Properties

Label 114.2.e.b.49.1
Level $114$
Weight $2$
Character 114.49
Analytic conductor $0.910$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.910294583043\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 114.49
Dual form 114.2.e.b.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -2.00000 q^{11} -1.00000 q^{12} +(1.50000 + 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +3.00000 q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} -3.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{34} +(-0.500000 + 0.866025i) q^{36} -5.00000 q^{37} +(3.50000 - 2.59808i) q^{38} +3.00000 q^{39} +(-2.00000 + 3.46410i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(4.50000 - 7.79423i) q^{43} +(1.00000 + 1.73205i) q^{44} -4.00000 q^{46} +(-5.00000 - 8.66025i) q^{47} +(0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +5.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(1.50000 - 2.59808i) q^{52} +(2.00000 + 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} -1.00000 q^{56} +(3.50000 - 2.59808i) q^{57} +(7.00000 - 12.1244i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-1.50000 + 2.59808i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{66} +(-1.50000 - 2.59808i) q^{67} +4.00000 q^{68} -4.00000 q^{69} +(-7.00000 + 12.1244i) q^{71} +(0.500000 + 0.866025i) q^{72} +(5.50000 - 9.52628i) q^{73} +(-2.50000 + 4.33013i) q^{74} +5.00000 q^{75} +(-0.500000 - 4.33013i) q^{76} -2.00000 q^{77} +(1.50000 - 2.59808i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +8.00000 q^{83} -1.00000 q^{84} +(-4.50000 - 7.79423i) q^{86} +2.00000 q^{88} +(7.00000 + 12.1244i) q^{89} +(1.50000 + 2.59808i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-1.50000 + 2.59808i) q^{93} -10.0000 q^{94} +1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} - q^{6} + 2q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} - q^{6} + 2q^{7} - 2q^{8} - q^{9} - 4q^{11} - 2q^{12} + 3q^{13} + q^{14} - q^{16} - 4q^{17} - 2q^{18} + 8q^{19} + q^{21} - 2q^{22} - 4q^{23} - q^{24} + 5q^{25} + 6q^{26} - 2q^{27} - q^{28} - 6q^{31} + q^{32} - 2q^{33} + 4q^{34} - q^{36} - 10q^{37} + 7q^{38} + 6q^{39} - 4q^{41} - q^{42} + 9q^{43} + 2q^{44} - 8q^{46} - 10q^{47} + q^{48} - 12q^{49} + 10q^{50} + 4q^{51} + 3q^{52} + 4q^{53} - q^{54} - 2q^{56} + 7q^{57} + 14q^{59} - 11q^{61} - 3q^{62} - q^{63} + 2q^{64} + 2q^{66} - 3q^{67} + 8q^{68} - 8q^{69} - 14q^{71} + q^{72} + 11q^{73} - 5q^{74} + 10q^{75} - q^{76} - 4q^{77} + 3q^{78} - q^{79} - q^{81} + 4q^{82} + 16q^{83} - 2q^{84} - 9q^{86} + 4q^{88} + 14q^{89} + 3q^{91} - 4q^{92} - 3q^{93} - 20q^{94} + 2q^{96} - 2q^{97} - 6q^{98} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.50000 + 2.59808i 0.416025 + 0.720577i 0.995535 0.0943882i \(-0.0300895\pi\)
−0.579510 + 0.814965i \(0.696756\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) −1.00000 −0.235702
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) 0 0
\(21\) 0.500000 0.866025i 0.109109 0.188982i
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 3.00000 0.588348
\(27\) −1.00000 −0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) 3.50000 2.59808i 0.567775 0.421464i
\(39\) 3.00000 0.480384
\(40\) 0 0
\(41\) −2.00000 + 3.46410i −0.312348 + 0.541002i −0.978870 0.204483i \(-0.934449\pi\)
0.666523 + 0.745485i \(0.267782\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) 4.50000 7.79423i 0.686244 1.18861i −0.286801 0.957990i \(-0.592592\pi\)
0.973044 0.230618i \(-0.0740749\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) −5.00000 8.66025i −0.729325 1.26323i −0.957169 0.289530i \(-0.906501\pi\)
0.227844 0.973698i \(-0.426832\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −6.00000 −0.857143
\(50\) 5.00000 0.707107
\(51\) 2.00000 + 3.46410i 0.280056 + 0.485071i
\(52\) 1.50000 2.59808i 0.208013 0.360288i
\(53\) 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 3.50000 2.59808i 0.463586 0.344124i
\(58\) 0 0
\(59\) 7.00000 12.1244i 0.911322 1.57846i 0.0991242 0.995075i \(-0.468396\pi\)
0.812198 0.583382i \(-0.198271\pi\)
\(60\) 0 0
\(61\) −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i \(-0.917971\pi\)
0.262776 0.964857i \(-0.415362\pi\)
\(62\) −1.50000 + 2.59808i −0.190500 + 0.329956i
\(63\) −0.500000 0.866025i −0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.00000 + 1.73205i 0.123091 + 0.213201i
\(67\) −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) 4.00000 0.485071
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) −7.00000 + 12.1244i −0.830747 + 1.43890i 0.0666994 + 0.997773i \(0.478753\pi\)
−0.897447 + 0.441123i \(0.854580\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i \(-0.610721\pi\)
0.984594 0.174855i \(-0.0559458\pi\)
\(74\) −2.50000 + 4.33013i −0.290619 + 0.503367i
\(75\) 5.00000 0.577350
\(76\) −0.500000 4.33013i −0.0573539 0.496700i
\(77\) −2.00000 −0.227921
\(78\) 1.50000 2.59808i 0.169842 0.294174i
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.00000 + 3.46410i 0.220863 + 0.382546i
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) −4.50000 7.79423i −0.485247 0.840473i
\(87\) 0 0
\(88\) 2.00000 0.213201
\(89\) 7.00000 + 12.1244i 0.741999 + 1.28518i 0.951584 + 0.307389i \(0.0994552\pi\)
−0.209585 + 0.977790i \(0.567211\pi\)
\(90\) 0 0
\(91\) 1.50000 + 2.59808i 0.157243 + 0.272352i
\(92\) −2.00000 + 3.46410i −0.208514 + 0.361158i
\(93\) −1.50000 + 2.59808i −0.155543 + 0.269408i
\(94\) −10.0000 −1.03142
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) −3.00000 + 5.19615i −0.303046 + 0.524891i
\(99\) 1.00000 + 1.73205i 0.100504 + 0.174078i
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) 4.00000 0.396059
\(103\) −3.00000 −0.295599 −0.147799 0.989017i \(-0.547219\pi\)
−0.147799 + 0.989017i \(0.547219\pi\)
\(104\) −1.50000 2.59808i −0.147087 0.254762i
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) 0 0
\(111\) −2.50000 + 4.33013i −0.237289 + 0.410997i
\(112\) −0.500000 + 0.866025i −0.0472456 + 0.0818317i
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) −0.500000 4.33013i −0.0468293 0.405554i
\(115\) 0 0
\(116\) 0 0
\(117\) 1.50000 2.59808i 0.138675 0.240192i
\(118\) −7.00000 12.1244i −0.644402 1.11614i
\(119\) −2.00000 + 3.46410i −0.183340 + 0.317554i
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −11.0000 −0.995893
\(123\) 2.00000 + 3.46410i 0.180334 + 0.312348i
\(124\) 1.50000 + 2.59808i 0.134704 + 0.233314i
\(125\) 0 0
\(126\) −1.00000 −0.0890871
\(127\) 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i \(-0.0511671\pi\)
−0.632166 + 0.774833i \(0.717834\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −4.50000 7.79423i −0.396203 0.686244i
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 2.00000 0.174078
\(133\) 4.00000 + 1.73205i 0.346844 + 0.150188i
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) −2.00000 + 3.46410i −0.170251 + 0.294884i
\(139\) 9.50000 + 16.4545i 0.805779 + 1.39565i 0.915764 + 0.401718i \(0.131587\pi\)
−0.109984 + 0.993933i \(0.535080\pi\)
\(140\) 0 0
\(141\) −10.0000 −0.842152
\(142\) 7.00000 + 12.1244i 0.587427 + 1.01745i
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −5.50000 9.52628i −0.455183 0.788400i
\(147\) −3.00000 + 5.19615i −0.247436 + 0.428571i
\(148\) 2.50000 + 4.33013i 0.205499 + 0.355934i
\(149\) 11.0000 19.0526i 0.901155 1.56085i 0.0751583 0.997172i \(-0.476054\pi\)
0.825997 0.563675i \(-0.190613\pi\)
\(150\) 2.50000 4.33013i 0.204124 0.353553i
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) −4.00000 1.73205i −0.324443 0.140488i
\(153\) 4.00000 0.323381
\(154\) −1.00000 + 1.73205i −0.0805823 + 0.139573i
\(155\) 0 0
\(156\) −1.50000 2.59808i −0.120096 0.208013i
\(157\) 10.5000 18.1865i 0.837991 1.45144i −0.0535803 0.998564i \(-0.517063\pi\)
0.891572 0.452880i \(-0.149603\pi\)
\(158\) 0.500000 + 0.866025i 0.0397779 + 0.0688973i
\(159\) 4.00000 0.317221
\(160\) 0 0
\(161\) −2.00000 3.46410i −0.157622 0.273009i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 4.00000 0.312348
\(165\) 0 0
\(166\) 4.00000 6.92820i 0.310460 0.537733i
\(167\) −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i \(-0.241242\pi\)
−0.958440 + 0.285295i \(0.907908\pi\)
\(168\) −0.500000 + 0.866025i −0.0385758 + 0.0668153i
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 0 0
\(171\) −0.500000 4.33013i −0.0382360 0.331133i
\(172\) −9.00000 −0.686244
\(173\) 12.0000 20.7846i 0.912343 1.58022i 0.101598 0.994826i \(-0.467605\pi\)
0.810745 0.585399i \(-0.199062\pi\)
\(174\) 0 0
\(175\) 2.50000 + 4.33013i 0.188982 + 0.327327i
\(176\) 1.00000 1.73205i 0.0753778 0.130558i
\(177\) −7.00000 12.1244i −0.526152 0.911322i
\(178\) 14.0000 1.04934
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 0 0
\(181\) 9.00000 + 15.5885i 0.668965 + 1.15868i 0.978194 + 0.207693i \(0.0665956\pi\)
−0.309229 + 0.950988i \(0.600071\pi\)
\(182\) 3.00000 0.222375
\(183\) −11.0000 −0.813143
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) 0 0
\(186\) 1.50000 + 2.59808i 0.109985 + 0.190500i
\(187\) 4.00000 6.92820i 0.292509 0.506640i
\(188\) −5.00000 + 8.66025i −0.364662 + 0.631614i
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i \(-0.678351\pi\)
0.999326 + 0.0366998i \(0.0116845\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 0 0
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 2.00000 0.142134
\(199\) −2.50000 4.33013i −0.177220 0.306955i 0.763707 0.645563i \(-0.223377\pi\)
−0.940927 + 0.338608i \(0.890044\pi\)
\(200\) −2.50000 4.33013i −0.176777 0.306186i
\(201\) −3.00000 −0.211604
\(202\) 10.0000 0.703598
\(203\) 0 0
\(204\) 2.00000 3.46410i 0.140028 0.242536i
\(205\) 0 0
\(206\) −1.50000 + 2.59808i −0.104510 + 0.181017i
\(207\) −2.00000 + 3.46410i −0.139010 + 0.240772i
\(208\) −3.00000 −0.208013
\(209\) −8.00000 3.46410i −0.553372 0.239617i
\(210\) 0 0
\(211\) −12.5000 + 21.6506i −0.860535 + 1.49049i 0.0108774 + 0.999941i \(0.496538\pi\)
−0.871413 + 0.490550i \(0.836796\pi\)
\(212\) 2.00000 3.46410i 0.137361 0.237915i
\(213\) 7.00000 + 12.1244i 0.479632 + 0.830747i
\(214\) −5.00000 + 8.66025i −0.341793 + 0.592003i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −3.00000 −0.203653
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) −5.50000 9.52628i −0.371656 0.643726i
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 2.50000 + 4.33013i 0.167789 + 0.290619i
\(223\) −4.50000 + 7.79423i −0.301342 + 0.521940i −0.976440 0.215788i \(-0.930768\pi\)
0.675098 + 0.737728i \(0.264101\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 2.50000 4.33013i 0.166667 0.288675i
\(226\) 5.00000 8.66025i 0.332595 0.576072i
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) −4.00000 1.73205i −0.264906 0.114708i
\(229\) −11.0000 −0.726900 −0.363450 0.931614i \(-0.618401\pi\)
−0.363450 + 0.931614i \(0.618401\pi\)
\(230\) 0 0
\(231\) −1.00000 + 1.73205i −0.0657952 + 0.113961i
\(232\) 0 0
\(233\) −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) −1.50000 2.59808i −0.0980581 0.169842i
\(235\) 0 0
\(236\) −14.0000 −0.911322
\(237\) 0.500000 + 0.866025i 0.0324785 + 0.0562544i
\(238\) 2.00000 + 3.46410i 0.129641 + 0.224544i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −12.5000 21.6506i −0.805196 1.39464i −0.916159 0.400815i \(-0.868727\pi\)
0.110963 0.993825i \(-0.464606\pi\)
\(242\) −3.50000 + 6.06218i −0.224989 + 0.389692i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −5.50000 + 9.52628i −0.352101 + 0.609858i
\(245\) 0 0
\(246\) 4.00000 0.255031
\(247\) 1.50000 + 12.9904i 0.0954427 + 0.826558i
\(248\) 3.00000 0.190500
\(249\) 4.00000 6.92820i 0.253490 0.439057i
\(250\) 0 0
\(251\) 9.00000 + 15.5885i 0.568075 + 0.983935i 0.996756 + 0.0804789i \(0.0256450\pi\)
−0.428681 + 0.903456i \(0.641022\pi\)
\(252\) −0.500000 + 0.866025i −0.0314970 + 0.0545545i
\(253\) 4.00000 + 6.92820i 0.251478 + 0.435572i
\(254\) 8.00000 0.501965
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) −9.00000 −0.560316
\(259\) −5.00000 −0.310685
\(260\) 0 0
\(261\) 0 0
\(262\) −3.00000 5.19615i −0.185341 0.321019i
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 1.00000 1.73205i 0.0615457 0.106600i
\(265\) 0 0
\(266\) 3.50000 2.59808i 0.214599 0.159298i
\(267\) 14.0000 0.856786
\(268\) −1.50000 + 2.59808i −0.0916271 + 0.158703i
\(269\) −1.00000 + 1.73205i −0.0609711 + 0.105605i −0.894900 0.446267i \(-0.852753\pi\)
0.833929 + 0.551872i \(0.186086\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) −2.00000 3.46410i −0.121268 0.210042i
\(273\) 3.00000 0.181568
\(274\) 6.00000 0.362473
\(275\) −5.00000 8.66025i −0.301511 0.522233i
\(276\) 2.00000 + 3.46410i 0.120386 + 0.208514i
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 19.0000 1.13954
\(279\) 1.50000 + 2.59808i 0.0898027 + 0.155543i
\(280\) 0 0
\(281\) 4.00000 + 6.92820i 0.238620 + 0.413302i 0.960319 0.278906i \(-0.0899716\pi\)
−0.721699 + 0.692207i \(0.756638\pi\)
\(282\) −5.00000 + 8.66025i −0.297746 + 0.515711i
\(283\) 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i \(-0.630708\pi\)
0.993626 0.112728i \(-0.0359589\pi\)
\(284\) 14.0000 0.830747
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) −2.00000 + 3.46410i −0.118056 + 0.204479i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 1.00000 + 1.73205i 0.0586210 + 0.101535i
\(292\) −11.0000 −0.643726
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 3.00000 + 5.19615i 0.174964 + 0.303046i
\(295\) 0 0
\(296\) 5.00000 0.290619
\(297\) 2.00000 0.116052
\(298\) −11.0000 19.0526i −0.637213 1.10369i
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) −2.50000 4.33013i −0.144338 0.250000i
\(301\) 4.50000 7.79423i 0.259376 0.449252i
\(302\) −10.0000 + 17.3205i −0.575435 + 0.996683i
\(303\) 10.0000 0.574485
\(304\) −3.50000 + 2.59808i −0.200739 + 0.149010i
\(305\) 0 0
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) 6.00000 10.3923i 0.342438 0.593120i −0.642447 0.766330i \(-0.722081\pi\)
0.984885 + 0.173210i \(0.0554140\pi\)
\(308\) 1.00000 + 1.73205i 0.0569803 + 0.0986928i
\(309\) −1.50000 + 2.59808i −0.0853320 + 0.147799i
\(310\) 0 0
\(311\) 10.0000 0.567048 0.283524 0.958965i \(-0.408496\pi\)
0.283524 + 0.958965i \(0.408496\pi\)
\(312\) −3.00000 −0.169842
\(313\) −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i \(-0.220905\pi\)
−0.938269 + 0.345907i \(0.887571\pi\)
\(314\) −10.5000 18.1865i −0.592549 1.02633i
\(315\) 0 0
\(316\) 1.00000 0.0562544
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) 2.00000 3.46410i 0.112154 0.194257i
\(319\) 0 0
\(320\) 0 0
\(321\) −5.00000 + 8.66025i −0.279073 + 0.483368i
\(322\) −4.00000 −0.222911
\(323\) −14.0000 + 10.3923i −0.778981 + 0.578243i
\(324\) 1.00000 0.0555556
\(325\) −7.50000 + 12.9904i −0.416025 + 0.720577i
\(326\) 5.50000 9.52628i 0.304617 0.527612i
\(327\) 7.00000 + 12.1244i 0.387101 + 0.670478i
\(328\) 2.00000 3.46410i 0.110432 0.191273i
\(329\) −5.00000 8.66025i −0.275659 0.477455i
\(330\) 0 0
\(331\) 15.0000 0.824475 0.412237 0.911077i \(-0.364747\pi\)
0.412237 + 0.911077i \(0.364747\pi\)
\(332\) −4.00000 6.92820i −0.219529 0.380235i
\(333\) 2.50000 + 4.33013i 0.136999 + 0.237289i
\(334\) −6.00000 −0.328305
\(335\) 0 0
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) 9.50000 16.4545i 0.517498 0.896333i −0.482295 0.876009i \(-0.660197\pi\)
0.999793 0.0203242i \(-0.00646983\pi\)
\(338\) −2.00000 3.46410i −0.108786 0.188422i
\(339\) 5.00000 8.66025i 0.271563 0.470360i
\(340\) 0 0
\(341\) 6.00000 0.324918
\(342\) −4.00000 1.73205i −0.216295 0.0936586i
\(343\) −13.0000 −0.701934
\(344\) −4.50000 + 7.79423i −0.242624 + 0.420237i
\(345\) 0 0
\(346\) −12.0000 20.7846i −0.645124 1.11739i
\(347\) −8.00000 + 13.8564i −0.429463 + 0.743851i −0.996826 0.0796169i \(-0.974630\pi\)
0.567363 + 0.823468i \(0.307964\pi\)
\(348\) 0 0
\(349\) −29.0000 −1.55233 −0.776167 0.630527i \(-0.782839\pi\)
−0.776167 + 0.630527i \(0.782839\pi\)
\(350\) 5.00000 0.267261
\(351\) −1.50000 2.59808i −0.0800641 0.138675i
\(352\) −1.00000 1.73205i −0.0533002 0.0923186i
\(353\) −12.0000 −0.638696 −0.319348 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) −14.0000 −0.744092
\(355\) 0 0
\(356\) 7.00000 12.1244i 0.370999 0.642590i
\(357\) 2.00000 + 3.46410i 0.105851 + 0.183340i
\(358\) 2.00000 3.46410i 0.105703 0.183083i
\(359\) 18.0000 31.1769i 0.950004 1.64545i 0.204595 0.978847i \(-0.434412\pi\)
0.745409 0.666608i \(-0.232254\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 18.0000 0.946059
\(363\) −3.50000 + 6.06218i −0.183702 + 0.318182i
\(364\) 1.50000 2.59808i 0.0786214 0.136176i
\(365\) 0 0
\(366\) −5.50000 + 9.52628i −0.287490 + 0.497947i
\(367\) −11.5000 19.9186i −0.600295 1.03974i −0.992776 0.119982i \(-0.961716\pi\)
0.392481 0.919760i \(-0.371617\pi\)
\(368\) 4.00000 0.208514
\(369\) 4.00000 0.208232
\(370\) 0 0
\(371\) 2.00000 + 3.46410i 0.103835 + 0.179847i
\(372\) 3.00000 0.155543
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) −4.00000 6.92820i −0.206835 0.358249i
\(375\) 0 0
\(376\) 5.00000 + 8.66025i 0.257855 + 0.446619i
\(377\) 0 0
\(378\) −0.500000 + 0.866025i −0.0257172 + 0.0445435i
\(379\) −13.0000 −0.667765 −0.333883 0.942615i \(-0.608359\pi\)
−0.333883 + 0.942615i \(0.608359\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) −4.00000 + 6.92820i −0.204658 + 0.354478i
\(383\) −7.00000 + 12.1244i −0.357683 + 0.619526i −0.987573 0.157159i \(-0.949767\pi\)
0.629890 + 0.776684i \(0.283100\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) −6.50000 11.2583i −0.330841 0.573034i
\(387\) −9.00000 −0.457496
\(388\) 2.00000 0.101535
\(389\) 8.00000 + 13.8564i 0.405616 + 0.702548i 0.994393 0.105748i \(-0.0337237\pi\)
−0.588777 + 0.808296i \(0.700390\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 6.00000 0.303046
\(393\) −3.00000 5.19615i −0.151330 0.262111i
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) 0 0
\(396\) 1.00000 1.73205i 0.0502519 0.0870388i
\(397\) −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i \(-0.956176\pi\)
0.614123 + 0.789210i \(0.289510\pi\)
\(398\) −5.00000 −0.250627
\(399\) 3.50000 2.59808i 0.175219 0.130066i
\(400\) −5.00000 −0.250000
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) −1.50000 + 2.59808i −0.0748132 + 0.129580i
\(403\) −4.50000 7.79423i −0.224161 0.388258i
\(404\) 5.00000 8.66025i 0.248759 0.430864i
\(405\) 0 0
\(406\) 0 0
\(407\) 10.0000 0.495682
\(408\) −2.00000 3.46410i −0.0990148 0.171499i
\(409\) 15.0000 + 25.9808i 0.741702 + 1.28467i 0.951720 + 0.306968i \(0.0993146\pi\)
−0.210017 + 0.977698i \(0.567352\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) 1.50000 + 2.59808i 0.0738997 + 0.127998i
\(413\) 7.00000 12.1244i 0.344447 0.596601i
\(414\) 2.00000 + 3.46410i 0.0982946 + 0.170251i
\(415\) 0 0
\(416\) −1.50000 + 2.59808i −0.0735436 + 0.127381i
\(417\) 19.0000 0.930434
\(418\) −7.00000 + 5.19615i −0.342381 + 0.254152i
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0 0
\(421\) −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i \(-0.911690\pi\)
0.718076 + 0.695965i \(0.245023\pi\)
\(422\) 12.5000 + 21.6506i 0.608490 + 1.05394i
\(423\) −5.00000 + 8.66025i −0.243108 + 0.421076i
\(424\) −2.00000 3.46410i −0.0971286 0.168232i
\(425\) −20.0000 −0.970143
\(426\) 14.0000 0.678302
\(427\) −5.50000 9.52628i −0.266164 0.461009i
\(428\) 5.00000 + 8.66025i 0.241684 + 0.418609i
\(429\) −6.00000 −0.289683
\(430\) 0 0
\(431\) 5.00000 + 8.66025i 0.240842 + 0.417150i 0.960954 0.276707i \(-0.0892433\pi\)
−0.720113 + 0.693857i \(0.755910\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 4.50000 + 7.79423i 0.216256 + 0.374567i 0.953660 0.300885i \(-0.0972820\pi\)
−0.737404 + 0.675452i \(0.763949\pi\)
\(434\) −1.50000 + 2.59808i −0.0720023 + 0.124712i
\(435\) 0 0
\(436\) 14.0000 0.670478
\(437\) −2.00000 17.3205i −0.0956730 0.828552i
\(438\) −11.0000 −0.525600
\(439\) −9.50000 + 16.4545i −0.453410 + 0.785330i −0.998595 0.0529862i \(-0.983126\pi\)
0.545185 + 0.838316i \(0.316459\pi\)
\(440\) 0 0
\(441\) 3.00000 + 5.19615i 0.142857 + 0.247436i
\(442\) −6.00000 + 10.3923i −0.285391 + 0.494312i
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) 5.00000 0.237289
\(445\) 0 0
\(446\) 4.50000 + 7.79423i 0.213081 + 0.369067i
\(447\) −11.0000 19.0526i −0.520282 0.901155i
\(448\) 1.00000 0.0472456
\(449\) −36.0000 −1.69895 −0.849473 0.527633i \(-0.823080\pi\)
−0.849473 + 0.527633i \(0.823080\pi\)
\(450\) −2.50000 4.33013i −0.117851 0.204124i
\(451\) 4.00000 6.92820i 0.188353 0.326236i
\(452\) −5.00000 8.66025i −0.235180 0.407344i
\(453\) −10.0000 + 17.3205i −0.469841 + 0.813788i
\(454\) 4.00000 6.92820i 0.187729 0.325157i
\(455\) 0 0
\(456\) −3.50000 + 2.59808i −0.163903 + 0.121666i
\(457\) 5.00000 0.233890 0.116945 0.993138i \(-0.462690\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(458\) −5.50000 + 9.52628i −0.256998 + 0.445134i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 0 0
\(461\) −3.00000 + 5.19615i −0.139724 + 0.242009i −0.927392 0.374091i \(-0.877955\pi\)
0.787668 + 0.616100i \(0.211288\pi\)
\(462\) 1.00000 + 1.73205i 0.0465242 + 0.0805823i
\(463\) −9.00000 −0.418265 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 9.00000 + 15.5885i 0.416917 + 0.722121i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) −3.00000 −0.138675
\(469\) −1.50000 2.59808i −0.0692636 0.119968i
\(470\) 0 0
\(471\) −10.5000 18.1865i −0.483814 0.837991i
\(472\) −7.00000 + 12.1244i −0.322201 + 0.558069i
\(473\) −9.00000 + 15.5885i −0.413820 + 0.716758i
\(474\) 1.00000 0.0459315
\(475\) 2.50000 + 21.6506i 0.114708 + 0.993399i
\(476\) 4.00000 0.183340
\(477\) 2.00000 3.46410i 0.0915737 0.158610i
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i \(-0.210436\pi\)
−0.926388 + 0.376571i \(0.877103\pi\)
\(480\) 0 0
\(481\) −7.50000 12.9904i −0.341971 0.592310i
\(482\) −25.0000 −1.13872
\(483\) −4.00000 −0.182006
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 5.50000 + 9.52628i 0.248973 + 0.431234i
\(489\) 5.50000 9.52628i 0.248719 0.430793i
\(490\) 0 0
\(491\) −15.0000 + 25.9808i −0.676941 + 1.17250i 0.298957 + 0.954267i \(0.403361\pi\)
−0.975898 + 0.218229i \(0.929972\pi\)
\(492\) 2.00000 3.46410i 0.0901670 0.156174i
\(493\) 0 0
\(494\) 12.0000 + 5.19615i 0.539906 + 0.233786i
\(495\) 0 0
\(496\) 1.50000 2.59808i 0.0673520 0.116657i
\(497\) −7.00000 + 12.1244i −0.313993 + 0.543852i
\(498\) −4.00000 6.92820i −0.179244 0.310460i
\(499\) −2.50000 + 4.33013i −0.111915 + 0.193843i −0.916542 0.399937i \(-0.869032\pi\)
0.804627 + 0.593780i \(0.202365\pi\)
\(500\) 0 0
\(501\) −6.00000 −0.268060
\(502\) 18.0000 0.803379
\(503\) −8.00000 13.8564i −0.356702 0.617827i 0.630705 0.776022i \(-0.282766\pi\)
−0.987408 + 0.158196i \(0.949432\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) 0 0
\(506\) 8.00000 0.355643
\(507\) −2.00000 3.46410i −0.0888231 0.153846i
\(508\) 4.00000 6.92820i 0.177471 0.307389i
\(509\) −13.0000 22.5167i −0.576215 0.998033i −0.995908 0.0903676i \(-0.971196\pi\)
0.419694 0.907666i \(-0.362138\pi\)
\(510\) 0 0
\(511\) 5.50000 9.52628i 0.243306 0.421418i
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 1.73205i −0.176604 0.0764719i
\(514\) 12.0000 0.529297
\(515\) 0 0
\(516\) −4.50000 + 7.79423i −0.198101 + 0.343122i
\(517\) 10.0000 + 17.3205i 0.439799 + 0.761755i
\(518\) −2.50000 + 4.33013i −0.109844 + 0.190255i
\(519\) −12.0000 20.7846i −0.526742 0.912343i
\(520\) 0 0
\(521\) 34.0000 1.48957 0.744784 0.667306i \(-0.232553\pi\)
0.744784 + 0.667306i \(0.232553\pi\)
\(522\) 0 0
\(523\) −18.5000 32.0429i −0.808949 1.40114i −0.913593 0.406630i \(-0.866704\pi\)
0.104644 0.994510i \(-0.466630\pi\)
\(524\) −6.00000 −0.262111
\(525\) 5.00000 0.218218
\(526\) 9.00000 + 15.5885i 0.392419 + 0.679689i
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) −1.00000 1.73205i −0.0435194 0.0753778i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) −14.0000 −0.607548
\(532\) −0.500000 4.33013i −0.0216777 0.187735i
\(533\) −12.0000 −0.519778
\(534\) 7.00000 12.1244i 0.302920 0.524672i
\(535\) 0 0
\(536\) 1.50000 + 2.59808i 0.0647901 + 0.112220i
\(537\) 2.00000 3.46410i 0.0863064 0.149487i
\(538\) 1.00000 + 1.73205i 0.0431131 + 0.0746740i
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) 15.5000 + 26.8468i 0.666397 + 1.15423i 0.978905 + 0.204318i \(0.0654977\pi\)
−0.312507 + 0.949915i \(0.601169\pi\)
\(542\) −8.00000 13.8564i −0.343629 0.595184i
\(543\) 18.0000 0.772454
\(544\) −4.00000 −0.171499
\(545\) 0 0
\(546\) 1.50000 2.59808i 0.0641941 0.111187i
\(547\) −5.50000 9.52628i −0.235163 0.407314i 0.724157 0.689635i \(-0.242229\pi\)
−0.959320 + 0.282321i \(0.908896\pi\)
\(548\) 3.00000 5.19615i 0.128154 0.221969i
\(549\) −5.50000 + 9.52628i −0.234734 + 0.406572i
\(550\) −10.0000 −0.426401
\(551\) 0 0
\(552\) 4.00000 0.170251
\(553\) −0.500000 + 0.866025i −0.0212622 + 0.0368271i
\(554\) −1.00000 + 1.73205i −0.0424859 + 0.0735878i
\(555\) 0 0
\(556\) 9.50000 16.4545i 0.402890 0.697826i
\(557\) −17.0000 29.4449i −0.720313 1.24762i −0.960874 0.276985i \(-0.910665\pi\)
0.240561 0.970634i \(-0.422669\pi\)
\(558\) 3.00000 0.127000
\(559\) 27.0000 1.14198
\(560\) 0 0
\(561\) −4.00000 6.92820i −0.168880 0.292509i
\(562\) 8.00000 0.337460
\(563\) −6.00000 −0.252870 −0.126435 0.991975i \(-0.540353\pi\)
−0.126435 + 0.991975i \(0.540353\pi\)
\(564\) 5.00000 + 8.66025i 0.210538 + 0.364662i
\(565\) 0 0
\(566\) −10.0000 17.3205i −0.420331 0.728035i
\(567\) −0.500000 + 0.866025i −0.0209980 + 0.0363696i
\(568\) 7.00000 12.1244i 0.293713 0.508727i
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) −3.00000 + 5.19615i −0.125436 + 0.217262i
\(573\) −4.00000 + 6.92820i −0.167102 + 0.289430i
\(574\) 2.00000 + 3.46410i 0.0834784 + 0.144589i
\(575\) 10.0000 17.3205i 0.417029 0.722315i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 1.00000 0.0415945
\(579\) −6.50000 11.2583i −0.270131 0.467880i
\(580\) 0 0
\(581\) 8.00000 0.331896
\(582\) 2.00000 0.0829027
\(583\) −4.00000 6.92820i −0.165663 0.286937i
\(584\) −5.50000 + 9.52628i −0.227592 + 0.394200i
\(585\) 0 0
\(586\) 7.00000 12.1244i 0.289167 0.500853i
\(587\) 1.00000 1.73205i 0.0412744 0.0714894i −0.844650 0.535319i \(-0.820192\pi\)
0.885925 + 0.463829i \(0.153525\pi\)
\(588\) 6.00000 0.247436
\(589\) −12.0000 5.19615i −0.494451 0.214104i
\(590\) 0 0
\(591\) −1.00000 + 1.73205i −0.0411345 + 0.0712470i
\(592\) 2.50000 4.33013i 0.102749 0.177967i
\(593\) −17.0000 29.4449i −0.698106 1.20916i −0.969122 0.246581i \(-0.920693\pi\)
0.271016 0.962575i \(-0.412640\pi\)
\(594\) 1.00000 1.73205i 0.0410305 0.0710669i
\(595\) 0 0
\(596\) −22.0000 −0.901155
\(597\) −5.00000 −0.204636
\(598\) −6.00000 10.3923i −0.245358 0.424973i
\(599\) 23.0000 + 39.8372i 0.939755 + 1.62770i 0.765928 + 0.642926i \(0.222280\pi\)
0.173826 + 0.984776i \(0.444387\pi\)
\(600\) −5.00000 −0.204124
\(601\) 27.0000 1.10135 0.550676 0.834719i \(-0.314370\pi\)
0.550676 + 0.834719i \(0.314370\pi\)
\(602\) −4.50000 7.79423i −0.183406 0.317669i
\(603\) −1.50000 + 2.59808i −0.0610847 + 0.105802i
\(604\) 10.0000 + 17.3205i 0.406894 + 0.704761i
\(605\) 0 0
\(606\) 5.00000 8.66025i 0.203111 0.351799i
\(607\) 5.00000 0.202944 0.101472 0.994838i \(-0.467645\pi\)
0.101472 + 0.994838i \(0.467645\pi\)
\(608\) 0.500000 + 4.33013i 0.0202777 + 0.175610i
\(609\) 0 0
\(610\) 0 0
\(611\) 15.0000 25.9808i 0.606835 1.05107i
\(612\) −2.00000 3.46410i −0.0808452 0.140028i
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) −6.00000 10.3923i −0.242140 0.419399i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i \(0.153988\pi\)
−0.0398207 + 0.999207i \(0.512679\pi\)
\(618\) 1.50000 + 2.59808i 0.0603388 + 0.104510i
\(619\) 1.00000 0.0401934 0.0200967 0.999798i \(-0.493603\pi\)
0.0200967 + 0.999798i \(0.493603\pi\)
\(620\) 0 0
\(621\) 2.00000 + 3.46410i 0.0802572 + 0.139010i
\(622\) 5.00000 8.66025i 0.200482 0.347245i
\(623\) 7.00000 + 12.1244i 0.280449 + 0.485752i
\(624\) −1.50000 + 2.59808i −0.0600481 + 0.104006i
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −6.00000 −0.239808
\(627\) −7.00000 + 5.19615i −0.279553 + 0.207514i
\(628\) −21.0000 −0.837991
\(629\) 10.0000 17.3205i 0.398726 0.690614i
\(630\) 0 0
\(631\) −8.50000 14.7224i −0.338380 0.586091i 0.645748 0.763550i \(-0.276545\pi\)
−0.984128 + 0.177459i \(0.943212\pi\)
\(632\) 0.500000 0.866025i 0.0198889 0.0344486i
\(633\) 12.5000 + 21.6506i 0.496830 + 0.860535i
\(634\) −12.0000 −0.476581
\(635\) 0 0
\(636\) −2.00000 3.46410i −0.0793052 0.137361i
\(637\) −9.00000 15.5885i −0.356593 0.617637i
\(638\) 0 0
\(639\) 14.0000 0.553831
\(640\) 0 0
\(641\) 7.00000 12.1244i 0.276483 0.478883i −0.694025 0.719951i \(-0.744164\pi\)
0.970508 + 0.241068i \(0.0774976\pi\)
\(642\) 5.00000 + 8.66025i 0.197334 + 0.341793i
\(643\) −18.5000 + 32.0429i −0.729569 + 1.26365i 0.227497 + 0.973779i \(0.426946\pi\)
−0.957066 + 0.289871i \(0.906387\pi\)
\(644\) −2.00000 + 3.46410i −0.0788110 + 0.136505i
\(645\) 0 0
\(646\) 2.00000 + 17.3205i 0.0786889 + 0.681466i
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −14.0000 + 24.2487i −0.549548 + 0.951845i
\(650\) 7.50000 + 12.9904i 0.294174 + 0.509525i
\(651\) −1.50000 + 2.59808i −0.0587896 + 0.101827i
\(652\) −5.50000 9.52628i −0.215397 0.373078i
\(653\) −42.0000 −1.64359 −0.821794 0.569785i \(-0.807026\pi\)
−0.821794 + 0.569785i \(0.807026\pi\)
\(654\) 14.0000 0.547443
\(655\) 0 0
\(656\) −2.00000 3.46410i −0.0780869 0.135250i
\(657\) −11.0000 −0.429151
\(658\) −10.0000 −0.389841
\(659\) 7.00000 + 12.1244i 0.272681 + 0.472298i 0.969548 0.244903i \(-0.0787562\pi\)
−0.696866 + 0.717201i \(0.745423\pi\)
\(660\) 0 0
\(661\) −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i \(-0.228968\pi\)
−0.946729 + 0.322031i \(0.895634\pi\)
\(662\) 7.50000 12.9904i 0.291496 0.504885i
\(663\) −6.00000 + 10.3923i −0.233021 + 0.403604i
\(664\) −8.00000 −0.310460
\(665\) 0 0
\(666\) 5.00000 0.193746
\(667\) 0 0
\(668\) −3.00000 + 5.19615i −0.116073 + 0.201045i
\(669\) 4.50000 + 7.79423i 0.173980 + 0.301342i
\(670\) 0 0
\(671\) 11.0000 + 19.0526i 0.424650 + 0.735516i
\(672\) 1.00000 0.0385758
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) −9.50000 16.4545i −0.365926 0.633803i
\(675\) −2.50000 4.33013i −0.0962250 0.166667i
\(676\) −4.00000 −0.153846
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −5.00000 8.66025i −0.192024 0.332595i
\(679\) −1.00000 + 1.73205i −0.0383765 + 0.0664700i
\(680\) 0 0
\(681\) 4.00000 6.92820i 0.153280 0.265489i
\(682\) 3.00000 5.19615i 0.114876 0.198971i
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) −3.50000 + 2.59808i −0.133826 + 0.0993399i
\(685\) 0 0
\(686\) −6.50000 + 11.2583i −0.248171 + 0.429845i
\(687\) −5.50000 + 9.52628i −0.209838 + 0.363450i
\(688\) 4.50000 + 7.79423i 0.171561 + 0.297152i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) −24.0000 −0.912343
\(693\) 1.00000 + 1.73205i 0.0379869 + 0.0657952i
\(694\) 8.00000 + 13.8564i 0.303676 + 0.525982i
\(695\) 0 0
\(696\) 0 0
\(697\) −8.00000 13.8564i −0.303022 0.524849i
\(698\) −14.5000 + 25.1147i −0.548833 + 0.950607i
\(699\) 9.00000 + 15.5885i 0.340411 + 0.589610i
\(700\) 2.50000 4.33013i 0.0944911 0.163663i
\(701\) 22.0000 38.1051i 0.830929 1.43921i −0.0663742 0.997795i \(-0.521143\pi\)
0.897303 0.441416i \(-0.145524\pi\)
\(702\) −3.00000 −0.113228
\(703\) −20.0000 8.66025i −0.754314 0.326628i
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) −6.00000 + 10.3923i −0.225813 + 0.391120i
\(707\) 5.00000 + 8.66025i 0.188044 + 0.325702i
\(708\) −7.00000 + 12.1244i −0.263076 + 0.455661i
\(709\) 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i \(0.0311079\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 0 0
\(711\) 1.00000 0.0375029
\(712\) −7.00000 12.1244i −0.262336 0.454379i
\(713\) 6.00000 + 10.3923i 0.224702 + 0.389195i
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) −18.0000 31.1769i −0.671754 1.16351i
\(719\) −20.0000 + 34.6410i −0.745874 + 1.29189i 0.203911 + 0.978989i \(0.434635\pi\)
−0.949785 + 0.312903i \(0.898699\pi\)
\(720\) 0 0
\(721\) −3.00000 −0.111726
\(722\) 18.5000 4.33013i 0.688499 0.161151i
\(723\) −25.0000 −0.929760
\(724\) 9.00000 15.5885i 0.334482 0.579340i
\(725\) 0 0
\(726\) 3.50000 + 6.06218i 0.129897 + 0.224989i
\(727\) −8.50000 + 14.7224i −0.315248 + 0.546025i −0.979490 0.201492i \(-0.935421\pi\)
0.664243 + 0.747517i \(0.268754\pi\)
\(728\) −1.50000 2.59808i −0.0555937 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 18.0000 + 31.1769i 0.665754 + 1.15312i
\(732\) 5.50000 + 9.52628i 0.203286 + 0.352101i
\(733\) −2.00000 −0.0738717 −0.0369358 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) −23.0000 −0.848945
\(735\) 0 0
\(736\) 2.00000 3.46410i 0.0737210 0.127688i
\(737\) 3.00000 + 5.19615i 0.110506 + 0.191403i
\(738\) 2.00000 3.46410i 0.0736210 0.127515i
\(739\) 2.50000 4.33013i 0.0919640 0.159286i −0.816373 0.577524i \(-0.804019\pi\)
0.908337 + 0.418238i \(0.137352\pi\)
\(740\) 0 0
\(741\) 12.0000 + 5.19615i 0.440831 + 0.190885i
\(742\) 4.00000 0.146845
\(743\) 9.00000 15.5885i 0.330178 0.571885i −0.652369 0.757902i \(-0.726225\pi\)
0.982547 + 0.186017i \(0.0595579\pi\)
\(744\) 1.50000 2.59808i 0.0549927 0.0952501i
\(745\) 0 0
\(746\) 13.0000 22.5167i 0.475964 0.824394i
\(747\) −4.00000 6.92820i −0.146352 0.253490i
\(748\) −8.00000 −0.292509
\(749\) −10.0000 −0.365392
\(750\) 0 0
\(751\) −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i \(-0.242893\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(752\) 10.0000 0.364662
\(753\) 18.0000 0.655956
\(754\) 0 0
\(755\) 0 0
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) −2.50000 + 4.33013i −0.0908640 + 0.157381i −0.907875 0.419241i \(-0.862296\pi\)
0.817011 + 0.576622i \(0.195630\pi\)
\(758\) −6.50000 + 11.2583i −0.236091 + 0.408921i
\(759\) 8.00000 0.290382
\(760\) 0 0
\(761\) −34.0000 −1.23250 −0.616250 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(762\) 4.00000 6.92820i 0.144905 0.250982i
\(763\) −7.00000 + 12.1244i −0.253417 + 0.438931i
\(764\) 4.00000 + 6.92820i 0.144715 + 0.250654i
\(765\) 0 0
\(766\) 7.00000 + 12.1244i 0.252920 + 0.438071i
\(767\) 42.0000 1.51653
\(768\) −1.00000 −0.0360844
\(769\) −13.5000 23.3827i −0.486822 0.843201i 0.513063 0.858351i \(-0.328511\pi\)
−0.999885 + 0.0151499i \(0.995177\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) −13.0000 −0.467880
\(773\) 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i \(-0.0617373\pi\)
−0.657542 + 0.753418i \(0.728404\pi\)
\(774\) −4.50000 + 7.79423i −0.161749 + 0.280158i
\(775\) −7.50000 12.9904i −0.269408 0.466628i
\(776\) 1.00000 1.73205i 0.0358979 0.0621770i
\(777\) −2.50000 + 4.33013i −0.0896870 + 0.155342i
\(778\) 16.0000 0.573628
\(779\) −14.0000 + 10.3923i −0.501602 + 0.372343i
\(780\) 0 0
\(781\) 14.0000 24.2487i 0.500959 0.867687i
\(782\) 8.00000 13.8564i 0.286079 0.495504i
\(783\) 0 0
\(784\) 3.00000 5.19615i 0.107143 0.185577i
\(785\) 0 0
\(786\) −6.00000 <