Properties

Label 294.2.e.a.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.a.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 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 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 \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 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 −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) −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 \(0.985065\pi\)
\(20\) 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 \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 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 −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) −1.00000 + 1.73205i −0.129099 + 0.223607i
\(61\) 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) 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 \(-0.634347\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) 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 \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 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 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 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 \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 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 −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 1.00000 1.73205i 0.0990148 0.171499i
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) −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 \(-0.828378\pi\)
−0.0155672 0.999879i \(-0.504955\pi\)
\(132\) −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 \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 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 −0.993608 0.112884i \(-0.963991\pi\)
0.594565 + 0.804048i \(0.297324\pi\)
\(158\) 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 \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 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 \(0.148628\pi\)
−0.0566411 + 0.998395i \(0.518039\pi\)
\(174\) −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 \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 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 −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) 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 \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 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 −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) −2.00000 + 3.46410i −0.132453 + 0.229416i
\(229\) −1.00000 1.73205i −0.0660819 0.114457i 0.831092 0.556136i \(-0.187717\pi\)
−0.897173 + 0.441679i \(0.854383\pi\)
\(230\) 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 −0.832019 0.554747i \(-0.812815\pi\)
0.896435 + 0.443176i \(0.146148\pi\)
\(242\) −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 \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 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 \(-0.781459\pi\)
−0.162247 0.986750i \(-0.551874\pi\)
\(258\) −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 \(-0.599335\pi\)
0.977711 0.209955i \(-0.0673317\pi\)
\(270\) −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 −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −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 \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 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 \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) −4.00000 + 6.92820i −0.226819 + 0.392862i −0.956864 0.290537i \(-0.906166\pi\)
0.730044 + 0.683400i \(0.239499\pi\)
\(312\) 3.00000 5.19615i 0.169842 0.294174i
\(313\) 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) 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 \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 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 \(0.460970\pi\)
−0.920677 + 0.390324i \(0.872363\pi\)
\(354\) 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 \(-0.518689\pi\)
0.893873 0.448320i \(-0.147978\pi\)
\(368\) −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 0.585973 0.810331i \(-0.300713\pi\)
−0.994753 + 0.102302i \(0.967379\pi\)
\(384\) 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 0.931436 0.363906i \(-0.118557\pi\)
−0.780870 + 0.624694i \(0.785224\pi\)
\(398\) −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 \(0.349725\pi\)
−0.998674 + 0.0514740i \(0.983608\pi\)
\(410\) −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 \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) 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 \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 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 \(-0.972552\pi\)
0.423556 0.905870i \(-0.360782\pi\)
\(440\) −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 \(-0.671214\pi\)
−0.512321 + 0.858794i \(0.671214\pi\)
\(462\) 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 \(0.0576619\pi\)
−0.335794 + 0.941935i \(0.609005\pi\)
\(468\) −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 −0.988861 0.148842i \(-0.952445\pi\)
0.623332 + 0.781958i \(0.285779\pi\)
\(480\) −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 \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 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 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) −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 −0.924229 0.381839i \(-0.875291\pi\)
0.792797 + 0.609486i \(0.208624\pi\)
\(522\) 1.00000 1.73205i 0.0437688 0.0758098i
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) 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 \(-0.455551\pi\)
0.788002 0.615673i \(-0.211116\pi\)
\(564\) 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 \(-0.583058\pi\)
0.965701 0.259656i \(-0.0836092\pi\)
\(578\) 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 \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 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 0.989501 0.144528i \(-0.0461663\pi\)
−0.619915 + 0.784669i \(0.712833\pi\)
\(594\) −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 \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 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 \(0.260772\pi\)
0.291353 + 0.956616i \(0.405895\pi\)
\(608\) 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 \(0.512000\pi\)
−0.846566 + 0.532284i \(0.821334\pi\)
\(620\) 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 \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 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 −0.527710 0.849425i \(-0.676949\pi\)
0.999478 + 0.0322975i \(0.0102824\pi\)
\(648\) −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 −0.884818 0.465937i \(-0.845717\pi\)
0.845922 + 0.533306i \(0.179051\pi\)
\(662\) 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 0.639618 0.768693i \(-0.279092\pi\)
−0.985517 + 0.169580i \(0.945759\pi\)
\(678\) −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 0.825473 0.564441i \(-0.190908\pi\)
−0.901557 + 0.432660i \(0.857575\pi\)
\(692\) −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 \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 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 0.916096 0.400959i \(-0.131323\pi\)
−0.805289 + 0.592883i \(0.797990\pi\)
\(734\) −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 0.594822 0.803857i \(-0.297222\pi\)
−0.993572 + 0.113203i \(0.963889\pi\)
\(762\) 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 \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 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 −0.883449 0.468528i \(-0.844785\pi\)
0.847481 + 0.530825i \(0.178118\pi\)
\(774\) 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