Properties

Label 1134.2.f.g.379.1
Level $1134$
Weight $2$
Character 1134.379
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 379.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.379
Dual form 1134.2.f.g.757.1

$q$-expansion

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

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(4\) −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 \(0.685750\pi\)
\(6\) 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 −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) 0 0
\(13\) −3.00000 5.19615i −0.832050 1.44115i −0.896410 0.443227i \(-0.853834\pi\)
0.0643593 0.997927i \(-0.479500\pi\)
\(14\) 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 \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 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 −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) 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 \(-0.773880\pi\)
0.943811 + 0.330487i \(0.107213\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) −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 \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 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 \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 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 \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) 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 0.717607 0.696449i \(-0.245238\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) −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 \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) −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 \(-0.762881\pi\)
0.954664 + 0.297686i \(0.0962148\pi\)
\(84\) 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 \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 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 −0.253837 0.967247i \(-0.581693\pi\)
0.964579 0.263795i \(-0.0849741\pi\)
\(98\) 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 \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) −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 \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 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 0.981003 + 0.193993i \(0.0621440\pi\)
−0.322498 + 0.946570i \(0.604523\pi\)
\(114\) 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 0.858137 + 0.513421i \(0.171622\pi\)
0.0155672 + 0.999879i \(0.495045\pi\)
\(132\) 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 \(-0.973826\pi\)
0.569442 + 0.822031i \(0.307159\pi\)
\(138\) 0 0
\(139\) −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i \(-0.220926\pi\)
−0.938293 + 0.345843i \(0.887593\pi\)
\(140\) −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 \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −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 0.993608 0.112884i \(-0.0360089\pi\)
−0.594565 + 0.804048i \(0.702676\pi\)
\(158\) 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 \(-0.0664952\pi\)
−0.668730 + 0.743505i \(0.733162\pi\)
\(168\) 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 0.0566411 + 0.998395i \(0.481961\pi\)
−0.892956 + 0.450145i \(0.851372\pi\)
\(174\) 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 \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 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 \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 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 −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) −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 −0.463409 0.886145i \(-0.653374\pi\)
0.999128 0.0417488i \(-0.0132929\pi\)
\(224\) −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 \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 0 0
\(229\) 1.00000 + 1.73205i 0.0660819 + 0.114457i 0.897173 0.441679i \(-0.145617\pi\)
−0.831092 + 0.556136i \(0.812283\pi\)
\(230\) 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 \(-0.756149\pi\)
−0.720634 + 0.693316i \(0.756149\pi\)
\(234\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) −1.00000 + 1.73205i −0.0644157 + 0.111571i −0.896435 0.443176i \(-0.853852\pi\)
0.832019 + 0.554747i \(0.187185\pi\)
\(242\) 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 \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 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 0.773427 + 0.633885i \(0.218541\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(258\) 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 −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) 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 \(-0.266002\pi\)
0.670682 + 0.741745i \(0.266002\pi\)
\(270\) 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 −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) 2.00000 0.119523
\(281\) −13.0000 + 22.5167i −0.775515 + 1.34323i 0.158990 + 0.987280i \(0.449176\pi\)
−0.934505 + 0.355951i \(0.884157\pi\)
\(282\) 0 0
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) −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 −0.855361 0.518032i \(-0.826665\pi\)
−0.0209480 0.999781i \(-0.506668\pi\)
\(294\) 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 \(-0.0938340\pi\)
−0.730044 + 0.683400i \(0.760501\pi\)
\(312\) 0 0
\(313\) −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i \(-0.924536\pi\)
0.689412 + 0.724370i \(0.257869\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) 0 0
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 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 −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −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 0.509676 0.860366i \(-0.329765\pi\)
−0.999937 + 0.0112091i \(0.996432\pi\)
\(338\) −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 \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) −11.0000 + 19.0526i −0.588817 + 1.01986i 0.405571 + 0.914063i \(0.367073\pi\)
−0.994388 + 0.105797i \(0.966261\pi\)
\(350\) 1.00000 0.0534522
\(351\) 0 0
\(352\) −4.00000 −0.213201
\(353\) 15.0000 25.9808i 0.798369 1.38282i −0.122308 0.992492i \(-0.539030\pi\)
0.920677 0.390324i \(-0.127637\pi\)
\(354\) 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 \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 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 0.0586798 + 0.998277i \(0.481311\pi\)
−0.893873 + 0.448320i \(0.852022\pi\)
\(368\) 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 −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) 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 \(-0.0326207\pi\)
−0.585973 + 0.810331i \(0.699287\pi\)
\(384\) 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 −0.321716 0.946836i \(-0.604260\pi\)
0.980842 0.194804i \(-0.0624070\pi\)
\(390\) 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 \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 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 0.998674 + 0.0514740i \(0.0163919\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(410\) −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 0.852047 + 0.523465i \(0.175361\pi\)
0.0273103 + 0.999627i \(0.491306\pi\)
\(420\) 0 0
\(421\) −3.00000 + 5.19615i −0.146211 + 0.253245i −0.929824 0.368004i \(-0.880041\pi\)
0.783613 + 0.621249i \(0.213375\pi\)
\(422\) 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 −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 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 \(-0.803041\pi\)
0.909618 + 0.415445i \(0.136374\pi\)
\(444\) 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 \(-0.203620\pi\)
0.802280 + 0.596948i \(0.203620\pi\)
\(450\) 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 −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) −2.00000 −0.0934539
\(459\) 0 0
\(460\) −16.0000 −0.746004
\(461\) −11.0000 + 19.0526i −0.512321 + 0.887366i 0.487577 + 0.873080i \(0.337881\pi\)
−0.999898 + 0.0142861i \(0.995452\pi\)
\(462\) 0 0
\(463\) 16.0000 + 27.7128i 0.743583 + 1.28792i 0.950854 + 0.309640i \(0.100209\pi\)
−0.207271 + 0.978284i \(0.566458\pi\)
\(464\) 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 \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 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 \(-0.714221\pi\)
0.988861 + 0.148842i \(0.0475547\pi\)
\(480\) 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 \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) 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 0.642578 + 0.766220i \(0.277865\pi\)
0.342277 + 0.939599i \(0.388802\pi\)
\(500\) −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 \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) 16.0000 27.7128i 0.711287 1.23198i
\(507\) 0 0
\(508\) 0 0
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 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 \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 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 −0.708772 0.705438i \(-0.750750\pi\)
0.965313 + 0.261095i \(0.0840836\pi\)
\(548\) 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 \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) 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 −0.788002 0.615673i \(-0.788884\pi\)
−0.139188 0.990266i \(-0.544449\pi\)
\(564\) 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 \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) −6.00000 10.3923i −0.251092 0.434904i 0.712735 0.701434i \(-0.247456\pi\)
−0.963827 + 0.266529i \(0.914123\pi\)
\(572\) 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 −0.417885 0.908500i \(-0.637228\pi\)
0.995726 0.0923513i \(-0.0294383\pi\)
\(588\) 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 \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 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 \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) 0 0
\(601\) −13.0000 + 22.5167i −0.530281 + 0.918474i 0.469095 + 0.883148i \(0.344580\pi\)
−0.999376 + 0.0353259i \(0.988753\pi\)
\(602\) 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 −0.682777 0.730627i \(-0.739228\pi\)
−0.291353 0.956616i \(-0.594105\pi\)
\(608\) 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 \(-0.0206365\pi\)
−0.555056 + 0.831813i \(0.687303\pi\)
\(618\) 0 0
\(619\) 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
\(621\) 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 \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 0 0
\(643\) 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i \(-0.141535\pi\)
−0.823891 + 0.566748i \(0.808201\pi\)
\(644\) 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 \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 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 \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) 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 −0.453221 0.891398i \(-0.649725\pi\)
0.998584 0.0531977i \(-0.0169414\pi\)
\(660\) 0 0
\(661\) 1.00000 + 1.73205i 0.0388955 + 0.0673690i 0.884818 0.465937i \(-0.154283\pi\)
−0.845922 + 0.533306i \(0.820949\pi\)
\(662\) 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 −0.884655 0.466246i \(-0.845606\pi\)
0.846108 + 0.533011i \(0.178940\pi\)
\(674\) 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 \(-0.720908\pi\)
0.985517 + 0.169580i \(0.0542410\pi\)
\(678\) 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 \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 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 −0.825473 0.564441i \(-0.809092\pi\)
0.901557 + 0.432660i \(0.142425\pi\)
\(692\) 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 \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 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 −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) −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 −0.782267 0.622944i \(-0.785937\pi\)
0.930618 + 0.365991i \(0.119270\pi\)
\(728\) −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 0.805289 0.592883i \(-0.202010\pi\)
−0.916096 + 0.400959i \(0.868677\pi\)
\(734\) −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 \(-0.311772\pi\)
−0.997707 + 0.0676840i \(0.978439\pi\)
\(744\) 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 −0.855938 0.517079i \(-0.827019\pi\)
−0.0198348 0.999803i \(-0.506314\pi\)
\(752\) 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 \(-0.0361109\pi\)
−0.594822 + 0.803857i \(0.702778\pi\)
\(762\) 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 0.964193 0.265200i \(-0.0854381\pi\)
−0.711767 + 0.702416i \(0.752105\pi\)
\(770\) 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 \(-0.511451\pi\)
−0.0359675 + 0.999353i \(0.511451\pi\)
\(774\) 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 0.985069 + 0.172162i \(0.0550751\pi\)
−0.343438 + 0.939175i \(0.611592\pi\)
\(788\) 5.00000 + 8.66025i 0.178118 + 0.308509i
\(789\) 0 0
\(790\) 0 0
\(791\) 14.0000 0.497783
\(792\) 0 0
\(793\)