Properties

Label 735.2.i.e.361.1
Level $735$
Weight $2$
Character 735.361
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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 735.361
Dual form 735.2.i.e.226.1

$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 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 −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 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 \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 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 0.904194 + 0.427121i \(0.140472\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 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 \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 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 −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 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 −0.286064 0.958211i \(-0.592347\pi\)
0.972867 0.231367i \(-0.0743197\pi\)
\(54\) −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 \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) 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
\(66\) 2.00000 3.46410i 0.246183 0.426401i
\(67\) −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 \(-0.657448\pi\)
−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 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 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 \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 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 \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) −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 \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 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 \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) −1.00000 + 1.73205i −0.0990148 + 0.171499i
\(103\) 8.00000 + 13.8564i 0.788263 + 1.36531i 0.927030 + 0.374987i \(0.122353\pi\)
−0.138767 + 0.990325i \(0.544314\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) −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 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) −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 −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 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 −0.825997 0.563675i \(-0.809387\pi\)
−0.0751583 0.997172i \(-0.523946\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −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 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 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 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) 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 0.973670 + 0.227964i \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) −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 0.201613 + 0.979465i \(0.435382\pi\)
−0.949048 + 0.315130i \(0.897952\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 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 −0.995610 0.0935936i \(-0.970165\pi\)
0.416751 0.909021i \(-0.363169\pi\)
\(192\) 3.50000 6.06218i 0.252591 0.437500i
\(193\) −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
\(195\) 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 \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) −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 \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 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 −0.315906 0.948790i \(-0.602309\pi\)
0.979630 0.200812i \(-0.0643581\pi\)
\(228\) −2.00000 + 3.46410i −0.132453 + 0.229416i
\(229\) −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
\(232\) −6.00000 −0.393919
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) −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 \(-0.684433\pi\)
0.998443 + 0.0557856i \(0.0177663\pi\)
\(242\) 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 \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −4.00000 6.92820i −0.250982 0.434714i
\(255\) 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 −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 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 −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) −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 \(-0.973692\pi\)
0.569789 + 0.821791i \(0.307025\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) −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 −0.941966 0.335707i \(-0.891025\pi\)
0.761714 + 0.647913i \(0.224358\pi\)
\(278\) −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 \(-0.717248\pi\)
0.987401 + 0.158237i \(0.0505811\pi\)
\(284\) −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 \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 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 \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) −3.00000 + 5.19615i −0.169842 + 0.294174i
\(313\) −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 0.892741 0.450570i \(-0.148779\pi\)
−0.836576 + 0.547852i \(0.815446\pi\)
\(318\) 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 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) 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 −0.195507 0.980702i \(-0.562635\pi\)
0.947067 0.321037i \(-0.104031\pi\)
\(348\) 1.00000 + 1.73205i 0.0536056 + 0.0928477i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 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 \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 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 0.986865 + 0.161546i \(0.0516481\pi\)
−0.353529 + 0.935423i \(0.615019\pi\)
\(360\) −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 −0.361874 0.932227i \(-0.617863\pi\)
0.988269 0.152721i \(-0.0488036\pi\)
\(368\) 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 0.977016 + 0.213165i \(0.0683772\pi\)
−0.303902 + 0.952703i \(0.598289\pi\)
\(374\) −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 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) −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 −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 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 \(-0.150684\pi\)
−0.839840 + 0.542834i \(0.817351\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) −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 0.341994 + 0.939702i \(0.388898\pi\)
−0.984803 + 0.173675i \(0.944436\pi\)
\(410\) 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 \(-0.468849\pi\)
0.0977064 + 0.995215i \(0.468849\pi\)
\(420\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 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 −0.735399 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 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 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 0.725059 0.688686i \(-0.241812\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 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 \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 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 −0.983637 0.180161i \(-0.942338\pi\)
0.335794 0.941935i \(-0.390995\pi\)
\(468\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) −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 0.233933 + 0.972253i \(0.424840\pi\)
−0.958962 + 0.283535i \(0.908493\pi\)
\(488\) 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 0.817781 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
\(507\) −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 0.946111 + 0.323843i \(0.104975\pi\)
−0.192599 + 0.981278i \(0.561692\pi\)
\(510\) 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 \(-0.903630\pi\)
0.735465 + 0.677563i \(0.236964\pi\)
\(522\) −1.00000 + 1.73205i −0.0437688 + 0.0758098i
\(523\) −2.00000 3.46410i −0.0874539 0.151475i 0.818980 0.573822i \(-0.194540\pi\)
−0.906434 + 0.422347i \(0.861206\pi\)
\(524\) 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 −0.984325 0.176367i \(-0.943566\pi\)
0.339424 0.940633i \(-0.389768\pi\)
\(542\) 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 −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) 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 \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) −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 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) 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
\(573\) −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 \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) −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 \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 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 −0.969122 0.246581i \(-0.920693\pi\)
0.271016 0.962575i \(-0.412640\pi\)
\(594\) −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 −0.772663 0.634816i \(-0.781076\pi\)
0.936099 + 0.351738i \(0.114409\pi\)
\(600\) 1.50000 + 2.59808i 0.0612372 + 0.106066i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 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 \(-0.114758\pi\)
−0.773358 + 0.633970i \(0.781424\pi\)
\(608\) −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 −0.998002 0.0631797i \(-0.979876\pi\)
0.553716 + 0.832705i \(0.313209\pi\)
\(614\) 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 \(-0.807718\pi\)
0.903416 + 0.428765i \(0.141051\pi\)
\(620\) 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 −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 6.00000 + 10.3923i 0.236801 + 0.410152i
\(643\) −36.0000 −1.41970 −0.709851 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) 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 0.358723 + 0.933444i \(0.383212\pi\)
−0.987748 + 0.156059i \(0.950121\pi\)
\(648\) −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 −0.827415 0.561591i \(-0.810189\pi\)
−0.0726446 0.997358i \(-0.523144\pi\)
\(654\) −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 \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) 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 \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 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 0.283491 + 0.958975i \(0.408507\pi\)
−0.972242 + 0.233977i \(0.924826\pi\)
\(684\) 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 0.892458 + 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
\(696\) −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 0.999908 0.0135434i \(-0.00431112\pi\)
−0.511683 + 0.859174i \(0.670978\pi\)
\(710\) −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 0.833744 + 0.552151i \(0.186193\pi\)
0.0613050 + 0.998119i \(0.480474\pi\)
\(720\) −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 \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 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 \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) 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 −0.104078 0.994569i \(-0.533189\pi\)
0.913361 0.407150i \(-0.133477\pi\)
\(740\) −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 0.682341 0.731034i \(-0.260962\pi\)
−0.974265 + 0.225407i \(0.927629\pi\)
\(752\) 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 \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) −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 \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 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 \(-0.867747\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(774\) 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 0.214013 + 0.370681i
\(787\)