Properties

Label 294.2.e.c.67.1
Level $294$
Weight $2$
Character 294.67
Analytic conductor $2.348$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.34760181943\)
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 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.2.e.c.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +(0.500000 + 0.866025i) q^{12} +6.00000 q^{13} +2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} -2.00000 q^{20} -4.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{26} -1.00000 q^{27} -2.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(-2.00000 - 3.46410i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(5.00000 + 8.66025i) q^{37} +(2.00000 - 3.46410i) q^{38} +(3.00000 - 5.19615i) q^{39} +(1.00000 + 1.73205i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(1.00000 - 1.73205i) q^{45} +(-4.00000 + 6.92820i) q^{46} -1.00000 q^{48} -1.00000 q^{50} +(1.00000 + 1.73205i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +8.00000 q^{55} +4.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-3.00000 - 5.19615i) q^{61} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(-2.00000 + 3.46410i) q^{66} +(-2.00000 + 3.46410i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{69} +8.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(5.00000 - 8.66025i) q^{74} +(-0.500000 - 0.866025i) q^{75} -4.00000 q^{76} -6.00000 q^{78} +(1.00000 - 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} -4.00000 q^{83} -4.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-1.00000 + 1.73205i) q^{87} +(2.00000 - 3.46410i) q^{88} +(3.00000 + 5.19615i) q^{89} -2.00000 q^{90} +8.00000 q^{92} +(-4.00000 + 6.92820i) q^{95} +(0.500000 + 0.866025i) q^{96} -14.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + 2q^{5} - 2q^{6} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + 2q^{5} - 2q^{6} + 2q^{8} - q^{9} + 2q^{10} + 4q^{11} + q^{12} + 12q^{13} + 4q^{15} - q^{16} - 2q^{17} - q^{18} + 4q^{19} - 4q^{20} - 8q^{22} - 8q^{23} + q^{24} + q^{25} - 6q^{26} - 2q^{27} - 4q^{29} - 2q^{30} - q^{32} - 4q^{33} + 4q^{34} + 2q^{36} + 10q^{37} + 4q^{38} + 6q^{39} + 2q^{40} - 12q^{41} - 8q^{43} + 4q^{44} + 2q^{45} - 8q^{46} - 2q^{48} - 2q^{50} + 2q^{51} - 6q^{52} - 6q^{53} + q^{54} + 16q^{55} + 8q^{57} + 2q^{58} - 4q^{59} - 2q^{60} - 6q^{61} + 2q^{64} + 12q^{65} - 4q^{66} - 4q^{67} - 2q^{68} - 16q^{69} + 16q^{71} - q^{72} - 10q^{73} + 10q^{74} - q^{75} - 8q^{76} - 12q^{78} + 2q^{80} - q^{81} + 6q^{82} - 8q^{83} - 8q^{85} + 4q^{86} - 2q^{87} + 4q^{88} + 6q^{89} - 4q^{90} + 16q^{92} - 8q^{95} + q^{96} - 28q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 1.73205i 0.316228 0.547723i
\(11\) 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
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) −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 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −3.00000 5.19615i −0.588348 1.01905i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −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
\(39\) 3.00000 5.19615i 0.480384 0.832050i
\(40\) 1.00000 + 1.73205i 0.158114 + 0.273861i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) −4.00000 + 6.92820i −0.589768 + 1.02151i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) −3.00000 + 5.19615i −0.416025 + 0.720577i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 8.00000 1.07872
\(56\) 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 −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) −1.00000 + 1.73205i −0.129099 + 0.223607i
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 + 10.3923i 0.744208 + 1.28901i
\(66\) −2.00000 + 3.46410i −0.246183 + 0.426401i
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −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
\(78\) −6.00000 −0.679366
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 1.00000 1.73205i 0.111803 0.193649i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) −1.00000 + 1.73205i −0.107211 + 0.185695i
\(88\) 2.00000 3.46410i 0.213201 0.369274i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 1.00000 1.73205i 0.0990148 0.171499i
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) −4.00000 6.92820i −0.381385 0.660578i
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) 8.00000 13.8564i 0.746004 1.29212i
\(116\) 1.00000 1.73205i 0.0928477 0.160817i
\(117\) −3.00000 5.19615i −0.277350 0.480384i
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) 2.00000 0.182574
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) −3.00000 + 5.19615i −0.271607 + 0.470438i
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) 6.00000 10.3923i 0.526235 0.911465i
\(131\) 10.0000 + 17.3205i 0.873704 + 1.51330i 0.858137 + 0.513421i \(0.171622\pi\)
0.0155672 + 0.999879i \(0.495045\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) −1.00000 1.73205i −0.0860663 0.149071i
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −5.00000 + 8.66025i −0.427179 + 0.739895i −0.996621 0.0821359i \(-0.973826\pi\)
0.569442 + 0.822031i \(0.307159\pi\)
\(138\) 4.00000 + 6.92820i 0.340503 + 0.589768i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.00000 6.92820i −0.335673 0.581402i
\(143\) 12.0000 20.7846i 1.00349 1.73810i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −2.00000 3.46410i −0.166091 0.287678i
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) −10.0000 −0.821995
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) −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 \(0.0611289\pi\)
\(152\) 2.00000 + 3.46410i 0.162221 + 0.280976i
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 + 5.19615i 0.240192 + 0.416025i
\(157\) 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i \(-0.702676\pi\)
0.993608 + 0.112884i \(0.0360089\pi\)
\(158\) 0 0
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) −2.00000 −0.158114
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 4.00000 6.92820i 0.311400 0.539360i
\(166\) 2.00000 + 3.46410i 0.155230 + 0.268866i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 2.00000 + 3.46410i 0.153393 + 0.265684i
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) −11.0000 19.0526i −0.836315 1.44854i −0.892956 0.450145i \(-0.851372\pi\)
0.0566411 0.998395i \(-0.481961\pi\)
\(174\) 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
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) −4.00000 6.92820i −0.294884 0.510754i
\(185\) −10.0000 + 17.3205i −0.735215 + 1.27343i
\(186\) 0 0
\(187\) 4.00000 + 6.92820i 0.292509 + 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 7.00000 + 12.1244i 0.502571 + 0.870478i
\(195\) 12.0000 0.859338
\(196\) 0 0
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 2.00000 + 3.46410i 0.142134 + 0.246183i
\(199\) −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i \(-0.924846\pi\)
0.688705 + 0.725042i \(0.258180\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 2.00000 + 3.46410i 0.141069 + 0.244339i
\(202\) −2.00000 −0.140720
\(203\) 0 0
\(204\) −2.00000 −0.140028
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) −4.00000 + 6.92820i −0.278693 + 0.482711i
\(207\) −4.00000 + 6.92820i −0.278019 + 0.481543i
\(208\) −3.00000 5.19615i −0.208013 0.360288i
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 4.00000 6.92820i 0.274075 0.474713i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −4.00000 6.92820i −0.272798 0.472500i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) 5.00000 + 8.66025i 0.337869 + 0.585206i
\(220\) −4.00000 + 6.92820i −0.269680 + 0.467099i
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) −5.00000 8.66025i −0.335578 0.581238i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 7.00000 + 12.1244i 0.465633 + 0.806500i
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) −2.00000 + 3.46410i −0.132453 + 0.229416i
\(229\) 1.00000 + 1.73205i 0.0660819 + 0.114457i 0.897173 0.441679i \(-0.145617\pi\)
−0.831092 + 0.556136i \(0.812283\pi\)
\(230\) −16.0000 −1.05501
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) 11.0000 + 19.0526i 0.720634 + 1.24817i 0.960746 + 0.277429i \(0.0894825\pi\)
−0.240112 + 0.970745i \(0.577184\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) 0 0
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 1.73205i −0.0645497 0.111803i
\(241\) −1.00000 + 1.73205i −0.0644157 + 0.111571i −0.896435 0.443176i \(-0.853852\pi\)
0.832019 + 0.554747i \(0.187185\pi\)
\(242\) −2.50000 + 4.33013i −0.160706 + 0.278351i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) 12.0000 + 20.7846i 0.763542 + 1.32249i
\(248\) 0 0
\(249\) −2.00000 + 3.46410i −0.126745 + 0.219529i
\(250\) −6.00000 10.3923i −0.379473 0.657267i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −32.0000 −2.01182
\(254\) 0 0
\(255\) −2.00000 + 3.46410i −0.125245 + 0.216930i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 15.0000 + 25.9808i 0.935674 + 1.62064i 0.773427 + 0.633885i \(0.218541\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(258\) 4.00000 0.249029
\(259\) 0 0
\(260\) −12.0000 −0.744208
\(261\) 1.00000 + 1.73205i 0.0618984 + 0.107211i
\(262\) 10.0000 17.3205i 0.617802 1.07006i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) −2.00000 3.46410i −0.123091 0.213201i
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) −2.00000 3.46410i −0.122169 0.211604i
\(269\) −11.0000 + 19.0526i −0.670682 + 1.16166i 0.307029 + 0.951700i \(0.400665\pi\)
−0.977711 + 0.209955i \(0.932668\pi\)
\(270\) −1.00000 + 1.73205i −0.0608581 + 0.105409i
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 4.00000 6.92820i 0.240772 0.417029i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −2.00000 3.46410i −0.119952 0.207763i
\(279\) 0 0
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 0 0
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) −4.00000 + 6.92820i −0.237356 + 0.411113i
\(285\) 4.00000 + 6.92820i 0.236940 + 0.410391i
\(286\) −24.0000 −1.41915
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −2.00000 + 3.46410i −0.117444 + 0.203419i
\(291\) −7.00000 + 12.1244i −0.410347 + 0.710742i
\(292\) −5.00000 8.66025i −0.292603 0.506803i
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 5.00000 + 8.66025i 0.290619 + 0.503367i
\(297\) −2.00000 + 3.46410i −0.116052 + 0.201008i
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) −24.0000 41.5692i −1.38796 2.40401i
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) −1.00000 1.73205i −0.0574485 0.0995037i
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 6.00000 10.3923i 0.343559 0.595062i
\(306\) −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
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i \(-0.760501\pi\)
0.956864 + 0.290537i \(0.0938340\pi\)
\(312\) 3.00000 5.19615i 0.169842 0.294174i
\(313\) −5.00000 8.66025i −0.282617 0.489506i 0.689412 0.724370i \(-0.257869\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) 0 0
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 3.00000 5.19615i 0.168232 0.291386i
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) 1.00000 + 1.73205i 0.0559017 + 0.0968246i
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 3.00000 5.19615i 0.166410 0.288231i
\(326\) −10.0000 + 17.3205i −0.553849 + 0.959294i
\(327\) −1.00000 1.73205i −0.0553001 0.0957826i
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) −8.00000 −0.440386
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) 2.00000 3.46410i 0.109764 0.190117i
\(333\) 5.00000 8.66025i 0.273998 0.474579i
\(334\) 4.00000 + 6.92820i 0.218870 + 0.379094i
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) −11.5000 19.9186i −0.625518 1.08343i
\(339\) −7.00000 + 12.1244i −0.380188 + 0.658505i
\(340\) 2.00000 3.46410i 0.108465 0.187867i
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) −8.00000 13.8564i −0.430706 0.746004i
\(346\) −11.0000 + 19.0526i −0.591364 + 1.02427i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) −1.00000 1.73205i −0.0536056 0.0928477i
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) 2.00000 + 3.46410i 0.106600 + 0.184637i
\(353\) 15.0000 25.9808i 0.798369 1.38282i −0.122308 0.992492i \(-0.539030\pi\)
0.920677 0.390324i \(-0.127637\pi\)
\(354\) 2.00000 3.46410i 0.106299 0.184115i
\(355\) 8.00000 + 13.8564i 0.424596 + 0.735422i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 4.00000 + 6.92820i 0.211112 + 0.365657i 0.952063 0.305903i \(-0.0989582\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(360\) 1.00000 1.73205i 0.0527046 0.0912871i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 9.00000 + 15.5885i 0.473029 + 0.819311i
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) −20.0000 −1.04685
\(366\) 3.00000 + 5.19615i 0.156813 + 0.271607i
\(367\) −16.0000 + 27.7128i −0.835193 + 1.44660i 0.0586798 + 0.998277i \(0.481311\pi\)
−0.893873 + 0.448320i \(0.852022\pi\)
\(368\) −4.00000 + 6.92820i −0.208514 + 0.361158i
\(369\) 3.00000 + 5.19615i 0.156174 + 0.270501i
\(370\) 20.0000 1.03975
\(371\) 0 0
\(372\) 0 0
\(373\) −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) 4.00000 6.92820i 0.206835 0.358249i
\(375\) 6.00000 10.3923i 0.309839 0.536656i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −4.00000 6.92820i −0.205196 0.355409i
\(381\) 0 0
\(382\) 0 0
\(383\) 8.00000 + 13.8564i 0.408781 + 0.708029i 0.994753 0.102302i \(-0.0326207\pi\)
−0.585973 + 0.810331i \(0.699287\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) 7.00000 12.1244i 0.355371 0.615521i
\(389\) 13.0000 22.5167i 0.659126 1.14164i −0.321716 0.946836i \(-0.604260\pi\)
0.980842 0.194804i \(-0.0624070\pi\)
\(390\) −6.00000 10.3923i −0.303822 0.526235i
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 20.0000 1.00887
\(394\) 5.00000 + 8.66025i 0.251896 + 0.436297i
\(395\) 0 0
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) −3.00000 5.19615i −0.150566 0.260787i 0.780870 0.624694i \(-0.214776\pi\)
−0.931436 + 0.363906i \(0.881443\pi\)
\(398\) 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 \(0.981709\pi\)
\(402\) 2.00000 3.46410i 0.0997509 0.172774i
\(403\) 0 0
\(404\) 1.00000 + 1.73205i 0.0497519 + 0.0861727i
\(405\) −2.00000 −0.0993808
\(406\) 0 0
\(407\) 40.0000 1.98273
\(408\) 1.00000 + 1.73205i 0.0495074 + 0.0857493i
\(409\) 11.0000 19.0526i 0.543915 0.942088i −0.454759 0.890614i \(-0.650275\pi\)
0.998674 0.0514740i \(-0.0163919\pi\)
\(410\) −6.00000 + 10.3923i −0.296319 + 0.513239i
\(411\) 5.00000 + 8.66025i 0.246632 + 0.427179i
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) −4.00000 6.92820i −0.196352 0.340092i
\(416\) −3.00000 + 5.19615i −0.147087 + 0.254762i
\(417\) 2.00000 3.46410i 0.0979404 0.169638i
\(418\) −8.00000 13.8564i −0.391293 0.677739i
\(419\) −36.0000 −1.75872 −0.879358 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) −10.0000 17.3205i −0.486792 0.843149i
\(423\) 0 0
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) −12.0000 20.7846i −0.579365 1.00349i
\(430\) −4.00000 + 6.92820i −0.192897 + 0.334108i
\(431\) 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
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) −4.00000 −0.191785
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) 16.0000 27.7128i 0.765384 1.32568i
\(438\) 5.00000 8.66025i 0.238909 0.413803i
\(439\) 12.0000 + 20.7846i 0.572729 + 0.991995i 0.996284 + 0.0861252i \(0.0274485\pi\)
−0.423556 + 0.905870i \(0.639218\pi\)
\(440\) 8.00000 0.381385
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) 2.00000 + 3.46410i 0.0950229 + 0.164584i 0.909618 0.415445i \(-0.136374\pi\)
−0.814595 + 0.580030i \(0.803041\pi\)
\(444\) −5.00000 + 8.66025i −0.237289 + 0.410997i
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) 34.0000 1.60456 0.802280 0.596948i \(-0.203620\pi\)
0.802280 + 0.596948i \(0.203620\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) −12.0000 + 20.7846i −0.565058 + 0.978709i
\(452\) 7.00000 12.1244i 0.329252 0.570282i
\(453\) −4.00000 6.92820i −0.187936 0.325515i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i \(-0.241812\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 1.00000 1.73205i 0.0467269 0.0809334i
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 8.00000 + 13.8564i 0.373002 + 0.646058i
\(461\) 22.0000 1.02464 0.512321 0.858794i \(-0.328786\pi\)
0.512321 + 0.858794i \(0.328786\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) 1.00000 + 1.73205i 0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) 11.0000 19.0526i 0.509565 0.882593i
\(467\) −14.0000 24.2487i −0.647843 1.12210i −0.983637 0.180161i \(-0.942338\pi\)
0.335794 0.941935i \(-0.390995\pi\)
\(468\) 6.00000 0.277350
\(469\) 0 0
\(470\) 0 0
\(471\) −5.00000 8.66025i −0.230388 0.399043i
\(472\) −2.00000 + 3.46410i −0.0920575 + 0.159448i
\(473\) −8.00000 + 13.8564i −0.367840 + 0.637118i
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) 8.00000 13.8564i 0.365529 0.633115i −0.623332 0.781958i \(-0.714221\pi\)
0.988861 + 0.148842i \(0.0475547\pi\)
\(480\) −1.00000 + 1.73205i −0.0456435 + 0.0790569i
\(481\) 30.0000 + 51.9615i 1.36788 + 2.36924i
\(482\) 2.00000 0.0910975
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) −14.0000 24.2487i −0.635707 1.10108i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −4.00000 + 6.92820i −0.181257 + 0.313947i −0.942309 0.334744i \(-0.891350\pi\)
0.761052 + 0.648691i \(0.224683\pi\)
\(488\) −3.00000 5.19615i −0.135804 0.235219i
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −3.00000 5.19615i −0.135250 0.234261i
\(493\) 2.00000 3.46410i 0.0900755 0.156015i
\(494\) 12.0000 20.7846i 0.539906 0.935144i
\(495\) −4.00000 6.92820i −0.179787 0.311400i
\(496\) 0 0
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) 22.0000 + 38.1051i 0.984855 + 1.70582i 0.642578 + 0.766220i \(0.277865\pi\)
0.342277 + 0.939599i \(0.388802\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) −4.00000 + 6.92820i −0.178707 + 0.309529i
\(502\) 6.00000 + 10.3923i 0.267793 + 0.463831i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) 16.0000 + 27.7128i 0.711287 + 1.23198i
\(507\) 11.5000 19.9186i 0.510733 0.884615i
\(508\) 0 0
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 4.00000 0.177123
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −2.00000 3.46410i −0.0883022 0.152944i
\(514\) 15.0000 25.9808i 0.661622 1.14596i
\(515\) 8.00000 13.8564i 0.352522 0.610586i
\(516\) −2.00000 3.46410i −0.0880451 0.152499i
\(517\) 0 0
\(518\) 0 0
\(519\) −22.0000 −0.965693
\(520\) 6.00000 + 10.3923i 0.263117 + 0.455733i
\(521\) 3.00000 5.19615i 0.131432 0.227648i −0.792797 0.609486i \(-0.791376\pi\)
0.924229 + 0.381839i \(0.124709\pi\)
\(522\) 1.00000 1.73205i 0.0437688 0.0758098i
\(523\) −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i \(-0.310721\pi\)
−0.997478 + 0.0709788i \(0.977388\pi\)
\(524\) −20.0000 −0.873704
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) −2.00000 + 3.46410i −0.0870388 + 0.150756i
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) 6.00000 + 10.3923i 0.260623 + 0.451413i
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) −36.0000 −1.55933
\(534\) −3.00000 5.19615i −0.129823 0.224860i
\(535\) 12.0000 20.7846i 0.518805 0.898597i
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) 22.0000 0.948487
\(539\) 0 0
\(540\) 2.00000 0.0860663
\(541\) −15.0000 25.9808i −0.644900 1.11700i −0.984325 0.176367i \(-0.943566\pi\)
0.339424 0.940633i \(-0.389768\pi\)
\(542\) 0 0
\(543\) −9.00000 + 15.5885i −0.386227 + 0.668965i
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −5.00000 8.66025i −0.213589 0.369948i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) −4.00000 6.92820i −0.170406 0.295151i
\(552\) −8.00000 −0.340503
\(553\) 0 0
\(554\) −10.0000 −0.424859
\(555\) 10.0000 + 17.3205i 0.424476 + 0.735215i
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 1.00000 1.73205i 0.0423714 0.0733893i −0.844062 0.536246i \(-0.819842\pi\)
0.886433 + 0.462856i \(0.153175\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) −13.0000 22.5167i −0.548372 0.949808i
\(563\) −22.0000 + 38.1051i −0.927189 + 1.60594i −0.139188 + 0.990266i \(0.544449\pi\)
−0.788002 + 0.615673i \(0.788884\pi\)
\(564\) 0 0
\(565\) −14.0000 24.2487i −0.588984 1.02015i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 4.00000 6.92820i 0.167542 0.290191i
\(571\) −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) 12.0000 + 20.7846i 0.501745 + 0.869048i
\(573\) 0 0
\(574\) 0 0
\(575\) −8.00000 −0.333623
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −17.0000 + 29.4449i −0.707719 + 1.22581i 0.257982 + 0.966150i \(0.416942\pi\)
−0.965701 + 0.259656i \(0.916391\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) 1.00000 + 1.73205i 0.0415586 + 0.0719816i
\(580\) 4.00000 0.166091
\(581\) 0 0
\(582\) 14.0000 0.580319
\(583\) 12.0000 + 20.7846i 0.496989 + 0.860811i
\(584\) −5.00000 + 8.66025i −0.206901 + 0.358364i
\(585\) 6.00000 10.3923i 0.248069 0.429669i
\(586\) −15.0000 25.9808i −0.619644 1.07326i
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 4.00000 + 6.92820i 0.164677 + 0.285230i
\(591\) −5.00000 + 8.66025i −0.205673 + 0.356235i
\(592\) 5.00000 8.66025i 0.205499 0.355934i
\(593\) −9.00000 15.5885i −0.369586 0.640141i 0.619915 0.784669i \(-0.287167\pi\)
−0.989501 + 0.144528i \(0.953834\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) 4.00000 + 6.92820i 0.163709 + 0.283552i
\(598\) −24.0000 + 41.5692i −0.981433 + 1.69989i
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 4.00000 + 6.92820i 0.162758 + 0.281905i
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) −1.00000 + 1.73205i −0.0406222 + 0.0703598i
\(607\) −24.0000 41.5692i −0.974130 1.68724i −0.682777 0.730627i \(-0.739228\pi\)
−0.291353 0.956616i \(-0.594105\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −12.0000 −0.485866
\(611\) 0 0
\(612\) −1.00000 + 1.73205i −0.0404226 + 0.0700140i
\(613\) 21.0000 36.3731i 0.848182 1.46909i −0.0346469 0.999400i \(-0.511031\pi\)
0.882829 0.469695i \(-0.155636\pi\)
\(614\) −14.0000 24.2487i −0.564994 0.978598i
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 4.00000 + 6.92820i 0.160904 + 0.278693i
\(619\) 22.0000 38.1051i 0.884255 1.53157i 0.0376891 0.999290i \(-0.488000\pi\)
0.846566 0.532284i \(-0.178666\pi\)
\(620\) 0 0
\(621\) 4.00000 + 6.92820i 0.160514 + 0.278019i
\(622\) −8.00000 −0.320771
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) −5.00000 + 8.66025i −0.199840 + 0.346133i
\(627\) 8.00000 13.8564i 0.319489 0.553372i
\(628\) 5.00000 + 8.66025i 0.199522 + 0.345582i
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 10.0000 17.3205i 0.397464 0.688428i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 8.00000 0.316723
\(639\) −4.00000 6.92820i −0.158238 0.274075i
\(640\) 1.00000 1.73205i 0.0395285 0.0684653i
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 6.00000 + 10.3923i 0.236801 + 0.410152i
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 4.00000 + 6.92820i 0.157378 + 0.272587i
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 8.00000 + 13.8564i 0.314027 + 0.543912i
\(650\) −6.00000 −0.235339
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) −1.00000 + 1.73205i −0.0391031 + 0.0677285i
\(655\) −20.0000 + 34.6410i −0.781465 + 1.35354i
\(656\) 3.00000 + 5.19615i 0.117130 + 0.202876i
\(657\) 10.0000 0.390137
\(658\) 0 0
\(659\) −28.0000 −1.09073 −0.545363 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 4.00000 + 6.92820i 0.155700 + 0.269680i
\(661\) 1.00000 1.73205i 0.0388955 0.0673690i −0.845922 0.533306i \(-0.820949\pi\)
0.884818 + 0.465937i \(0.154283\pi\)
\(662\) 2.00000 3.46410i 0.0777322 0.134636i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) 8.00000 + 13.8564i 0.309761 + 0.536522i
\(668\) 4.00000 6.92820i 0.154765 0.268060i
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) 4.00000 + 6.92820i 0.154533 + 0.267660i
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) −9.00000 15.5885i −0.346667 0.600445i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) −11.5000 + 19.9186i −0.442308 + 0.766099i
\(677\) 9.00000 + 15.5885i 0.345898 + 0.599113i 0.985517 0.169580i \(-0.0542410\pi\)
−0.639618 + 0.768693i \(0.720908\pi\)
\(678\) 14.0000 0.537667
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) 6.00000 + 10.3923i 0.229920 + 0.398234i
\(682\) 0 0
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 2.00000 + 3.46410i 0.0764719 + 0.132453i
\(685\) −20.0000 −0.764161
\(686\) 0 0
\(687\) 2.00000 0.0763048
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −18.0000 + 31.1769i −0.685745 + 1.18775i
\(690\) −8.00000 + 13.8564i −0.304555 + 0.527504i
\(691\) 2.00000 + 3.46410i 0.0760836 + 0.131781i 0.901557 0.432660i \(-0.142425\pi\)
−0.825473 + 0.564441i \(0.809092\pi\)
\(692\) 22.0000 0.836315
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 4.00000 + 6.92820i 0.151729 + 0.262802i
\(696\) −1.00000 + 1.73205i −0.0379049 + 0.0656532i
\(697\) 6.00000 10.3923i 0.227266 0.393637i
\(698\) −11.0000 19.0526i −0.416356 0.721150i
\(699\) 22.0000 0.832116
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 3.00000 + 5.19615i 0.113228 + 0.196116i
\(703\) −20.0000 + 34.6410i −0.754314 + 1.30651i
\(704\) 2.00000 3.46410i 0.0753778 0.130558i
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 8.00000 13.8564i 0.300235 0.520022i
\(711\) 0 0
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) 48.0000 1.79510
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) 4.00000 6.92820i 0.149279 0.258558i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) 1.00000 + 1.73205i 0.0371904 + 0.0644157i
\(724\) 9.00000 15.5885i 0.334482 0.579340i
\(725\) −1.00000 + 1.73205i −0.0371391 + 0.0643268i
\(726\) 2.50000 + 4.33013i 0.0927837 + 0.160706i
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 10.0000 + 17.3205i 0.370117 + 0.641061i
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) 3.00000 5.19615i 0.110883 0.192055i
\(733\) −3.00000 5.19615i −0.110808 0.191924i 0.805289 0.592883i \(-0.202010\pi\)
−0.916096 + 0.400959i \(0.868677\pi\)
\(734\) 32.0000 1.18114
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 8.00000 + 13.8564i 0.294684 + 0.510407i
\(738\) 3.00000 5.19615i 0.110432 0.191273i
\(739\) 6.00000 10.3923i 0.220714 0.382287i −0.734311 0.678813i \(-0.762495\pi\)
0.955025 + 0.296526i \(0.0958281\pi\)
\(740\) −10.0000 17.3205i −0.367607 0.636715i
\(741\) 24.0000 0.881662
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 6.00000 10.3923i 0.219823 0.380745i
\(746\) −11.0000 + 19.0526i −0.402739 + 0.697564i
\(747\) 2.00000 + 3.46410i 0.0731762 + 0.126745i
\(748\) −8.00000 −0.292509
\(749\) 0 0
\(750\) −12.0000 −0.438178
\(751\) −24.0000 41.5692i −0.875772 1.51688i −0.855938 0.517079i \(-0.827019\pi\)
−0.0198348 0.999803i \(-0.506314\pi\)
\(752\) 0 0
\(753\) −6.00000 + 10.3923i −0.218652 + 0.378717i
\(754\) 6.00000 + 10.3923i 0.218507 + 0.378465i
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 10.0000 + 17.3205i 0.363216 + 0.629109i
\(759\) −16.0000 + 27.7128i −0.580763 + 1.00591i
\(760\) −4.00000 + 6.92820i −0.145095 + 0.251312i
\(761\) 11.0000 + 19.0526i 0.398750 + 0.690655i 0.993572 0.113203i \(-0.0361109\pi\)
−0.594822 + 0.803857i \(0.702778\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.00000 + 3.46410i 0.0723102 + 0.125245i
\(766\) 8.00000 13.8564i 0.289052 0.500652i
\(767\) −12.0000 + 20.7846i −0.433295 + 0.750489i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 30.0000 1.08042
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) 1.00000 1.73205i 0.0359675 0.0622975i −0.847481 0.530825i \(-0.821882\pi\)
0.883449 + 0.468528i \(0.155215\pi\)
\(774\) 2.00000 3.46410i 0.0718885 0.124515i
\(775\) 0 0
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) −26.0000 −0.932145
\(779\) −12.0000 20.7846i −0.429945 0.744686i
\(780\) −6.00000 + 10.3923i −0.214834 + 0.372104i
\(781\) 16.0000 27.7128i 0.572525 0.991642i
\(782\) −8.00000 13.8564i −0.286079 0.495504i
\(783\) 2.00000 0.0714742
\(784\) 0 0
\(785\) 20.0000 0.713831
\(786\) −10.0000 17.3205i −0.356688 0.617802i
\(787\) 18.0000 31.1769i 0.641631 1.11134i