Properties

Label 1134.2.f.j.757.1
Level $1134$
Weight $2$
Character 1134.757
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
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 757.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.757
Dual form 1134.2.f.j.379.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(-3.00000 + 5.19615i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} -4.00000 q^{19} +(-1.00000 - 1.73205i) q^{20} +(2.00000 - 3.46410i) q^{22} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} -6.00000 q^{26} -1.00000 q^{28} +(-1.00000 - 1.73205i) q^{29} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{34} -2.00000 q^{35} -10.0000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(1.00000 - 1.73205i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +4.00000 q^{44} +8.00000 q^{46} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.00000 - 5.19615i) q^{52} -6.00000 q^{53} +8.00000 q^{55} +(-0.500000 - 0.866025i) q^{56} +(1.00000 - 1.73205i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-1.00000 - 1.73205i) q^{70} -8.00000 q^{71} +10.0000 q^{73} +(-5.00000 - 8.66025i) q^{74} +(2.00000 - 3.46410i) q^{76} +(2.00000 - 3.46410i) q^{77} +2.00000 q^{80} -6.00000 q^{82} +(-2.00000 - 3.46410i) q^{83} +(2.00000 - 3.46410i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(2.00000 + 3.46410i) q^{88} +6.00000 q^{89} -6.00000 q^{91} +(4.00000 + 6.92820i) q^{92} +(4.00000 - 6.92820i) q^{95} +(7.00000 + 12.1244i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - 2q^{5} + q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - 2q^{5} + q^{7} - 2q^{8} - 4q^{10} - 4q^{11} - 6q^{13} - q^{14} - q^{16} - 4q^{17} - 8q^{19} - 2q^{20} + 4q^{22} + 8q^{23} + q^{25} - 12q^{26} - 2q^{28} - 2q^{29} + q^{32} - 2q^{34} - 4q^{35} - 20q^{37} - 4q^{38} + 2q^{40} - 6q^{41} + 4q^{43} + 8q^{44} + 16q^{46} - q^{49} - q^{50} - 6q^{52} - 12q^{53} + 16q^{55} - q^{56} + 2q^{58} + 4q^{59} - 6q^{61} + 2q^{64} - 12q^{65} - 4q^{67} + 2q^{68} - 2q^{70} - 16q^{71} + 20q^{73} - 10q^{74} + 4q^{76} + 4q^{77} + 4q^{80} - 12q^{82} - 4q^{83} + 4q^{85} - 4q^{86} + 4q^{88} + 12q^{89} - 12q^{91} + 8q^{92} + 8q^{95} + 14q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −2.00000 −0.632456
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) −3.00000 + 5.19615i −0.832050 + 1.44115i 0.0643593 + 0.997927i \(0.479500\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −1.00000 1.73205i −0.223607 0.387298i
\(21\) 0 0
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i \(-0.519345\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −6.00000 −1.17670
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i \(-0.226120\pi\)
−0.943811 + 0.330487i \(0.892787\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.00000 1.73205i −0.171499 0.297044i
\(35\) −2.00000 −0.338062
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −2.00000 3.46410i −0.324443 0.561951i
\(39\) 0 0
\(40\) 1.00000 1.73205i 0.158114 0.273861i
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −3.00000 5.19615i −0.416025 0.720577i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 0 0
\(58\) 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 0
\(61\) −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
\(66\) 0 0
\(67\) −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
\(69\) 0 0
\(70\) −1.00000 1.73205i −0.119523 0.207020i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) −5.00000 8.66025i −0.581238 1.00673i
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) 2.00000 3.46410i 0.227921 0.394771i
\(78\) 0 0
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 2.00000 0.223607
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) −2.00000 3.46410i −0.219529 0.380235i 0.735135 0.677920i \(-0.237119\pi\)
−0.954664 + 0.297686i \(0.903785\pi\)
\(84\) 0 0
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) 2.00000 + 3.46410i 0.213201 + 0.369274i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 4.00000 + 6.92820i 0.417029 + 0.722315i
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 0 0
\(97\) 7.00000 + 12.1244i 0.710742 + 1.23104i 0.964579 + 0.263795i \(0.0849741\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 3.00000 5.19615i 0.294174 0.509525i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 4.00000 + 6.92820i 0.381385 + 0.660578i
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) −7.00000 + 12.1244i −0.658505 + 1.14056i 0.322498 + 0.946570i \(0.395477\pi\)
−0.981003 + 0.193993i \(0.937856\pi\)
\(114\) 0 0
\(115\) 8.00000 + 13.8564i 0.746004 + 1.29212i
\(116\) 2.00000 0.185695
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) −1.00000 1.73205i −0.0916698 0.158777i
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 3.00000 5.19615i 0.271607 0.470438i
\(123\) 0 0
\(124\) 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
\(129\) 0 0
\(130\) 6.00000 10.3923i 0.526235 0.911465i
\(131\) −10.0000 + 17.3205i −0.873704 + 1.51330i −0.0155672 + 0.999879i \(0.504955\pi\)
−0.858137 + 0.513421i \(0.828378\pi\)
\(132\) 0 0
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) 5.00000 + 8.66025i 0.427179 + 0.739895i 0.996621 0.0821359i \(-0.0261741\pi\)
−0.569442 + 0.822031i \(0.692841\pi\)
\(138\) 0 0
\(139\) −2.00000 + 3.46410i −0.169638 + 0.293821i −0.938293 0.345843i \(-0.887593\pi\)
0.768655 + 0.639664i \(0.220926\pi\)
\(140\) 1.00000 1.73205i 0.0845154 0.146385i
\(141\) 0 0
\(142\) −4.00000 6.92820i −0.335673 0.581402i
\(143\) 24.0000 2.00698
\(144\) 0 0
\(145\) 4.00000 0.332182
\(146\) 5.00000 + 8.66025i 0.413803 + 0.716728i
\(147\) 0 0
\(148\) 5.00000 8.66025i 0.410997 0.711868i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 4.00000 0.324443
\(153\) 0 0
\(154\) 4.00000 0.322329
\(155\) 0 0
\(156\) 0 0
\(157\) 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
\(159\) 0 0
\(160\) 1.00000 + 1.73205i 0.0790569 + 0.136931i
\(161\) 8.00000 0.630488
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) −4.00000 + 6.92820i −0.309529 + 0.536120i −0.978259 0.207385i \(-0.933505\pi\)
0.668730 + 0.743505i \(0.266838\pi\)
\(168\) 0 0
\(169\) −11.5000 19.9186i −0.884615 1.53220i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 11.0000 + 19.0526i 0.836315 + 1.44854i 0.892956 + 0.450145i \(0.148628\pi\)
−0.0566411 + 0.998395i \(0.518039\pi\)
\(174\) 0 0
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) −2.00000 + 3.46410i −0.150756 + 0.261116i
\(177\) 0 0
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) −3.00000 5.19615i −0.222375 0.385164i
\(183\) 0 0
\(184\) −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 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −7.00000 + 12.1244i −0.502571 + 0.870478i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) 1.00000 1.73205i 0.0703598 0.121867i
\(203\) 1.00000 1.73205i 0.0701862 0.121566i
\(204\) 0 0
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 6.00000 0.416025
\(209\) 8.00000 + 13.8564i 0.553372 + 0.958468i
\(210\) 0 0
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) 0 0
\(218\) −1.00000 1.73205i −0.0677285 0.117309i
\(219\) 0 0
\(220\) −4.00000 + 6.92820i −0.269680 + 0.467099i
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) 8.00000 + 13.8564i 0.535720 + 0.927894i 0.999128 + 0.0417488i \(0.0132929\pi\)
−0.463409 + 0.886145i \(0.653374\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −14.0000 −0.931266
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) 0 0
\(229\) 1.00000 1.73205i 0.0660819 0.114457i −0.831092 0.556136i \(-0.812283\pi\)
0.897173 + 0.441679i \(0.145617\pi\)
\(230\) −8.00000 + 13.8564i −0.527504 + 0.913664i
\(231\) 0 0
\(232\) 1.00000 + 1.73205i 0.0656532 + 0.113715i
\(233\) 22.0000 1.44127 0.720634 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) 0 0
\(238\) 1.00000 1.73205i 0.0648204 0.112272i
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i \(-0.187185\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) 6.00000 0.384111
\(245\) −1.00000 1.73205i −0.0638877 0.110657i
\(246\) 0 0
\(247\) 12.0000 20.7846i 0.763542 1.32249i
\(248\) 0 0
\(249\) 0 0
\(250\) −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
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −15.0000 + 25.9808i −0.935674 + 1.62064i −0.162247 + 0.986750i \(0.551874\pi\)
−0.773427 + 0.633885i \(0.781459\pi\)
\(258\) 0 0
\(259\) −5.00000 8.66025i −0.310685 0.538122i
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) −20.0000 −1.23560
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) 6.00000 10.3923i 0.368577 0.638394i
\(266\) 2.00000 3.46410i 0.122628 0.212398i
\(267\) 0 0
\(268\) −2.00000 3.46410i −0.122169 0.211604i
\(269\) −22.0000 −1.34136 −0.670682 0.741745i \(-0.733998\pi\)
−0.670682 + 0.741745i \(0.733998\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) −5.00000 + 8.66025i −0.302061 + 0.523185i
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) 2.00000 0.119523
\(281\) 13.0000 + 22.5167i 0.775515 + 1.34323i 0.934505 + 0.355951i \(0.115843\pi\)
−0.158990 + 0.987280i \(0.550824\pi\)
\(282\) 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
\(285\) 0 0
\(286\) 12.0000 + 20.7846i 0.709575 + 1.22902i
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 2.00000 + 3.46410i 0.117444 + 0.203419i
\(291\) 0 0
\(292\) −5.00000 + 8.66025i −0.292603 + 0.506803i
\(293\) 15.0000 25.9808i 0.876309 1.51781i 0.0209480 0.999781i \(-0.493332\pi\)
0.855361 0.518032i \(-0.173335\pi\)
\(294\) 0 0
\(295\) 4.00000 + 6.92820i 0.232889 + 0.403376i
\(296\) 10.0000 0.581238
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 24.0000 + 41.5692i 1.38796 + 2.40401i
\(300\) 0 0
\(301\) −2.00000 + 3.46410i −0.115278 + 0.199667i
\(302\) −4.00000 + 6.92820i −0.230174 + 0.398673i
\(303\) 0 0
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 12.0000 0.687118
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 2.00000 + 3.46410i 0.113961 + 0.197386i
\(309\) 0 0
\(310\) 0 0
\(311\) −4.00000 + 6.92820i −0.226819 + 0.392862i −0.956864 0.290537i \(-0.906166\pi\)
0.730044 + 0.683400i \(0.239499\pi\)
\(312\) 0 0
\(313\) −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 \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) 0 0
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) −1.00000 + 1.73205i −0.0559017 + 0.0968246i
\(321\) 0 0
\(322\) 4.00000 + 6.92820i 0.222911 + 0.386094i
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) −6.00000 −0.332820
\(326\) 10.0000 + 17.3205i 0.553849 + 0.959294i
\(327\) 0 0
\(328\) 3.00000 5.19615i 0.165647 0.286910i
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) 4.00000 0.219529
\(333\) 0 0
\(334\) −8.00000 −0.437741
\(335\) −4.00000 6.92820i −0.218543 0.378528i
\(336\) 0 0
\(337\) −9.00000 + 15.5885i −0.490261 + 0.849157i −0.999937 0.0112091i \(-0.996432\pi\)
0.509676 + 0.860366i \(0.329765\pi\)
\(338\) 11.5000 19.9186i 0.625518 1.08343i
\(339\) 0 0
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −2.00000 3.46410i −0.107833 0.186772i
\(345\) 0 0
\(346\) −11.0000 + 19.0526i −0.591364 + 1.02427i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) −11.0000 19.0526i −0.588817 1.01986i −0.994388 0.105797i \(-0.966261\pi\)
0.405571 0.914063i \(-0.367073\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 0 0
\(352\) −4.00000 −0.213201
\(353\) −15.0000 25.9808i −0.798369 1.38282i −0.920677 0.390324i \(-0.872363\pi\)
0.122308 0.992492i \(-0.460970\pi\)
\(354\) 0 0
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) −3.00000 + 5.19615i −0.159000 + 0.275396i
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −9.00000 15.5885i −0.473029 0.819311i
\(363\) 0 0
\(364\) 3.00000 5.19615i 0.157243 0.272352i
\(365\) −10.0000 + 17.3205i −0.523424 + 0.906597i
\(366\) 0 0
\(367\) −16.0000 27.7128i −0.835193 1.44660i −0.893873 0.448320i \(-0.852022\pi\)
0.0586798 0.998277i \(-0.481311\pi\)
\(368\) −8.00000 −0.417029
\(369\) 0 0
\(370\) 20.0000 1.03975
\(371\) −3.00000 5.19615i −0.155752 0.269771i
\(372\) 0 0
\(373\) −11.0000 + 19.0526i −0.569558 + 0.986504i 0.427051 + 0.904227i \(0.359552\pi\)
−0.996610 + 0.0822766i \(0.973781\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) 0 0
\(376\) 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 \(-0.967379\pi\)
0.585973 + 0.810331i \(0.300713\pi\)
\(384\) 0 0
\(385\) 4.00000 + 6.92820i 0.203859 + 0.353094i
\(386\) −2.00000 −0.101797
\(387\) 0 0
\(388\) −14.0000 −0.710742
\(389\) −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i \(-0.937593\pi\)
0.321716 0.946836i \(-0.395740\pi\)
\(390\) 0 0
\(391\) −8.00000 + 13.8564i −0.404577 + 0.700749i
\(392\) 0.500000 0.866025i 0.0252538 0.0437409i
\(393\) 0 0
\(394\) 5.00000 + 8.66025i 0.251896 + 0.436297i
\(395\) 0 0
\(396\) 0 0
\(397\) 6.00000 0.301131 0.150566 0.988600i \(-0.451890\pi\)
0.150566 + 0.988600i \(0.451890\pi\)
\(398\) 4.00000 + 6.92820i 0.200502 + 0.347279i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 2.00000 0.0995037
\(405\) 0 0
\(406\) 2.00000 0.0992583
\(407\) 20.0000 + 34.6410i 0.991363 + 1.71709i
\(408\) 0 0
\(409\) 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
\(411\) 0 0
\(412\) −4.00000 6.92820i −0.197066 0.341328i
\(413\) 4.00000 0.196827
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) 3.00000 + 5.19615i 0.147087 + 0.254762i
\(417\) 0 0
\(418\) −8.00000 + 13.8564i −0.391293 + 0.677739i
\(419\) −18.0000 + 31.1769i −0.879358 + 1.52309i −0.0273103 + 0.999627i \(0.508694\pi\)
−0.852047 + 0.523465i \(0.824639\pi\)
\(420\) 0 0
\(421\) −3.00000 5.19615i −0.146211 0.253245i 0.783613 0.621249i \(-0.213375\pi\)
−0.929824 + 0.368004i \(0.880041\pi\)
\(422\) −20.0000 −0.973585
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) −1.00000 1.73205i −0.0485071 0.0840168i
\(426\) 0 0
\(427\) 3.00000 5.19615i 0.145180 0.251459i
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 0 0
\(430\) −4.00000 6.92820i −0.192897 0.334108i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) −16.0000 + 27.7128i −0.765384 + 1.32568i
\(438\) 0 0
\(439\) 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 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 0 0
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) 24.0000 1.13012
\(452\) −7.00000 12.1244i −0.329252 0.570282i
\(453\) 0 0
\(454\) −6.00000 + 10.3923i −0.281594 + 0.487735i
\(455\) 6.00000 10.3923i 0.281284 0.487199i
\(456\) 0 0
\(457\) −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i \(-0.241812\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 2.00000 0.0934539
\(459\) 0 0
\(460\) −16.0000 −0.746004
\(461\) 11.0000 + 19.0526i 0.512321 + 0.887366i 0.999898 + 0.0142861i \(0.00454755\pi\)
−0.487577 + 0.873080i \(0.662119\pi\)
\(462\) 0 0
\(463\) 16.0000 27.7128i 0.743583 1.28792i −0.207271 0.978284i \(-0.566458\pi\)
0.950854 0.309640i \(-0.100209\pi\)
\(464\) −1.00000 + 1.73205i −0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) 11.0000 + 19.0526i 0.509565 + 0.882593i
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 0 0
\(471\) 0 0
\(472\) −2.00000 + 3.46410i −0.0920575 + 0.159448i
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) 0 0
\(475\) −2.00000 3.46410i −0.0917663 0.158944i
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) 0 0
\(479\) −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i \(-0.285779\pi\)
−0.988861 + 0.148842i \(0.952445\pi\)
\(480\) 0 0
\(481\) 30.0000 51.9615i 1.36788 2.36924i
\(482\) 1.00000 1.73205i 0.0455488 0.0788928i
\(483\) 0 0
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) −28.0000 −1.27141
\(486\) 0 0
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 3.00000 + 5.19615i 0.135804 + 0.235219i
\(489\) 0 0
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 0 0
\(493\) 2.00000 + 3.46410i 0.0900755 + 0.156015i
\(494\) 24.0000 1.07981
\(495\) 0 0
\(496\) 0 0
\(497\) −4.00000 6.92820i −0.179425 0.310772i
\(498\) 0 0
\(499\) 22.0000 38.1051i 0.984855 1.70582i 0.342277 0.939599i \(-0.388802\pi\)
0.642578 0.766220i \(-0.277865\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 0 0
\(502\) 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
\(507\) 0 0
\(508\) 0 0
\(509\) 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) 0 0
\(511\) 5.00000 + 8.66025i 0.221187 + 0.383107i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −30.0000 −1.32324
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 0 0
\(517\) 0 0
\(518\) 5.00000 8.66025i 0.219687 0.380510i
\(519\) 0 0
\(520\) 6.00000 + 10.3923i 0.263117 + 0.455733i
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −10.0000 17.3205i −0.436852 0.756650i
\(525\) 0 0
\(526\) 12.0000 20.7846i 0.523225 0.906252i
\(527\) 0 0
\(528\) 0 0
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) 12.0000 0.521247
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) −18.0000 31.1769i −0.779667 1.35042i
\(534\) 0 0
\(535\) 12.0000 20.7846i 0.518805 0.898597i
\(536\) 2.00000 3.46410i 0.0863868 0.149626i
\(537\) 0 0
\(538\) −11.0000 19.0526i −0.474244 0.821414i
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) 2.00000 3.46410i 0.0856706 0.148386i
\(546\) 0 0
\(547\) 6.00000 + 10.3923i 0.256541 + 0.444343i 0.965313 0.261095i \(-0.0840836\pi\)
−0.708772 + 0.705438i \(0.750750\pi\)
\(548\) −10.0000 −0.427179
\(549\) 0 0
\(550\) 4.00000 0.170561
\(551\) 4.00000 + 6.92820i 0.170406 + 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) −5.00000 + 8.66025i −0.212430 + 0.367939i
\(555\) 0 0
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 1.00000 + 1.73205i 0.0422577 + 0.0731925i
\(561\) 0 0
\(562\) −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 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) −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
\(574\) −3.00000 5.19615i −0.125218 0.216883i
\(575\) 8.00000 0.333623
\(576\) 0 0
\(577\) 34.0000 1.41544 0.707719 0.706494i \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) 0 0
\(580\) −2.00000 + 3.46410i −0.0830455 + 0.143839i
\(581\) 2.00000 3.46410i 0.0829740 0.143715i
\(582\) 0 0
\(583\) 12.0000 + 20.7846i 0.496989 + 0.860811i
\(584\) −10.0000 −0.413803
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) −14.0000 24.2487i −0.577842 1.00085i −0.995726 0.0923513i \(-0.970562\pi\)
0.417885 0.908500i \(-0.362772\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −4.00000 + 6.92820i −0.164677 + 0.285230i
\(591\) 0 0
\(592\) 5.00000 + 8.66025i 0.205499 + 0.355934i
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 0 0
\(598\) −24.0000 + 41.5692i −0.981433 + 1.69989i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) −13.0000 22.5167i −0.530281 0.918474i −0.999376 0.0353259i \(-0.988753\pi\)
0.469095 0.883148i \(-0.344580\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) −8.00000 −0.325515
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 0 0
\(607\) −24.0000 + 41.5692i −0.974130 + 1.68724i −0.291353 + 0.956616i \(0.594105\pi\)
−0.682777 + 0.730627i \(0.739228\pi\)
\(608\) −2.00000 + 3.46410i −0.0811107 + 0.140488i
\(609\) 0 0
\(610\) 6.00000 + 10.3923i 0.242933 + 0.420772i
\(611\) 0 0
\(612\) 0 0
\(613\) −42.0000 −1.69636 −0.848182 0.529705i \(-0.822303\pi\)
−0.848182 + 0.529705i \(0.822303\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) −2.00000 + 3.46410i −0.0805823 + 0.139573i
\(617\) −11.0000 + 19.0526i −0.442843 + 0.767027i −0.997899 0.0647859i \(-0.979364\pi\)
0.555056 + 0.831813i \(0.312697\pi\)
\(618\) 0 0
\(619\) 22.0000 + 38.1051i 0.884255 + 1.53157i 0.846566 + 0.532284i \(0.178666\pi\)
0.0376891 + 0.999290i \(0.488000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −8.00000 −0.320771
\(623\) 3.00000 + 5.19615i 0.120192 + 0.208179i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 5.00000 8.66025i 0.199840 0.346133i
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 0 0
\(636\) 0 0
\(637\) −3.00000 5.19615i −0.118864 0.205879i
\(638\) −8.00000 −0.316723
\(639\) 0 0
\(640\) −2.00000 −0.0790569
\(641\) 1.00000 + 1.73205i 0.0394976 + 0.0684119i 0.885098 0.465404i \(-0.154091\pi\)
−0.845601 + 0.533816i \(0.820758\pi\)
\(642\) 0 0
\(643\) 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i \(-0.808201\pi\)
0.902764 + 0.430137i \(0.141535\pi\)
\(644\) −4.00000 + 6.92820i −0.157622 + 0.273009i
\(645\) 0 0
\(646\) 4.00000 + 6.92820i 0.157378 + 0.272587i
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 0 0
\(649\) −16.0000 −0.628055
\(650\) −3.00000 5.19615i −0.117670 0.203810i
\(651\) 0 0
\(652\) −10.0000 + 17.3205i −0.391630 + 0.678323i
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 0 0
\(655\) −20.0000 34.6410i −0.781465 1.35354i
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 0 0
\(659\) −14.0000 24.2487i −0.545363 0.944596i −0.998584 0.0531977i \(-0.983059\pi\)
0.453221 0.891398i \(-0.350275\pi\)
\(660\) 0 0
\(661\) 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
\(663\) 0 0
\(664\) 2.00000 + 3.46410i 0.0776151 + 0.134433i
\(665\) 8.00000 0.310227
\(666\) 0 0
\(667\) −16.0000 −0.619522
\(668\) −4.00000 6.92820i −0.154765 0.268060i
\(669\) 0 0
\(670\) 4.00000 6.92820i 0.154533 0.267660i
\(671\) −12.0000 + 20.7846i −0.463255 + 0.802381i
\(672\) 0 0
\(673\) −1.00000 1.73205i −0.0385472 0.0667657i 0.846108 0.533011i \(-0.178940\pi\)
−0.884655 + 0.466246i \(0.845606\pi\)
\(674\) −18.0000 −0.693334
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) −9.00000 15.5885i −0.345898 0.599113i 0.639618 0.768693i \(-0.279092\pi\)
−0.985517 + 0.169580i \(0.945759\pi\)
\(678\) 0 0
\(679\) −7.00000 + 12.1244i −0.268635 + 0.465290i
\(680\) −2.00000 + 3.46410i −0.0766965 + 0.132842i
\(681\) 0 0
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) −20.0000 −0.764161
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 18.0000 31.1769i 0.685745 1.18775i
\(690\) 0 0
\(691\) 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
\(696\) 0 0
\(697\) 6.00000 10.3923i 0.227266 0.393637i
\(698\) 11.0000 19.0526i 0.416356 0.721150i
\(699\) 0 0
\(700\) −0.500000 0.866025i −0.0188982 0.0327327i
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) 40.0000 1.50863
\(704\) −2.00000 3.46410i −0.0753778 0.130558i
\(705\) 0 0
\(706\) 15.0000 25.9808i 0.564532 0.977799i
\(707\) 1.00000 1.73205i 0.0376089 0.0651405i
\(708\) 0 0
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 16.0000 0.600469
\(711\) 0 0
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) −24.0000 + 41.5692i −0.897549 + 1.55460i
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 0 0
\(718\) 4.00000 + 6.92820i 0.149279 + 0.258558i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) −1.50000 2.59808i −0.0558242 0.0966904i
\(723\) 0 0
\(724\) 9.00000 15.5885i 0.334482 0.579340i
\(725\) 1.00000 1.73205i 0.0371391 0.0643268i
\(726\) 0 0
\(727\) 4.00000 + 6.92820i 0.148352 + 0.256953i 0.930618 0.365991i \(-0.119270\pi\)
−0.782267 + 0.622944i \(0.785937\pi\)
\(728\) 6.00000 0.222375
\(729\) 0 0
\(730\) −20.0000 −0.740233
\(731\) −4.00000 6.92820i −0.147945 0.256249i
\(732\) 0 0
\(733\) −3.00000 + 5.19615i −0.110808 + 0.191924i −0.916096 0.400959i \(-0.868677\pi\)
0.805289 + 0.592883i \(0.202010\pi\)
\(734\) 16.0000 27.7128i 0.590571 1.02290i
\(735\) 0 0
\(736\) −4.00000 6.92820i −0.147442 0.255377i
\(737\) 16.0000 0.589368
\(738\) 0 0
\(739\) −12.0000 −0.441427 −0.220714 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 10.0000 + 17.3205i 0.367607 + 0.636715i
\(741\) 0 0
\(742\) 3.00000 5.19615i 0.110133 0.190757i
\(743\) 12.0000 20.7846i 0.440237 0.762513i −0.557470 0.830197i \(-0.688228\pi\)
0.997707 + 0.0676840i \(0.0215610\pi\)
\(744\) 0 0
\(745\) 6.00000 + 10.3923i 0.219823 + 0.380745i
\(746\) −22.0000 −0.805477
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) −6.00000 10.3923i −0.219235 0.379727i
\(750\) 0 0
\(751\) −24.0000 + 41.5692i −0.875772 + 1.51688i −0.0198348 + 0.999803i \(0.506314\pi\)
−0.855938 + 0.517079i \(0.827019\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 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
\(759\) 0 0
\(760\) −4.00000 + 6.92820i −0.145095 + 0.251312i
\(761\) −11.0000 + 19.0526i −0.398750 + 0.690655i −0.993572 0.113203i \(-0.963889\pi\)
0.594822 + 0.803857i \(0.297222\pi\)
\(762\) 0 0
\(763\) −1.00000 1.73205i −0.0362024 0.0627044i
\(764\) 0 0
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 0 0
\(769\) 7.00000 12.1244i 0.252426 0.437215i −0.711767 0.702416i \(-0.752105\pi\)
0.964193 + 0.265200i \(0.0854381\pi\)
\(770\) −4.00000 + 6.92820i −0.144150 + 0.249675i
\(771\) 0 0
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) 2.00000 0.0719350 0.0359675 0.999353i \(-0.488549\pi\)
0.0359675 + 0.999353i \(0.488549\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −7.00000 12.1244i −0.251285 0.435239i
\(777\) 0 0
\(778\) 13.0000 22.5167i 0.466073 0.807261i
\(779\) 12.0000 20.7846i 0.429945 0.744686i
\(780\) 0 0
\(781\) 16.0000 + 27.7128i 0.572525 + 0.991642i
\(782\) −16.0000 −0.572159
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 10.0000 + 17.3205i 0.356915 + 0.618195i
\(786\) 0 0
\(787\) 18.0000 31.1769i 0.641631 1.11134i −0.343438 0.939175i \(-0.611592\pi\)
0.985069 0.172162i \(-0.0550751\pi\)
\(788\) −5.00000 + 8.66025i −0.178118 + 0.308509i
\(789\) 0 0
\(790\) 0 0
\(791\) −14.0000 −0.497783
\(792\) 0 0
\(793\) 36.0000 1.27840