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 2.00000 + 3.46410i 0.106299 + 0.184115i
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −20.0000 −1.05703
\(359\) 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i \(-0.615019\pi\)
0.986865 0.161546i \(-0.0516481\pi\)
\(360\) 1.50000 + 2.59808i 0.0790569 + 0.136931i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 5.00000 8.66025i 0.262794 0.455173i
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) 1.00000 1.73205i 0.0522708 0.0905357i
\(367\) −12.0000 20.7846i −0.626395 1.08495i −0.988269 0.152721i \(-0.951196\pi\)
0.361874 0.932227i \(-0.382137\pi\)
\(368\) 0 0
\(369\) 5.00000 8.66025i 0.260290 0.450835i
\(370\) −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
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 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
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) 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 \(0.956560\pi\)
\(384\) 3.00000 0.153093
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) −2.00000 + 3.46410i −0.101666 + 0.176090i
\(388\) −1.00000 1.73205i −0.0507673 0.0879316i
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) −1.00000 + 1.73205i −0.0506370 + 0.0877058i
\(391\) 0 0
\(392\) 0 0
\(393\) 12.0000 0.605320
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 0 0
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 6.00000 + 10.3923i 0.299253 + 0.518321i
\(403\) 0 0
\(404\) −3.00000 + 5.19615i −0.149256 + 0.258518i
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 40.0000 1.98273
\(408\) 3.00000 5.19615i 0.148522 0.257248i
\(409\) 13.0000 + 22.5167i 0.642809 + 1.11338i 0.984803 + 0.173675i \(0.0555643\pi\)
−0.341994 + 0.939702i \(0.611102\pi\)
\(410\) 5.00000 + 8.66025i 0.246932 + 0.427699i
\(411\) 3.00000 5.19615i 0.147979 0.256307i
\(412\) −16.0000 −0.788263
\(413\) 0 0
\(414\) 0 0
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) 5.00000 + 8.66025i 0.245145 + 0.424604i
\(417\) −2.00000 3.46410i −0.0979404 0.169638i
\(418\) 8.00000 13.8564i 0.391293 0.677739i
\(419\) −4.00000 −0.195413 −0.0977064 0.995215i \(-0.531151\pi\)
−0.0977064 + 0.995215i \(0.531151\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 4.00000 + 6.92820i 0.194487 + 0.336861i
\(424\) 15.0000 + 25.9808i 0.728464 + 1.26174i
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 8.00000 0.387601
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 4.00000 6.92820i 0.193122 0.334497i
\(430\) −2.00000 3.46410i −0.0964486 0.167054i
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 2.00000 0.0958927
\(436\) 7.00000 12.1244i 0.335239 0.580651i
\(437\) 0 0
\(438\) −5.00000 8.66025i −0.238909 0.413803i
\(439\) 20.0000 34.6410i 0.954548 1.65333i 0.219149 0.975691i \(-0.429672\pi\)
0.735399 0.677634i \(-0.236995\pi\)
\(440\) 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 \(0.0746503\pi\)
\(444\) −5.00000 8.66025i −0.237289 0.410997i
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) −4.00000 + 6.92820i −0.189405 + 0.328060i
\(447\) 22.0000 1.04056
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0.500000 0.866025i 0.0235702 0.0408248i
\(451\) −20.0000 34.6410i −0.941763 1.63118i
\(452\) 1.00000 + 1.73205i 0.0470360 + 0.0814688i
\(453\) 4.00000 6.92820i 0.187936 0.325515i
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) −12.0000 −0.561951
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) −3.00000 5.19615i −0.140181 0.242800i
\(459\) 1.00000 + 1.73205i 0.0466760 + 0.0808452i
\(460\) 0 0
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) −1.00000 + 1.73205i −0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 14.0000 24.2487i 0.647843 1.12210i −0.335794 0.941935i \(-0.609005\pi\)
0.983637 0.180161i \(-0.0576619\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) 7.00000 12.1244i 0.322543 0.558661i
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) 8.00000 + 13.8564i 0.367840 + 0.637118i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) −8.00000 + 13.8564i −0.365911 + 0.633777i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) −2.50000 4.33013i −0.114109 0.197642i
\(481\) 10.0000 17.3205i 0.455961 0.789747i
\(482\) −14.0000 −0.637683
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −16.0000 27.7128i −0.725029 1.25579i −0.958962 0.283535i \(-0.908493\pi\)
0.233933 0.972253i \(-0.424840\pi\)
\(488\) −3.00000 + 5.19615i −0.135804 + 0.235219i
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) −5.00000 + 8.66025i −0.225417 + 0.390434i
\(493\) −2.00000 3.46410i −0.0900755 0.156015i
\(494\) −4.00000 6.92820i −0.179969 0.311715i
\(495\) −2.00000 + 3.46410i −0.0898933 + 0.155700i
\(496\) 0 0
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −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
\(507\) 4.50000 + 7.79423i 0.199852 + 0.346154i
\(508\) −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 \(0.895025\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) 2.00000 3.46410i 0.0883022 0.152944i
\(514\) −9.00000 15.5885i −0.396973 0.687577i
\(515\) 8.00000 + 13.8564i 0.352522 + 0.610586i
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 32.0000 1.40736
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) 5.00000 + 8.66025i 0.219054 + 0.379413i 0.954519 0.298150i \(-0.0963696\pi\)
−0.735465 + 0.677563i \(0.763036\pi\)
\(522\) −1.00000 1.73205i −0.0437688 0.0758098i
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) 0 0
\(528\) −2.00000 3.46410i −0.0870388 0.150756i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 5.00000 8.66025i 0.217186 0.376177i
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) −20.0000 −0.866296
\(534\) 3.00000 5.19615i 0.129823 0.224860i
\(535\) −6.00000 10.3923i −0.259403 0.449299i
\(536\) −18.0000 31.1769i −0.777482 1.34664i
\(537\) −10.0000 + 17.3205i −0.431532 + 0.747435i
\(538\) 14.0000 0.603583
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) −15.0000 + 25.9808i −0.644900 + 1.11700i 0.339424 + 0.940633i \(0.389768\pi\)
−0.984325 + 0.176367i \(0.943566\pi\)
\(542\) −8.00000 13.8564i −0.343629 0.595184i
\(543\) −5.00000 8.66025i −0.214571 0.371647i
\(544\) −5.00000 + 8.66025i −0.214373 + 0.371305i
\(545\) −14.0000 −0.599694
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −3.00000 + 5.19615i −0.128154 + 0.221969i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) −4.00000 + 6.92820i −0.170406 + 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) −6.00000 −0.254916
\(555\) −5.00000 + 8.66025i −0.212238 + 0.367607i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) −3.00000 + 5.19615i −0.126547 + 0.219186i
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) −4.00000 6.92820i −0.168430 0.291730i
\(565\) 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 \(0.126528\pi\)
\(570\) 2.00000 + 3.46410i 0.0837708 + 0.145095i
\(571\) 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
\(573\) 16.0000 0.668410
\(574\) 0 0
\(575\) 0 0
\(576\) −3.50000 + 6.06218i −0.145833 + 0.252591i
\(577\) 1.00000 + 1.73205i 0.0416305 + 0.0721062i 0.886090 0.463513i \(-0.153411\pi\)
−0.844459 + 0.535620i \(0.820078\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) −1.00000 + 1.73205i −0.0415586 + 0.0719816i
\(580\) −2.00000 −0.0830455
\(581\) 0 0
\(582\) 2.00000 0.0829027
\(583\) −20.0000 + 34.6410i −0.828315 + 1.43468i
\(584\) 15.0000 + 25.9808i 0.620704 + 1.07509i
\(585\) 1.00000 + 1.73205i 0.0413449 + 0.0716115i
\(586\) −3.00000 + 5.19615i −0.123929 + 0.214651i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −2.00000 + 3.46410i −0.0823387 + 0.142615i
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) −5.00000 8.66025i −0.205499 0.355934i
\(593\) 17.0000 29.4449i 0.698106 1.20916i −0.271016 0.962575i \(-0.587360\pi\)
0.969122 0.246581i \(-0.0793071\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −22.0000 −0.901155
\(597\) −4.00000 + 6.92820i −0.163709 + 0.283552i
\(598\) 0 0
\(599\) 4.00000 + 6.92820i 0.163436 + 0.283079i 0.936099 0.351738i \(-0.114409\pi\)
−0.772663 + 0.634816i \(0.781076\pi\)
\(600\) −1.50000 + 2.59808i −0.0612372 + 0.106066i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) 2.50000 + 4.33013i 0.101639 + 0.176045i
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 20.0000 0.811107
\(609\) 0 0
\(610\) 2.00000 0.0809776
\(611\) 8.00000 13.8564i 0.323645 0.560570i
\(612\) −1.00000 1.73205i −0.0404226 0.0700140i
\(613\) −11.0000 19.0526i −0.444286 0.769526i 0.553716 0.832705i \(-0.313209\pi\)
−0.998002 + 0.0631797i \(0.979876\pi\)
\(614\) −14.0000 + 24.2487i −0.564994 + 0.978598i
\(615\) 10.0000 0.403239
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 8.00000 13.8564i 0.321807 0.557386i
\(619\) −2.00000 3.46410i −0.0803868 0.139234i 0.823029 0.567999i \(-0.192282\pi\)
−0.903416 + 0.428765i \(0.858949\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −13.0000 22.5167i −0.519584 0.899947i
\(627\) −8.00000 13.8564i −0.319489 0.553372i
\(628\) −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
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) −1.00000 1.73205i −0.0397151 0.0687885i
\(635\) −4.00000 + 6.92820i −0.158735 + 0.274937i
\(636\) 10.0000 0.396526
\(637\) 0 0
\(638\) −8.00000 −0.316723
\(639\) 4.00000 6.92820i 0.158238 0.274075i
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) 15.0000 + 25.9808i 0.592464 + 1.02618i 0.993899 + 0.110291i \(0.0351782\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(642\) −6.00000 + 10.3923i −0.236801 + 0.410152i
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 4.00000 6.92820i 0.157378 0.272587i
\(647\) 16.0000 + 27.7128i 0.629025 + 1.08950i 0.987748 + 0.156059i \(0.0498790\pi\)
−0.358723 + 0.933444i \(0.616788\pi\)
\(648\) −1.50000 2.59808i −0.0589256 0.102062i
\(649\) 8.00000 13.8564i 0.314027 0.543912i
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −23.0000 + 39.8372i −0.900060 + 1.55895i −0.0726446 + 0.997358i \(0.523144\pi\)
−0.827415 + 0.561591i \(0.810189\pi\)
\(654\) 7.00000 + 12.1244i 0.273722 + 0.474100i
\(655\) 6.00000 + 10.3923i 0.234439 + 0.406061i
\(656\) −5.00000 + 8.66025i −0.195217 + 0.338126i
\(657\) −10.0000 −0.390137
\(658\) 0 0
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 2.00000 3.46410i 0.0778499 0.134840i
\(661\) 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 6.00000 + 10.3923i 0.233197 + 0.403908i
\(663\) 2.00000 3.46410i 0.0776736 0.134535i
\(664\) −36.0000 −1.39707
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 0 0
\(668\) 0 0
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) −6.00000 + 10.3923i −0.231800 + 0.401490i
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) −30.0000 −1.15642 −0.578208 0.815890i \(-0.696248\pi\)
−0.578208 + 0.815890i \(0.696248\pi\)
\(674\) −7.00000 + 12.1244i −0.269630 + 0.467013i
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) −4.50000 7.79423i −0.173077 0.299778i
\(677\) 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 0 0
\(680\) 6.00000 0.230089
\(681\) −10.0000 + 17.3205i −0.383201 + 0.663723i
\(682\) 0 0
\(683\) −18.0000 31.1769i −0.688751 1.19295i −0.972242 0.233977i \(-0.924826\pi\)
0.283491 0.958975i \(-0.408507\pi\)
\(684\) −2.00000 + 3.46410i −0.0764719 + 0.132453i
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) −6.00000 −0.228914
\(688\) 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 \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) 3.00000 + 5.19615i 0.113715 + 0.196960i
\(697\) −10.0000 17.3205i −0.378777 0.656061i
\(698\) 1.00000 1.73205i 0.0378506 0.0655591i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 1.00000 1.73205i 0.0377426 0.0653720i
\(703\) −20.0000 34.6410i −0.754314 1.30651i
\(704\) 14.0000 + 24.2487i 0.527645 + 0.913908i
\(705\) −4.00000 + 6.92820i −0.150649 + 0.260931i
\(706\) 18.0000 0.677439
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i \(-0.670978\pi\)
0.999908 + 0.0135434i \(0.00431112\pi\)
\(710\) 4.00000 + 6.92820i 0.150117 + 0.260011i
\(711\) 0 0
\(712\) −9.00000 + 15.5885i −0.337289 + 0.584202i
\(713\) 0 0
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) 10.0000 17.3205i 0.373718 0.647298i
\(717\) 8.00000 + 13.8564i 0.298765 + 0.517477i
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) −24.0000 + 41.5692i −0.895049 + 1.55027i −0.0613050 + 0.998119i \(0.519526\pi\)
−0.833744 + 0.552151i \(0.813807\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) −7.00000 + 12.1244i −0.260333 + 0.450910i
\(724\) 5.00000 + 8.66025i 0.185824 + 0.321856i
\(725\) 1.00000 + 1.73205i 0.0371391 + 0.0643268i
\(726\) 2.50000 4.33013i 0.0927837 0.160706i
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 5.00000 8.66025i 0.185058 0.320530i
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 1.00000 + 1.73205i 0.0369611 + 0.0640184i
\(733\) 7.00000 12.1244i 0.258551 0.447823i −0.707303 0.706910i \(-0.750088\pi\)
0.965854 + 0.259087i \(0.0834217\pi\)
\(734\) −24.0000 −0.885856
\(735\) 0 0
\(736\) 0 0
\(737\) 24.0000 41.5692i 0.884051 1.53122i
\(738\) −5.00000 8.66025i −0.184053 0.318788i
\(739\) 22.0000 + 38.1051i 0.809283 + 1.40172i 0.913361 + 0.407150i \(0.133477\pi\)
−0.104078 + 0.994569i \(0.533189\pi\)
\(740\) 5.00000 8.66025i 0.183804 0.318357i
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) 11.0000 + 19.0526i 0.403009 + 0.698032i
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) −8.00000 −0.292509
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) −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
\(753\) 6.00000 + 10.3923i 0.218652 + 0.378717i
\(754\) −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 \(0.201351\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) −1.00000 + 1.73205i −0.0361551 + 0.0626224i
\(766\) 12.0000 + 20.7846i 0.433578 + 0.750978i
\(767\) −4.00000 6.92820i −0.144432 0.250163i
\(768\) 8.50000 14.7224i 0.306717 0.531250i
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 1.00000 1.73205i 0.0359908 0.0623379i
\(773\) 3.00000 + 5.19615i 0.107903 + 0.186893i 0.914920 0.403634i \(-0.132253\pi\)
−0.807018 + 0.590527i \(0.798920\pi\)
\(774\) 2.00000 + 3.46410i 0.0718885 + 0.124515i
\(775\) 0 0
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) −20.0000 + 34.6410i −0.716574 + 1.24114i
\(780\) −1.00000 1.73205i −0.0358057 0.0620174i
\(781\) −16.0000 27.7128i −0.572525 0.991642i
\(782\) 0 0
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) 14.0000 0.499681
\(786\) 6.00000 10.3923i