Properties

Label 1014.2.e.a.529.1
Level $1014$
Weight $2$
Character 1014.529
Analytic conductor $8.097$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1014.529
Dual form 1014.2.e.a.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(3.00000 - 5.19615i) q^{11} +1.00000 q^{12} -2.00000 q^{14} +(1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(1.00000 + 1.73205i) q^{19} +(1.50000 + 2.59808i) q^{20} -2.00000 q^{21} +(3.00000 + 5.19615i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{24} +4.00000 q^{25} +1.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(1.50000 + 2.59808i) q^{30} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} -3.00000 q^{34} +(-3.00000 - 5.19615i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.50000 + 6.06218i) q^{37} -2.00000 q^{38} -3.00000 q^{40} +(-1.50000 + 2.59808i) q^{41} +(1.00000 - 1.73205i) q^{42} +(5.00000 + 8.66025i) q^{43} -6.00000 q^{44} +(1.50000 + 2.59808i) q^{45} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} -3.00000 q^{51} +3.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-9.00000 + 15.5885i) q^{55} +(1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} -3.00000 q^{60} +(3.50000 + 6.06218i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(-5.00000 + 8.66025i) q^{67} +(1.50000 - 2.59808i) q^{68} +(3.00000 + 5.19615i) q^{69} +6.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} +13.0000 q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(1.00000 - 1.73205i) q^{76} +12.0000 q^{77} -4.00000 q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.50000 - 2.59808i) q^{82} +6.00000 q^{83} +(1.00000 + 1.73205i) q^{84} +(-4.50000 - 7.79423i) q^{85} -10.0000 q^{86} +(-1.50000 - 2.59808i) q^{87} +(3.00000 - 5.19615i) q^{88} +(9.00000 - 15.5885i) q^{89} -3.00000 q^{90} -6.00000 q^{92} +(-2.00000 + 3.46410i) q^{93} +(3.00000 - 5.19615i) q^{94} +(-3.00000 - 5.19615i) q^{95} +1.00000 q^{96} +(7.00000 + 12.1244i) q^{97} +(1.50000 + 2.59808i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} - 6 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} - 6 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - q^{9} + 3 q^{10} + 6 q^{11} + 2 q^{12} - 4 q^{14} + 3 q^{15} - q^{16} + 3 q^{17} + 2 q^{18} + 2 q^{19} + 3 q^{20} - 4 q^{21} + 6 q^{22} + 6 q^{23} - q^{24} + 8 q^{25} + 2 q^{27} + 2 q^{28} - 3 q^{29} + 3 q^{30} + 8 q^{31} - q^{32} + 6 q^{33} - 6 q^{34} - 6 q^{35} - q^{36} - 7 q^{37} - 4 q^{38} - 6 q^{40} - 3 q^{41} + 2 q^{42} + 10 q^{43} - 12 q^{44} + 3 q^{45} + 6 q^{46} - 12 q^{47} - q^{48} + 3 q^{49} - 4 q^{50} - 6 q^{51} + 6 q^{53} - q^{54} - 18 q^{55} + 2 q^{56} - 4 q^{57} - 3 q^{58} - 6 q^{60} + 7 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} - 12 q^{66} - 10 q^{67} + 3 q^{68} + 6 q^{69} + 12 q^{70} + 6 q^{71} - q^{72} + 26 q^{73} - 7 q^{74} - 4 q^{75} + 2 q^{76} + 24 q^{77} - 8 q^{79} + 3 q^{80} - q^{81} - 3 q^{82} + 12 q^{83} + 2 q^{84} - 9 q^{85} - 20 q^{86} - 3 q^{87} + 6 q^{88} + 18 q^{89} - 6 q^{90} - 12 q^{92} - 4 q^{93} + 6 q^{94} - 6 q^{95} + 2 q^{96} + 14 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) −2.00000 −0.534522
\(15\) 1.50000 2.59808i 0.387298 0.670820i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 1.50000 + 2.59808i 0.335410 + 0.580948i
\(21\) −2.00000 −0.436436
\(22\) 3.00000 + 5.19615i 0.639602 + 1.10782i
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 1.00000 1.73205i 0.188982 0.327327i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) −3.00000 −0.514496
\(35\) −3.00000 5.19615i −0.507093 0.878310i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) −2.00000 −0.324443
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) 1.00000 1.73205i 0.154303 0.267261i
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) −6.00000 −0.904534
\(45\) 1.50000 + 2.59808i 0.223607 + 0.387298i
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −9.00000 + 15.5885i −1.21356 + 2.10195i
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) −2.00000 −0.264906
\(58\) −1.50000 2.59808i −0.196960 0.341144i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) −3.00000 −0.387298
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) −2.00000 + 3.46410i −0.254000 + 0.439941i
\(63\) 1.00000 1.73205i 0.125988 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.00000 −0.738549
\(67\) −5.00000 + 8.66025i −0.610847 + 1.05802i 0.380251 + 0.924883i \(0.375838\pi\)
−0.991098 + 0.133135i \(0.957496\pi\)
\(68\) 1.50000 2.59808i 0.181902 0.315063i
\(69\) 3.00000 + 5.19615i 0.361158 + 0.625543i
\(70\) 6.00000 0.717137
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 13.0000 1.52153 0.760767 0.649025i \(-0.224823\pi\)
0.760767 + 0.649025i \(0.224823\pi\)
\(74\) −3.50000 6.06218i −0.406867 0.704714i
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) 1.00000 1.73205i 0.114708 0.198680i
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.50000 2.59808i 0.167705 0.290474i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 1.00000 + 1.73205i 0.109109 + 0.188982i
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) −10.0000 −1.07833
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) 9.00000 15.5885i 0.953998 1.65237i 0.217354 0.976093i \(-0.430258\pi\)
0.736644 0.676280i \(-0.236409\pi\)
\(90\) −3.00000 −0.316228
\(91\) 0 0
\(92\) −6.00000 −0.625543
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 1.00000 0.102062
\(97\) 7.00000 + 12.1244i 0.710742 + 1.23104i 0.964579 + 0.263795i \(0.0849741\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) −6.00000 −0.603023
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −7.50000 + 12.9904i −0.746278 + 1.29259i 0.203317 + 0.979113i \(0.434828\pi\)
−0.949595 + 0.313478i \(0.898506\pi\)
\(102\) 1.50000 2.59808i 0.148522 0.257248i
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) 6.00000 0.585540
\(106\) −1.50000 + 2.59808i −0.145693 + 0.252347i
\(107\) 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i \(-0.739671\pi\)
0.973814 + 0.227345i \(0.0730044\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) −9.00000 15.5885i −0.858116 1.48630i
\(111\) −3.50000 6.06218i −0.332205 0.575396i
\(112\) −2.00000 −0.188982
\(113\) 1.50000 + 2.59808i 0.141108 + 0.244406i 0.927914 0.372794i \(-0.121600\pi\)
−0.786806 + 0.617200i \(0.788267\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) −9.00000 + 15.5885i −0.839254 + 1.45363i
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) 0 0
\(119\) −3.00000 + 5.19615i −0.275010 + 0.476331i
\(120\) 1.50000 2.59808i 0.136931 0.237171i
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) −7.00000 −0.633750
\(123\) −1.50000 2.59808i −0.135250 0.234261i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 3.00000 0.268328
\(126\) 1.00000 + 1.73205i 0.0890871 + 0.154303i
\(127\) 2.00000 3.46410i 0.177471 0.307389i −0.763542 0.645758i \(-0.776542\pi\)
0.941014 + 0.338368i \(0.109875\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −10.0000 −0.880451
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 3.00000 5.19615i 0.261116 0.452267i
\(133\) −2.00000 + 3.46410i −0.173422 + 0.300376i
\(134\) −5.00000 8.66025i −0.431934 0.748132i
\(135\) −3.00000 −0.258199
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) −6.00000 −0.510754
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) −3.00000 + 5.19615i −0.253546 + 0.439155i
\(141\) 3.00000 5.19615i 0.252646 0.437595i
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 4.50000 7.79423i 0.373705 0.647275i
\(146\) −6.50000 + 11.2583i −0.537944 + 0.931746i
\(147\) 1.50000 + 2.59808i 0.123718 + 0.214286i
\(148\) 7.00000 0.575396
\(149\) −4.50000 7.79423i −0.368654 0.638528i 0.620701 0.784047i \(-0.286848\pi\)
−0.989355 + 0.145519i \(0.953515\pi\)
\(150\) −2.00000 3.46410i −0.163299 0.282843i
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) 1.50000 2.59808i 0.121268 0.210042i
\(154\) −6.00000 + 10.3923i −0.483494 + 0.837436i
\(155\) −12.0000 −0.963863
\(156\) 0 0
\(157\) 5.00000 0.399043 0.199522 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) 2.00000 3.46410i 0.159111 0.275589i
\(159\) −1.50000 + 2.59808i −0.118958 + 0.206041i
\(160\) 1.50000 + 2.59808i 0.118585 + 0.205396i
\(161\) 12.0000 0.945732
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) 3.00000 0.234261
\(165\) −9.00000 15.5885i −0.700649 1.21356i
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) −2.00000 −0.154303
\(169\) 0 0
\(170\) 9.00000 0.690268
\(171\) 1.00000 1.73205i 0.0764719 0.132453i
\(172\) 5.00000 8.66025i 0.381246 0.660338i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 3.00000 0.227429
\(175\) 4.00000 + 6.92820i 0.302372 + 0.523723i
\(176\) 3.00000 + 5.19615i 0.226134 + 0.391675i
\(177\) 0 0
\(178\) 9.00000 + 15.5885i 0.674579 + 1.16840i
\(179\) −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i \(-0.905320\pi\)
0.731858 + 0.681457i \(0.238654\pi\)
\(180\) 1.50000 2.59808i 0.111803 0.193649i
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) −7.00000 −0.517455
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) 10.5000 18.1865i 0.771975 1.33710i
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 18.0000 1.31629
\(188\) 3.00000 + 5.19615i 0.218797 + 0.378968i
\(189\) 1.00000 + 1.73205i 0.0727393 + 0.125988i
\(190\) 6.00000 0.435286
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 11.5000 19.9186i 0.827788 1.43377i −0.0719816 0.997406i \(-0.522932\pi\)
0.899770 0.436365i \(-0.143734\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 3.00000 5.19615i 0.213741 0.370211i −0.739141 0.673550i \(-0.764768\pi\)
0.952882 + 0.303340i \(0.0981018\pi\)
\(198\) 3.00000 5.19615i 0.213201 0.369274i
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) 4.00000 0.282843
\(201\) −5.00000 8.66025i −0.352673 0.610847i
\(202\) −7.50000 12.9904i −0.527698 0.914000i
\(203\) −6.00000 −0.421117
\(204\) 1.50000 + 2.59808i 0.105021 + 0.181902i
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) −7.00000 + 12.1244i −0.487713 + 0.844744i
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) −3.00000 + 5.19615i −0.207020 + 0.358569i
\(211\) 8.00000 13.8564i 0.550743 0.953914i −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) −6.00000 −0.411113
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) −15.0000 25.9808i −1.02299 1.77187i
\(216\) 1.00000 0.0680414
\(217\) 4.00000 + 6.92820i 0.271538 + 0.470317i
\(218\) 7.00000 12.1244i 0.474100 0.821165i
\(219\) −6.50000 + 11.2583i −0.439229 + 0.760767i
\(220\) 18.0000 1.21356
\(221\) 0 0
\(222\) 7.00000 0.469809
\(223\) 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i \(-0.747017\pi\)
0.968309 + 0.249756i \(0.0803503\pi\)
\(224\) 1.00000 1.73205i 0.0668153 0.115728i
\(225\) −2.00000 3.46410i −0.133333 0.230940i
\(226\) −3.00000 −0.199557
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) −9.00000 15.5885i −0.593442 1.02787i
\(231\) −6.00000 + 10.3923i −0.394771 + 0.683763i
\(232\) −1.50000 + 2.59808i −0.0984798 + 0.170572i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 18.0000 1.17419
\(236\) 0 0
\(237\) 2.00000 3.46410i 0.129914 0.225018i
\(238\) −3.00000 5.19615i −0.194461 0.336817i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 1.50000 + 2.59808i 0.0968246 + 0.167705i
\(241\) −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i \(-0.176921\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(242\) 25.0000 1.60706
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 3.50000 6.06218i 0.224065 0.388091i
\(245\) −4.50000 + 7.79423i −0.287494 + 0.497955i
\(246\) 3.00000 0.191273
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) 6.00000 + 10.3923i 0.378717 + 0.655956i 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) −2.00000 −0.125988
\(253\) −18.0000 31.1769i −1.13165 1.96008i
\(254\) 2.00000 + 3.46410i 0.125491 + 0.217357i
\(255\) 9.00000 0.563602
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) 5.00000 8.66025i 0.311286 0.539164i
\(259\) −14.0000 −0.869918
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) 0 0
\(263\) 3.00000 5.19615i 0.184988 0.320408i −0.758585 0.651575i \(-0.774109\pi\)
0.943572 + 0.331166i \(0.107442\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) −9.00000 −0.552866
\(266\) −2.00000 3.46410i −0.122628 0.212398i
\(267\) 9.00000 + 15.5885i 0.550791 + 0.953998i
\(268\) 10.0000 0.610847
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 1.50000 2.59808i 0.0912871 0.158114i
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −9.00000 −0.543710
\(275\) 12.0000 20.7846i 0.723627 1.25336i
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i \(-0.996047\pi\)
0.489207 0.872167i \(-0.337286\pi\)
\(278\) −4.00000 −0.239904
\(279\) −2.00000 3.46410i −0.119737 0.207390i
\(280\) −3.00000 5.19615i −0.179284 0.310530i
\(281\) −9.00000 −0.536895 −0.268447 0.963294i \(-0.586511\pi\)
−0.268447 + 0.963294i \(0.586511\pi\)
\(282\) 3.00000 + 5.19615i 0.178647 + 0.309426i
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) 6.00000 0.355409
\(286\) 0 0
\(287\) −6.00000 −0.354169
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 4.50000 + 7.79423i 0.264249 + 0.457693i
\(291\) −14.0000 −0.820695
\(292\) −6.50000 11.2583i −0.380384 0.658844i
\(293\) −10.5000 18.1865i −0.613417 1.06247i −0.990660 0.136355i \(-0.956461\pi\)
0.377244 0.926114i \(-0.376872\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) −3.50000 + 6.06218i −0.203433 + 0.352357i
\(297\) 3.00000 5.19615i 0.174078 0.301511i
\(298\) 9.00000 0.521356
\(299\) 0 0
\(300\) 4.00000 0.230940
\(301\) −10.0000 + 17.3205i −0.576390 + 0.998337i
\(302\) −5.00000 + 8.66025i −0.287718 + 0.498342i
\(303\) −7.50000 12.9904i −0.430864 0.746278i
\(304\) −2.00000 −0.114708
\(305\) −10.5000 18.1865i −0.601228 1.04136i
\(306\) 1.50000 + 2.59808i 0.0857493 + 0.148522i
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) −6.00000 10.3923i −0.341882 0.592157i
\(309\) −7.00000 + 12.1244i −0.398216 + 0.689730i
\(310\) 6.00000 10.3923i 0.340777 0.590243i
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −2.50000 + 4.33013i −0.141083 + 0.244363i
\(315\) −3.00000 + 5.19615i −0.169031 + 0.292770i
\(316\) 2.00000 + 3.46410i 0.112509 + 0.194871i
\(317\) −3.00000 −0.168497 −0.0842484 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) −1.50000 2.59808i −0.0841158 0.145693i
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) −3.00000 −0.167705
\(321\) 3.00000 + 5.19615i 0.167444 + 0.290021i
\(322\) −6.00000 + 10.3923i −0.334367 + 0.579141i
\(323\) −3.00000 + 5.19615i −0.166924 + 0.289122i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) 7.00000 12.1244i 0.387101 0.670478i
\(328\) −1.50000 + 2.59808i −0.0828236 + 0.143455i
\(329\) −6.00000 10.3923i −0.330791 0.572946i
\(330\) 18.0000 0.990867
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 7.00000 0.383598
\(334\) 0 0
\(335\) 15.0000 25.9808i 0.819538 1.41948i
\(336\) 1.00000 1.73205i 0.0545545 0.0944911i
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 0 0
\(339\) −3.00000 −0.162938
\(340\) −4.50000 + 7.79423i −0.244047 + 0.422701i
\(341\) 12.0000 20.7846i 0.649836 1.12555i
\(342\) 1.00000 + 1.73205i 0.0540738 + 0.0936586i
\(343\) 20.0000 1.07990
\(344\) 5.00000 + 8.66025i 0.269582 + 0.466930i
\(345\) −9.00000 15.5885i −0.484544 0.839254i
\(346\) −6.00000 −0.322562
\(347\) 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i \(0.131298\pi\)
−0.110885 + 0.993833i \(0.535369\pi\)
\(348\) −1.50000 + 2.59808i −0.0804084 + 0.139272i
\(349\) −5.00000 + 8.66025i −0.267644 + 0.463573i −0.968253 0.249973i \(-0.919578\pi\)
0.700609 + 0.713545i \(0.252912\pi\)
\(350\) −8.00000 −0.427618
\(351\) 0 0
\(352\) −6.00000 −0.319801
\(353\) −7.50000 + 12.9904i −0.399185 + 0.691408i −0.993626 0.112731i \(-0.964040\pi\)
0.594441 + 0.804139i \(0.297373\pi\)
\(354\) 0 0
\(355\) −9.00000 15.5885i −0.477670 0.827349i
\(356\) −18.0000 −0.953998
\(357\) −3.00000 5.19615i −0.158777 0.275010i
\(358\) −3.00000 5.19615i −0.158555 0.274625i
\(359\) −6.00000 −0.316668 −0.158334 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(360\) 1.50000 + 2.59808i 0.0790569 + 0.136931i
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 3.50000 6.06218i 0.183956 0.318621i
\(363\) 25.0000 1.31216
\(364\) 0 0
\(365\) −39.0000 −2.04135
\(366\) 3.50000 6.06218i 0.182948 0.316875i
\(367\) −1.00000 + 1.73205i −0.0521996 + 0.0904123i −0.890945 0.454112i \(-0.849957\pi\)
0.838745 + 0.544524i \(0.183290\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 3.00000 0.156174
\(370\) 10.5000 + 18.1865i 0.545869 + 0.945473i
\(371\) 3.00000 + 5.19615i 0.155752 + 0.269771i
\(372\) 4.00000 0.207390
\(373\) −14.5000 25.1147i −0.750782 1.30039i −0.947444 0.319921i \(-0.896344\pi\)
0.196663 0.980471i \(-0.436990\pi\)
\(374\) −9.00000 + 15.5885i −0.465379 + 0.806060i
\(375\) −1.50000 + 2.59808i −0.0774597 + 0.134164i
\(376\) −6.00000 −0.309426
\(377\) 0 0
\(378\) −2.00000 −0.102869
\(379\) 10.0000 17.3205i 0.513665 0.889695i −0.486209 0.873843i \(-0.661621\pi\)
0.999874 0.0158521i \(-0.00504609\pi\)
\(380\) −3.00000 + 5.19615i −0.153897 + 0.266557i
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) −12.0000 −0.613973
\(383\) 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) −36.0000 −1.83473
\(386\) 11.5000 + 19.9186i 0.585335 + 1.01383i
\(387\) 5.00000 8.66025i 0.254164 0.440225i
\(388\) 7.00000 12.1244i 0.355371 0.615521i
\(389\) 39.0000 1.97738 0.988689 0.149979i \(-0.0479205\pi\)
0.988689 + 0.149979i \(0.0479205\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 1.50000 2.59808i 0.0757614 0.131223i
\(393\) 0 0
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) 12.0000 0.603786
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) 7.00000 + 12.1244i 0.351320 + 0.608504i 0.986481 0.163876i \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) −10.0000 −0.501255
\(399\) −2.00000 3.46410i −0.100125 0.173422i
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 10.0000 0.498755
\(403\) 0 0
\(404\) 15.0000 0.746278
\(405\) 1.50000 2.59808i 0.0745356 0.129099i
\(406\) 3.00000 5.19615i 0.148888 0.257881i
\(407\) 21.0000 + 36.3731i 1.04093 + 1.80295i
\(408\) −3.00000 −0.148522
\(409\) −0.500000 0.866025i −0.0247234 0.0428222i 0.853399 0.521258i \(-0.174537\pi\)
−0.878122 + 0.478436i \(0.841204\pi\)
\(410\) 4.50000 + 7.79423i 0.222239 + 0.384930i
\(411\) −9.00000 −0.443937
\(412\) −7.00000 12.1244i −0.344865 0.597324i
\(413\) 0 0
\(414\) 3.00000 5.19615i 0.147442 0.255377i
\(415\) −18.0000 −0.883585
\(416\) 0 0
\(417\) −4.00000 −0.195881
\(418\) −6.00000 + 10.3923i −0.293470 + 0.508304i
\(419\) −12.0000 + 20.7846i −0.586238 + 1.01539i 0.408481 + 0.912767i \(0.366058\pi\)
−0.994720 + 0.102628i \(0.967275\pi\)
\(420\) −3.00000 5.19615i −0.146385 0.253546i
\(421\) −29.0000 −1.41337 −0.706687 0.707527i \(-0.749811\pi\)
−0.706687 + 0.707527i \(0.749811\pi\)
\(422\) 8.00000 + 13.8564i 0.389434 + 0.674519i
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 3.00000 0.145693
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 3.00000 5.19615i 0.145350 0.251754i
\(427\) −7.00000 + 12.1244i −0.338754 + 0.586739i
\(428\) −6.00000 −0.290021
\(429\) 0 0
\(430\) 30.0000 1.44673
\(431\) −3.00000 + 5.19615i −0.144505 + 0.250290i −0.929188 0.369607i \(-0.879492\pi\)
0.784683 + 0.619897i \(0.212826\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 6.50000 + 11.2583i 0.312370 + 0.541041i 0.978875 0.204460i \(-0.0655438\pi\)
−0.666505 + 0.745501i \(0.732210\pi\)
\(434\) −8.00000 −0.384012
\(435\) 4.50000 + 7.79423i 0.215758 + 0.373705i
\(436\) 7.00000 + 12.1244i 0.335239 + 0.580651i
\(437\) 12.0000 0.574038
\(438\) −6.50000 11.2583i −0.310582 0.537944i
\(439\) −7.00000 + 12.1244i −0.334092 + 0.578664i −0.983310 0.181938i \(-0.941763\pi\)
0.649218 + 0.760602i \(0.275096\pi\)
\(440\) −9.00000 + 15.5885i −0.429058 + 0.743151i
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) −3.50000 + 6.06218i −0.166103 + 0.287698i
\(445\) −27.0000 + 46.7654i −1.27992 + 2.21689i
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 9.00000 0.425685
\(448\) 1.00000 + 1.73205i 0.0472456 + 0.0818317i
\(449\) 9.00000 + 15.5885i 0.424736 + 0.735665i 0.996396 0.0848262i \(-0.0270335\pi\)
−0.571660 + 0.820491i \(0.693700\pi\)
\(450\) 4.00000 0.188562
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) 1.50000 2.59808i 0.0705541 0.122203i
\(453\) −5.00000 + 8.66025i −0.234920 + 0.406894i
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) −11.0000 + 19.0526i −0.513996 + 0.890268i
\(459\) 1.50000 + 2.59808i 0.0700140 + 0.121268i
\(460\) 18.0000 0.839254
\(461\) 7.50000 + 12.9904i 0.349310 + 0.605022i 0.986127 0.165992i \(-0.0530827\pi\)
−0.636817 + 0.771015i \(0.719749\pi\)
\(462\) −6.00000 10.3923i −0.279145 0.483494i
\(463\) −38.0000 −1.76601 −0.883005 0.469364i \(-0.844483\pi\)
−0.883005 + 0.469364i \(0.844483\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 6.00000 10.3923i 0.278243 0.481932i
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −18.0000 −0.832941 −0.416470 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 0 0
\(469\) −20.0000 −0.923514
\(470\) −9.00000 + 15.5885i −0.415139 + 0.719042i
\(471\) −2.50000 + 4.33013i −0.115194 + 0.199522i
\(472\) 0 0
\(473\) 60.0000 2.75880
\(474\) 2.00000 + 3.46410i 0.0918630 + 0.159111i
\(475\) 4.00000 + 6.92820i 0.183533 + 0.317888i
\(476\) 6.00000 0.275010
\(477\) −1.50000 2.59808i −0.0686803 0.118958i
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) −3.00000 −0.136931
\(481\) 0 0
\(482\) 1.00000 0.0455488
\(483\) −6.00000 + 10.3923i −0.273009 + 0.472866i
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) −21.0000 36.3731i −0.953561 1.65162i
\(486\) 1.00000 0.0453609
\(487\) 1.00000 + 1.73205i 0.0453143 + 0.0784867i 0.887793 0.460243i \(-0.152238\pi\)
−0.842479 + 0.538730i \(0.818904\pi\)
\(488\) 3.50000 + 6.06218i 0.158438 + 0.274422i
\(489\) 4.00000 0.180886
\(490\) −4.50000 7.79423i −0.203289 0.352107i
\(491\) 9.00000 15.5885i 0.406164 0.703497i −0.588292 0.808649i \(-0.700199\pi\)
0.994456 + 0.105151i \(0.0335327\pi\)
\(492\) −1.50000 + 2.59808i −0.0676252 + 0.117130i
\(493\) −9.00000 −0.405340
\(494\) 0 0
\(495\) 18.0000 0.809040
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) −32.0000 −1.43252 −0.716258 0.697835i \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) −3.00000 5.19615i −0.133763 0.231685i 0.791361 0.611349i \(-0.209373\pi\)
−0.925124 + 0.379664i \(0.876040\pi\)
\(504\) 1.00000 1.73205i 0.0445435 0.0771517i
\(505\) 22.5000 38.9711i 1.00124 1.73419i
\(506\) 36.0000 1.60040
\(507\) 0 0
\(508\) −4.00000 −0.177471
\(509\) 1.50000 2.59808i 0.0664863 0.115158i −0.830866 0.556473i \(-0.812154\pi\)
0.897352 + 0.441315i \(0.145488\pi\)
\(510\) −4.50000 + 7.79423i −0.199263 + 0.345134i
\(511\) 13.0000 + 22.5167i 0.575086 + 0.996078i
\(512\) 1.00000 0.0441942
\(513\) 1.00000 + 1.73205i 0.0441511 + 0.0764719i
\(514\) 1.50000 + 2.59808i 0.0661622 + 0.114596i
\(515\) −42.0000 −1.85074
\(516\) 5.00000 + 8.66025i 0.220113 + 0.381246i
\(517\) −18.0000 + 31.1769i −0.791639 + 1.37116i
\(518\) 7.00000 12.1244i 0.307562 0.532714i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 33.0000 1.44576 0.722878 0.690976i \(-0.242819\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(522\) −1.50000 + 2.59808i −0.0656532 + 0.113715i
\(523\) 17.0000 29.4449i 0.743358 1.28753i −0.207600 0.978214i \(-0.566565\pi\)
0.950958 0.309320i \(-0.100101\pi\)
\(524\) 0 0
\(525\) −8.00000 −0.349149
\(526\) 3.00000 + 5.19615i 0.130806 + 0.226563i
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) −6.00000 −0.261116
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) 0 0
\(534\) −18.0000 −0.778936
\(535\) −9.00000 + 15.5885i −0.389104 + 0.673948i
\(536\) −5.00000 + 8.66025i −0.215967 + 0.374066i
\(537\) −3.00000 5.19615i −0.129460 0.224231i
\(538\) 18.0000 0.776035
\(539\) −9.00000 15.5885i −0.387657 0.671442i
\(540\) 1.50000 + 2.59808i 0.0645497 + 0.111803i
\(541\) −29.0000 −1.24681 −0.623404 0.781900i \(-0.714251\pi\)
−0.623404 + 0.781900i \(0.714251\pi\)
\(542\) −8.00000 13.8564i −0.343629 0.595184i
\(543\) 3.50000 6.06218i 0.150199 0.260153i
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) 42.0000 1.79908
\(546\) 0 0
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) 3.50000 6.06218i 0.149376 0.258727i
\(550\) 12.0000 + 20.7846i 0.511682 + 0.886259i
\(551\) −6.00000 −0.255609
\(552\) 3.00000 + 5.19615i 0.127688 + 0.221163i
\(553\) −4.00000 6.92820i −0.170097 0.294617i
\(554\) 17.0000 0.722261
\(555\) 10.5000 + 18.1865i 0.445700 + 0.771975i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 1.50000 2.59808i 0.0635570 0.110084i −0.832496 0.554031i \(-0.813089\pi\)
0.896053 + 0.443947i \(0.146422\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) 6.00000 0.253546
\(561\) −9.00000 + 15.5885i −0.379980 + 0.658145i
\(562\) 4.50000 7.79423i 0.189821 0.328780i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) −6.00000 −0.252646
\(565\) −4.50000 7.79423i −0.189316 0.327906i
\(566\) −7.00000 12.1244i −0.294232 0.509625i
\(567\) −2.00000 −0.0839921
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) −3.00000 + 5.19615i −0.125656 + 0.217643i
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 3.00000 5.19615i 0.125218 0.216883i
\(575\) 12.0000 20.7846i 0.500435 0.866778i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −11.0000 −0.457936 −0.228968 0.973434i \(-0.573535\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) 11.5000 + 19.9186i 0.477924 + 0.827788i
\(580\) −9.00000 −0.373705
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) 7.00000 12.1244i 0.290159 0.502571i
\(583\) 9.00000 15.5885i 0.372742 0.645608i
\(584\) 13.0000 0.537944
\(585\) 0 0
\(586\) 21.0000 0.867502
\(587\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(588\) 1.50000 2.59808i 0.0618590 0.107143i
\(589\) 4.00000 + 6.92820i 0.164817 + 0.285472i
\(590\) 0 0
\(591\) 3.00000 + 5.19615i 0.123404 + 0.213741i
\(592\) −3.50000 6.06218i −0.143849 0.249154i
\(593\) −9.00000 −0.369586 −0.184793 0.982777i \(-0.559161\pi\)
−0.184793 + 0.982777i \(0.559161\pi\)
\(594\) 3.00000 + 5.19615i 0.123091 + 0.213201i
\(595\) 9.00000 15.5885i 0.368964 0.639064i
\(596\) −4.50000 + 7.79423i −0.184327 + 0.319264i
\(597\) −10.0000 −0.409273
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −2.00000 + 3.46410i −0.0816497 + 0.141421i
\(601\) 18.5000 32.0429i 0.754631 1.30706i −0.190927 0.981604i \(-0.561149\pi\)
0.945558 0.325455i \(-0.105517\pi\)
\(602\) −10.0000 17.3205i −0.407570 0.705931i
\(603\) 10.0000 0.407231
\(604\) −5.00000 8.66025i −0.203447 0.352381i
\(605\) 37.5000 + 64.9519i 1.52459 + 2.64067i
\(606\) 15.0000 0.609333
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 1.00000 1.73205i 0.0405554 0.0702439i
\(609\) 3.00000 5.19615i 0.121566 0.210559i
\(610\) 21.0000 0.850265
\(611\) 0 0
\(612\) −3.00000 −0.121268
\(613\) −15.5000 + 26.8468i −0.626039 + 1.08433i 0.362300 + 0.932062i \(0.381992\pi\)
−0.988339 + 0.152270i \(0.951342\pi\)
\(614\) −5.00000 + 8.66025i −0.201784 + 0.349499i
\(615\) 4.50000 + 7.79423i 0.181458 + 0.314294i
\(616\) 12.0000 0.483494
\(617\) −7.50000 12.9904i −0.301939 0.522973i 0.674636 0.738150i \(-0.264300\pi\)
−0.976575 + 0.215177i \(0.930967\pi\)
\(618\) −7.00000 12.1244i −0.281581 0.487713i
\(619\) −8.00000 −0.321547 −0.160774 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(620\) 6.00000 + 10.3923i 0.240966 + 0.417365i
\(621\) 3.00000 5.19615i 0.120386 0.208514i
\(622\) 15.0000 25.9808i 0.601445 1.04173i
\(623\) 36.0000 1.44231
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 5.00000 8.66025i 0.199840 0.346133i
\(627\) −6.00000 + 10.3923i −0.239617 + 0.415029i
\(628\) −2.50000 4.33013i −0.0997609 0.172791i
\(629\) −21.0000 −0.837325
\(630\) −3.00000 5.19615i −0.119523 0.207020i
\(631\) 10.0000 + 17.3205i 0.398094 + 0.689519i 0.993491 0.113913i \(-0.0363385\pi\)
−0.595397 + 0.803432i \(0.703005\pi\)
\(632\) −4.00000 −0.159111
\(633\) 8.00000 + 13.8564i 0.317971 + 0.550743i
\(634\) 1.50000 2.59808i 0.0595726 0.103183i
\(635\) −6.00000 + 10.3923i −0.238103 + 0.412406i
\(636\) 3.00000 0.118958
\(637\) 0 0
\(638\) −18.0000 −0.712627
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) −6.00000 −0.236801
\(643\) −8.00000 13.8564i −0.315489 0.546443i 0.664052 0.747686i \(-0.268835\pi\)
−0.979541 + 0.201243i \(0.935502\pi\)
\(644\) −6.00000 10.3923i −0.236433 0.409514i
\(645\) 30.0000 1.18125
\(646\) −3.00000 5.19615i −0.118033 0.204440i
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 0 0
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) −2.00000 + 3.46410i −0.0783260 + 0.135665i
\(653\) −21.0000 + 36.3731i −0.821794 + 1.42339i 0.0825519 + 0.996587i \(0.473693\pi\)
−0.904345 + 0.426801i \(0.859640\pi\)
\(654\) 7.00000 + 12.1244i 0.273722 + 0.474100i
\(655\) 0 0
\(656\) −1.50000 2.59808i −0.0585652 0.101438i
\(657\) −6.50000 11.2583i −0.253589 0.439229i
\(658\) 12.0000 0.467809
\(659\) −12.0000 20.7846i −0.467454 0.809653i 0.531855 0.846836i \(-0.321495\pi\)
−0.999309 + 0.0371821i \(0.988162\pi\)
\(660\) −9.00000 + 15.5885i −0.350325 + 0.606780i
\(661\) 2.50000 4.33013i 0.0972387 0.168422i −0.813302 0.581842i \(-0.802332\pi\)
0.910541 + 0.413419i \(0.135666\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 6.00000 10.3923i 0.232670 0.402996i
\(666\) −3.50000 + 6.06218i −0.135622 + 0.234905i
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 0 0
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 15.0000 + 25.9808i 0.579501 + 1.00372i
\(671\) 42.0000 1.62139
\(672\) 1.00000 + 1.73205i 0.0385758 + 0.0668153i
\(673\) 6.50000 11.2583i 0.250557 0.433977i −0.713123 0.701039i \(-0.752720\pi\)
0.963679 + 0.267063i \(0.0860531\pi\)
\(674\) −11.5000 + 19.9186i −0.442963 + 0.767235i
\(675\) 4.00000 0.153960
\(676\) 0 0
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 1.50000 2.59808i 0.0576072 0.0997785i
\(679\) −14.0000 + 24.2487i −0.537271 + 0.930580i
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) −18.0000 −0.689761
\(682\) 12.0000 + 20.7846i 0.459504 + 0.795884i
\(683\) −24.0000 41.5692i −0.918334 1.59060i −0.801945 0.597398i \(-0.796201\pi\)
−0.116390 0.993204i \(-0.537132\pi\)
\(684\) −2.00000 −0.0764719
\(685\) −13.5000 23.3827i −0.515808 0.893407i
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) −11.0000 + 19.0526i −0.419676 + 0.726900i
\(688\) −10.0000 −0.381246
\(689\) 0 0
\(690\) 18.0000 0.685248
\(691\) 13.0000 22.5167i 0.494543 0.856574i −0.505437 0.862864i \(-0.668669\pi\)
0.999980 + 0.00628943i \(0.00200200\pi\)
\(692\) 3.00000 5.19615i 0.114043 0.197528i
\(693\) −6.00000 10.3923i −0.227921 0.394771i
\(694\) −30.0000 −1.13878
\(695\) −6.00000 10.3923i −0.227593 0.394203i
\(696\) −1.50000 2.59808i −0.0568574 0.0984798i
\(697\) −9.00000 −0.340899
\(698\) −5.00000 8.66025i −0.189253 0.327795i
\(699\) 3.00000 5.19615i 0.113470 0.196537i
\(700\) 4.00000 6.92820i 0.151186 0.261861i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −14.0000 −0.528020
\(704\) 3.00000 5.19615i 0.113067 0.195837i
\(705\) −9.00000 + 15.5885i −0.338960 + 0.587095i
\(706\) −7.50000 12.9904i −0.282266 0.488899i
\(707\) −30.0000 −1.12827
\(708\) 0 0
\(709\) 2.50000 + 4.33013i 0.0938895 + 0.162621i 0.909145 0.416481i \(-0.136737\pi\)
−0.815255 + 0.579102i \(0.803403\pi\)
\(710\) 18.0000 0.675528
\(711\) 2.00000 + 3.46410i 0.0750059 + 0.129914i
\(712\) 9.00000 15.5885i 0.337289 0.584202i
\(713\) 12.0000 20.7846i 0.449404 0.778390i
\(714\) 6.00000 0.224544
\(715\) 0 0
\(716\) 6.00000 0.224231
\(717\) 3.00000 5.19615i 0.112037 0.194054i
\(718\) 3.00000 5.19615i 0.111959 0.193919i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) −3.00000 −0.111803
\(721\) 14.0000 + 24.2487i 0.521387 + 0.903069i
\(722\) 7.50000 + 12.9904i 0.279121 + 0.483452i
\(723\) 1.00000 0.0371904
\(724\) 3.50000 + 6.06218i 0.130076 + 0.225299i
\(725\) −6.00000 + 10.3923i −0.222834 + 0.385961i
\(726\) −12.5000 + 21.6506i −0.463919 + 0.803530i
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 19.5000 33.7750i 0.721727 1.25007i
\(731\) −15.0000 + 25.9808i −0.554795 + 0.960933i
\(732\) 3.50000 + 6.06218i 0.129364 + 0.224065i
\(733\) 31.0000 1.14501 0.572506 0.819901i \(-0.305971\pi\)
0.572506 + 0.819901i \(0.305971\pi\)
\(734\) −1.00000 1.73205i −0.0369107 0.0639312i
\(735\) −4.50000 7.79423i −0.165985 0.287494i
\(736\) −6.00000 −0.221163
\(737\) 30.0000 + 51.9615i 1.10506 + 1.91403i
\(738\) −1.50000 + 2.59808i −0.0552158 + 0.0956365i
\(739\) −8.00000 + 13.8564i −0.294285 + 0.509716i −0.974818 0.223001i \(-0.928415\pi\)
0.680534 + 0.732717i \(0.261748\pi\)
\(740\) −21.0000 −0.771975
\(741\) 0 0
\(742\) −6.00000 −0.220267
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) −2.00000 + 3.46410i −0.0733236 + 0.127000i
\(745\) 13.5000 + 23.3827i 0.494602 + 0.856675i
\(746\) 29.0000 1.06177
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) −9.00000 15.5885i −0.329073 0.569970i
\(749\) 12.0000 0.438470
\(750\) −1.50000 2.59808i −0.0547723 0.0948683i
\(751\) −7.00000 + 12.1244i −0.255434 + 0.442424i −0.965013 0.262201i \(-0.915552\pi\)
0.709580 + 0.704625i \(0.248885\pi\)
\(752\) 3.00000 5.19615i 0.109399 0.189484i
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) −30.0000 −1.09181
\(756\) 1.00000 1.73205i 0.0363696 0.0629941i
\(757\) 17.0000 29.4449i 0.617876 1.07019i −0.371997 0.928234i \(-0.621327\pi\)
0.989873 0.141958i \(-0.0453398\pi\)
\(758\) 10.0000 + 17.3205i 0.363216 + 0.629109i
\(759\) 36.0000 1.30672
\(760\) −3.00000 5.19615i −0.108821 0.188484i
\(761\) −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i \(-0.983671\pi\)
0.454935 0.890525i \(-0.349663\pi\)
\(762\) −4.00000 −0.144905
\(763\) −14.0000 24.2487i −0.506834 0.877862i
\(764\) 6.00000 10.3923i 0.217072 0.375980i
\(765\) −4.50000 + 7.79423i −0.162698 + 0.281801i
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 7.00000 12.1244i 0.252426 0.437215i −0.711767 0.702416i \(-0.752105\pi\)
0.964193 + 0.265200i \(0.0854381\pi\)
\(770\) 18.0000 31.1769i 0.648675 1.12354i
\(771\) 1.50000 + 2.59808i 0.0540212 + 0.0935674i
\(772\) −23.0000 −0.827788
\(773\) −15.0000 25.9808i −0.539513 0.934463i −0.998930 0.0462427i \(-0.985275\pi\)
0.459418 0.888220i \(-0.348058\pi\)
\(774\) 5.00000 + 8.66025i 0.179721 + 0.311286i
\(775\) 16.0000 0.574737
\(776\) 7.00000 + 12.1244i 0.251285 + 0.435239i
\(777\) 7.00000 12.1244i 0.251124 0.434959i
\(778\) −19.5000 + 33.7750i −0.699109 + 1.21089i