Properties

Label 114.2.e.a.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.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{10} +2.00000 q^{11} -1.00000 q^{12} +(3.50000 + 6.06218i) q^{13} +(1.50000 - 2.59808i) q^{14} +(-2.00000 - 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} -4.00000 q^{20} +(-1.50000 + 2.59808i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-5.50000 - 9.52628i) q^{25} -7.00000 q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-2.00000 - 3.46410i) q^{29} +4.00000 q^{30} +1.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} +(-6.00000 + 10.3923i) q^{35} +(-0.500000 + 0.866025i) q^{36} +7.00000 q^{37} +(0.500000 - 4.33013i) q^{38} +7.00000 q^{39} +(2.00000 - 3.46410i) q^{40} +(-2.00000 + 3.46410i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(-3.50000 + 6.06218i) q^{43} +(-1.00000 - 1.73205i) q^{44} -4.00000 q^{45} -4.00000 q^{46} +(-1.00000 - 1.73205i) q^{47} +(0.500000 + 0.866025i) q^{48} +2.00000 q^{49} +11.0000 q^{50} +(3.50000 - 6.06218i) q^{52} +(2.00000 + 3.46410i) q^{53} +(0.500000 - 0.866025i) q^{54} +(4.00000 - 6.92820i) q^{55} -3.00000 q^{56} +(-0.500000 + 4.33013i) q^{57} +4.00000 q^{58} +(3.00000 - 5.19615i) q^{59} +(-2.00000 + 3.46410i) q^{60} +(0.500000 + 0.866025i) q^{61} +(-0.500000 + 0.866025i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +28.0000 q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.50000 - 2.59808i) q^{67} +4.00000 q^{69} +(-6.00000 - 10.3923i) q^{70} +(-1.00000 + 1.73205i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.50000 - 2.59808i) q^{73} +(-3.50000 + 6.06218i) q^{74} -11.0000 q^{75} +(3.50000 + 2.59808i) q^{76} -6.00000 q^{77} +(-3.50000 + 6.06218i) q^{78} +(-2.50000 + 4.33013i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.00000 - 3.46410i) q^{82} -12.0000 q^{83} +3.00000 q^{84} +(-3.50000 - 6.06218i) q^{86} -4.00000 q^{87} +2.00000 q^{88} +(-9.00000 - 15.5885i) q^{89} +(2.00000 - 3.46410i) q^{90} +(-10.5000 - 18.1865i) q^{91} +(2.00000 - 3.46410i) q^{92} +(0.500000 - 0.866025i) q^{93} +2.00000 q^{94} +(-2.00000 + 17.3205i) q^{95} -1.00000 q^{96} +(-5.00000 + 8.66025i) q^{97} +(-1.00000 + 1.73205i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + 4q^{5} + q^{6} - 6q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + 4q^{5} + q^{6} - 6q^{7} + 2q^{8} - q^{9} + 4q^{10} + 4q^{11} - 2q^{12} + 7q^{13} + 3q^{14} - 4q^{15} - q^{16} + 2q^{18} - 8q^{19} - 8q^{20} - 3q^{21} - 2q^{22} + 4q^{23} + q^{24} - 11q^{25} - 14q^{26} - 2q^{27} + 3q^{28} - 4q^{29} + 8q^{30} + 2q^{31} - q^{32} + 2q^{33} - 12q^{35} - q^{36} + 14q^{37} + q^{38} + 14q^{39} + 4q^{40} - 4q^{41} - 3q^{42} - 7q^{43} - 2q^{44} - 8q^{45} - 8q^{46} - 2q^{47} + q^{48} + 4q^{49} + 22q^{50} + 7q^{52} + 4q^{53} + q^{54} + 8q^{55} - 6q^{56} - q^{57} + 8q^{58} + 6q^{59} - 4q^{60} + q^{61} - q^{62} + 3q^{63} + 2q^{64} + 56q^{65} + 2q^{66} - 3q^{67} + 8q^{69} - 12q^{70} - 2q^{71} - q^{72} + 3q^{73} - 7q^{74} - 22q^{75} + 7q^{76} - 12q^{77} - 7q^{78} - 5q^{79} + 4q^{80} - q^{81} - 4q^{82} - 24q^{83} + 6q^{84} - 7q^{86} - 8q^{87} + 4q^{88} - 18q^{89} + 4q^{90} - 21q^{91} + 4q^{92} + q^{93} + 4q^{94} - 4q^{95} - 2q^{96} - 10q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

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
\(5\) 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 2.00000 + 3.46410i 0.632456 + 1.09545i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.50000 + 6.06218i 0.970725 + 1.68135i 0.693375 + 0.720577i \(0.256123\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 1.50000 2.59808i 0.400892 0.694365i
\(15\) −2.00000 3.46410i −0.516398 0.894427i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.00000 + 1.73205i −0.917663 + 0.397360i
\(20\) −4.00000 −0.894427
\(21\) −1.50000 + 2.59808i −0.327327 + 0.566947i
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) −7.00000 −1.37281
\(27\) −1.00000 −0.192450
\(28\) 1.50000 + 2.59808i 0.283473 + 0.490990i
\(29\) −2.00000 3.46410i −0.371391 0.643268i 0.618389 0.785872i \(-0.287786\pi\)
−0.989780 + 0.142605i \(0.954452\pi\)
\(30\) 4.00000 0.730297
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) 0 0
\(35\) −6.00000 + 10.3923i −1.01419 + 1.75662i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 0.500000 4.33013i 0.0811107 0.702439i
\(39\) 7.00000 1.12090
\(40\) 2.00000 3.46410i 0.316228 0.547723i
\(41\) −2.00000 + 3.46410i −0.312348 + 0.541002i −0.978870 0.204483i \(-0.934449\pi\)
0.666523 + 0.745485i \(0.267782\pi\)
\(42\) −1.50000 2.59808i −0.231455 0.400892i
\(43\) −3.50000 + 6.06218i −0.533745 + 0.924473i 0.465478 + 0.885059i \(0.345882\pi\)
−0.999223 + 0.0394140i \(0.987451\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) −4.00000 −0.596285
\(46\) −4.00000 −0.589768
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 2.00000 0.285714
\(50\) 11.0000 1.55563
\(51\) 0 0
\(52\) 3.50000 6.06218i 0.485363 0.840673i
\(53\) 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
\(55\) 4.00000 6.92820i 0.539360 0.934199i
\(56\) −3.00000 −0.400892
\(57\) −0.500000 + 4.33013i −0.0662266 + 0.573539i
\(58\) 4.00000 0.525226
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) −2.00000 + 3.46410i −0.258199 + 0.447214i
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −0.500000 + 0.866025i −0.0635001 + 0.109985i
\(63\) 1.50000 + 2.59808i 0.188982 + 0.327327i
\(64\) 1.00000 0.125000
\(65\) 28.0000 3.47297
\(66\) 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 \(0.891996\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) −6.00000 10.3923i −0.717137 1.24212i
\(71\) −1.00000 + 1.73205i −0.118678 + 0.205557i −0.919244 0.393688i \(-0.871199\pi\)
0.800566 + 0.599245i \(0.204532\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 1.50000 2.59808i 0.175562 0.304082i −0.764794 0.644275i \(-0.777159\pi\)
0.940356 + 0.340193i \(0.110493\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) −11.0000 −1.27017
\(76\) 3.50000 + 2.59808i 0.401478 + 0.298020i
\(77\) −6.00000 −0.683763
\(78\) −3.50000 + 6.06218i −0.396297 + 0.686406i
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) 2.00000 + 3.46410i 0.223607 + 0.387298i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.00000 3.46410i −0.220863 0.382546i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 3.00000 0.327327
\(85\) 0 0
\(86\) −3.50000 6.06218i −0.377415 0.653701i
\(87\) −4.00000 −0.428845
\(88\) 2.00000 0.213201
\(89\) −9.00000 15.5885i −0.953998 1.65237i −0.736644 0.676280i \(-0.763591\pi\)
−0.217354 0.976093i \(-0.569742\pi\)
\(90\) 2.00000 3.46410i 0.210819 0.365148i
\(91\) −10.5000 18.1865i −1.10070 1.90647i
\(92\) 2.00000 3.46410i 0.208514 0.361158i
\(93\) 0.500000 0.866025i 0.0518476 0.0898027i
\(94\) 2.00000 0.206284
\(95\) −2.00000 + 17.3205i −0.205196 + 1.77705i
\(96\) −1.00000 −0.102062
\(97\) −5.00000 + 8.66025i −0.507673 + 0.879316i 0.492287 + 0.870433i \(0.336161\pi\)
−0.999961 + 0.00888289i \(0.997172\pi\)
\(98\) −1.00000 + 1.73205i −0.101015 + 0.174964i
\(99\) −1.00000 1.73205i −0.100504 0.174078i
\(100\) −5.50000 + 9.52628i −0.550000 + 0.952628i
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) 9.00000 0.886796 0.443398 0.896325i \(-0.353773\pi\)
0.443398 + 0.896325i \(0.353773\pi\)
\(104\) 3.50000 + 6.06218i 0.343203 + 0.594445i
\(105\) 6.00000 + 10.3923i 0.585540 + 1.01419i
\(106\) −4.00000 −0.388514
\(107\) 2.00000 0.193347 0.0966736 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −3.00000 + 5.19615i −0.287348 + 0.497701i −0.973176 0.230063i \(-0.926107\pi\)
0.685828 + 0.727764i \(0.259440\pi\)
\(110\) 4.00000 + 6.92820i 0.381385 + 0.660578i
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 1.50000 2.59808i 0.141737 0.245495i
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −3.50000 2.59808i −0.327805 0.243332i
\(115\) 16.0000 1.49201
\(116\) −2.00000 + 3.46410i −0.185695 + 0.321634i
\(117\) 3.50000 6.06218i 0.323575 0.560449i
\(118\) 3.00000 + 5.19615i 0.276172 + 0.478345i
\(119\) 0 0
\(120\) −2.00000 3.46410i −0.182574 0.316228i
\(121\) −7.00000 −0.636364
\(122\) −1.00000 −0.0905357
\(123\) 2.00000 + 3.46410i 0.180334 + 0.312348i
\(124\) −0.500000 0.866025i −0.0449013 0.0777714i
\(125\) −24.0000 −2.14663
\(126\) −3.00000 −0.267261
\(127\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 3.50000 + 6.06218i 0.308158 + 0.533745i
\(130\) −14.0000 + 24.2487i −1.22788 + 2.12675i
\(131\) 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) −2.00000 −0.174078
\(133\) 12.0000 5.19615i 1.04053 0.450564i
\(134\) 3.00000 0.259161
\(135\) −2.00000 + 3.46410i −0.172133 + 0.298142i
\(136\) 0 0
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) −2.00000 + 3.46410i −0.170251 + 0.294884i
\(139\) −10.5000 18.1865i −0.890598 1.54256i −0.839159 0.543885i \(-0.816953\pi\)
−0.0514389 0.998676i \(-0.516381\pi\)
\(140\) 12.0000 1.01419
\(141\) −2.00000 −0.168430
\(142\) −1.00000 1.73205i −0.0839181 0.145350i
\(143\) 7.00000 + 12.1244i 0.585369 + 1.01389i
\(144\) 1.00000 0.0833333
\(145\) −16.0000 −1.32873
\(146\) 1.50000 + 2.59808i 0.124141 + 0.215018i
\(147\) 1.00000 1.73205i 0.0824786 0.142857i
\(148\) −3.50000 6.06218i −0.287698 0.498308i
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 5.50000 9.52628i 0.449073 0.777817i
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) −4.00000 + 1.73205i −0.324443 + 0.140488i
\(153\) 0 0
\(154\) 3.00000 5.19615i 0.241747 0.418718i
\(155\) 2.00000 3.46410i 0.160644 0.278243i
\(156\) −3.50000 6.06218i −0.280224 0.485363i
\(157\) −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) −2.50000 4.33013i −0.198889 0.344486i
\(159\) 4.00000 0.317221
\(160\) −4.00000 −0.316228
\(161\) −6.00000 10.3923i −0.472866 0.819028i
\(162\) −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
\(165\) −4.00000 6.92820i −0.311400 0.539360i
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i \(-0.241242\pi\)
−0.958440 + 0.285295i \(0.907908\pi\)
\(168\) −1.50000 + 2.59808i −0.115728 + 0.200446i
\(169\) −18.0000 + 31.1769i −1.38462 + 2.39822i
\(170\) 0 0
\(171\) 3.50000 + 2.59808i 0.267652 + 0.198680i
\(172\) 7.00000 0.533745
\(173\) −6.00000 + 10.3923i −0.456172 + 0.790112i −0.998755 0.0498898i \(-0.984113\pi\)
0.542583 + 0.840002i \(0.317446\pi\)
\(174\) 2.00000 3.46410i 0.151620 0.262613i
\(175\) 16.5000 + 28.5788i 1.24728 + 2.16036i
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) −3.00000 5.19615i −0.225494 0.390567i
\(178\) 18.0000 1.34916
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 2.00000 + 3.46410i 0.149071 + 0.258199i
\(181\) 1.00000 + 1.73205i 0.0743294 + 0.128742i 0.900794 0.434246i \(-0.142985\pi\)
−0.826465 + 0.562988i \(0.809652\pi\)
\(182\) 21.0000 1.55662
\(183\) 1.00000 0.0739221
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) 14.0000 24.2487i 1.02930 1.78280i
\(186\) 0.500000 + 0.866025i 0.0366618 + 0.0635001i
\(187\) 0 0
\(188\) −1.00000 + 1.73205i −0.0729325 + 0.126323i
\(189\) 3.00000 0.218218
\(190\) −14.0000 10.3923i −1.01567 0.753937i
\(191\) −20.0000 −1.44715 −0.723575 0.690246i \(-0.757502\pi\)
−0.723575 + 0.690246i \(0.757502\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 10.5000 18.1865i 0.755807 1.30910i −0.189166 0.981945i \(-0.560578\pi\)
0.944972 0.327150i \(-0.106088\pi\)
\(194\) −5.00000 8.66025i −0.358979 0.621770i
\(195\) 14.0000 24.2487i 1.00256 1.73649i
\(196\) −1.00000 1.73205i −0.0714286 0.123718i
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 2.00000 0.142134
\(199\) 3.50000 + 6.06218i 0.248108 + 0.429736i 0.963001 0.269498i \(-0.0868577\pi\)
−0.714893 + 0.699234i \(0.753524\pi\)
\(200\) −5.50000 9.52628i −0.388909 0.673610i
\(201\) −3.00000 −0.211604
\(202\) 2.00000 0.140720
\(203\) 6.00000 + 10.3923i 0.421117 + 0.729397i
\(204\) 0 0
\(205\) 8.00000 + 13.8564i 0.558744 + 0.967773i
\(206\) −4.50000 + 7.79423i −0.313530 + 0.543050i
\(207\) 2.00000 3.46410i 0.139010 0.240772i
\(208\) −7.00000 −0.485363
\(209\) −8.00000 + 3.46410i −0.553372 + 0.239617i
\(210\) −12.0000 −0.828079
\(211\) −4.50000 + 7.79423i −0.309793 + 0.536577i −0.978317 0.207114i \(-0.933593\pi\)
0.668524 + 0.743690i \(0.266926\pi\)
\(212\) 2.00000 3.46410i 0.137361 0.237915i
\(213\) 1.00000 + 1.73205i 0.0685189 + 0.118678i
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) 14.0000 + 24.2487i 0.954792 + 1.65375i
\(216\) −1.00000 −0.0680414
\(217\) −3.00000 −0.203653
\(218\) −3.00000 5.19615i −0.203186 0.351928i
\(219\) −1.50000 2.59808i −0.101361 0.175562i
\(220\) −8.00000 −0.539360
\(221\) 0 0
\(222\) 3.50000 + 6.06218i 0.234905 + 0.406867i
\(223\) −2.50000 + 4.33013i −0.167412 + 0.289967i −0.937509 0.347960i \(-0.886874\pi\)
0.770097 + 0.637927i \(0.220208\pi\)
\(224\) 1.50000 + 2.59808i 0.100223 + 0.173591i
\(225\) −5.50000 + 9.52628i −0.366667 + 0.635085i
\(226\) −1.00000 + 1.73205i −0.0665190 + 0.115214i
\(227\) 4.00000 0.265489 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) 4.00000 1.73205i 0.264906 0.114708i
\(229\) −7.00000 −0.462573 −0.231287 0.972886i \(-0.574293\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) −8.00000 + 13.8564i −0.527504 + 0.913664i
\(231\) −3.00000 + 5.19615i −0.197386 + 0.341882i
\(232\) −2.00000 3.46410i −0.131306 0.227429i
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 3.50000 + 6.06218i 0.228802 + 0.396297i
\(235\) −8.00000 −0.521862
\(236\) −6.00000 −0.390567
\(237\) 2.50000 + 4.33013i 0.162392 + 0.281272i
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 4.00000 0.258199
\(241\) −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i \(-0.176921\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(242\) 3.50000 6.06218i 0.224989 0.389692i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0.500000 0.866025i 0.0320092 0.0554416i
\(245\) 4.00000 6.92820i 0.255551 0.442627i
\(246\) −4.00000 −0.255031
\(247\) −24.5000 18.1865i −1.55890 1.15718i
\(248\) 1.00000 0.0635001
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 12.0000 20.7846i 0.758947 1.31453i
\(251\) −7.00000 12.1244i −0.441836 0.765283i 0.555990 0.831189i \(-0.312339\pi\)
−0.997826 + 0.0659066i \(0.979006\pi\)
\(252\) 1.50000 2.59808i 0.0944911 0.163663i
\(253\) 4.00000 + 6.92820i 0.251478 + 0.435572i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 14.0000 + 24.2487i 0.873296 + 1.51259i 0.858567 + 0.512702i \(0.171355\pi\)
0.0147291 + 0.999892i \(0.495311\pi\)
\(258\) −7.00000 −0.435801
\(259\) −21.0000 −1.30488
\(260\) −14.0000 24.2487i −0.868243 1.50384i
\(261\) −2.00000 + 3.46410i −0.123797 + 0.214423i
\(262\) 9.00000 + 15.5885i 0.556022 + 0.963058i
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 1.00000 1.73205i 0.0615457 0.106600i
\(265\) 16.0000 0.982872
\(266\) −1.50000 + 12.9904i −0.0919709 + 0.796491i
\(267\) −18.0000 −1.10158
\(268\) −1.50000 + 2.59808i −0.0916271 + 0.158703i
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) −2.00000 3.46410i −0.121716 0.210819i
\(271\) 4.00000 6.92820i 0.242983 0.420858i −0.718580 0.695444i \(-0.755208\pi\)
0.961563 + 0.274586i \(0.0885408\pi\)
\(272\) 0 0
\(273\) −21.0000 −1.27098
\(274\) −2.00000 −0.120824
\(275\) −11.0000 19.0526i −0.663325 1.14891i
\(276\) −2.00000 3.46410i −0.120386 0.208514i
\(277\) −26.0000 −1.56219 −0.781094 0.624413i \(-0.785338\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 21.0000 1.25950
\(279\) −0.500000 0.866025i −0.0299342 0.0518476i
\(280\) −6.00000 + 10.3923i −0.358569 + 0.621059i
\(281\) −2.00000 3.46410i −0.119310 0.206651i 0.800184 0.599754i \(-0.204735\pi\)
−0.919494 + 0.393103i \(0.871402\pi\)
\(282\) 1.00000 1.73205i 0.0595491 0.103142i
\(283\) 6.00000 10.3923i 0.356663 0.617758i −0.630738 0.775996i \(-0.717248\pi\)
0.987401 + 0.158237i \(0.0505811\pi\)
\(284\) 2.00000 0.118678
\(285\) 14.0000 + 10.3923i 0.829288 + 0.615587i
\(286\) −14.0000 −0.827837
\(287\) 6.00000 10.3923i 0.354169 0.613438i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 8.00000 13.8564i 0.469776 0.813676i
\(291\) 5.00000 + 8.66025i 0.293105 + 0.507673i
\(292\) −3.00000 −0.175562
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 1.00000 + 1.73205i 0.0583212 + 0.101015i
\(295\) −12.0000 20.7846i −0.698667 1.21013i
\(296\) 7.00000 0.406867
\(297\) −2.00000 −0.116052
\(298\) 9.00000 + 15.5885i 0.521356 + 0.903015i
\(299\) −14.0000 + 24.2487i −0.809641 + 1.40234i
\(300\) 5.50000 + 9.52628i 0.317543 + 0.550000i
\(301\) 10.5000 18.1865i 0.605210 1.04825i
\(302\) −10.0000 + 17.3205i −0.575435 + 0.996683i
\(303\) −2.00000 −0.114897
\(304\) 0.500000 4.33013i 0.0286770 0.248350i
\(305\) 4.00000 0.229039
\(306\) 0 0
\(307\) −6.00000 + 10.3923i −0.342438 + 0.593120i −0.984885 0.173210i \(-0.944586\pi\)
0.642447 + 0.766330i \(0.277919\pi\)
\(308\) 3.00000 + 5.19615i 0.170941 + 0.296078i
\(309\) 4.50000 7.79423i 0.255996 0.443398i
\(310\) 2.00000 + 3.46410i 0.113592 + 0.196748i
\(311\) 34.0000 1.92796 0.963982 0.265969i \(-0.0856919\pi\)
0.963982 + 0.265969i \(0.0856919\pi\)
\(312\) 7.00000 0.396297
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) −3.50000 6.06218i −0.197516 0.342108i
\(315\) 12.0000 0.676123
\(316\) 5.00000 0.281272
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) −2.00000 + 3.46410i −0.112154 + 0.194257i
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) 2.00000 3.46410i 0.111803 0.193649i
\(321\) 1.00000 1.73205i 0.0558146 0.0966736i
\(322\) 12.0000 0.668734
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 38.5000 66.6840i 2.13560 3.69896i
\(326\) −5.50000 + 9.52628i −0.304617 + 0.527612i
\(327\) 3.00000 + 5.19615i 0.165900 + 0.287348i
\(328\) −2.00000 + 3.46410i −0.110432 + 0.191273i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) 8.00000 0.440386
\(331\) 23.0000 1.26419 0.632097 0.774889i \(-0.282194\pi\)
0.632097 + 0.774889i \(0.282194\pi\)
\(332\) 6.00000 + 10.3923i 0.329293 + 0.570352i
\(333\) −3.50000 6.06218i −0.191799 0.332205i
\(334\) 6.00000 0.328305
\(335\) −12.0000 −0.655630
\(336\) −1.50000 2.59808i −0.0818317 0.141737i
\(337\) −6.50000 + 11.2583i −0.354078 + 0.613280i −0.986960 0.160968i \(-0.948538\pi\)
0.632882 + 0.774248i \(0.281872\pi\)
\(338\) −18.0000 31.1769i −0.979071 1.69580i
\(339\) 1.00000 1.73205i 0.0543125 0.0940721i
\(340\) 0 0
\(341\) 2.00000 0.108306
\(342\) −4.00000 + 1.73205i −0.216295 + 0.0936586i
\(343\) 15.0000 0.809924
\(344\) −3.50000 + 6.06218i −0.188707 + 0.326851i
\(345\) 8.00000 13.8564i 0.430706 0.746004i
\(346\) −6.00000 10.3923i −0.322562 0.558694i
\(347\) −14.0000 + 24.2487i −0.751559 + 1.30174i 0.195507 + 0.980702i \(0.437365\pi\)
−0.947067 + 0.321037i \(0.895969\pi\)
\(348\) 2.00000 + 3.46410i 0.107211 + 0.185695i
\(349\) 31.0000 1.65939 0.829696 0.558216i \(-0.188514\pi\)
0.829696 + 0.558216i \(0.188514\pi\)
\(350\) −33.0000 −1.76392
\(351\) −3.50000 6.06218i −0.186816 0.323575i
\(352\) −1.00000 1.73205i −0.0533002 0.0923186i
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 6.00000 0.318896
\(355\) 4.00000 + 6.92820i 0.212298 + 0.367711i
\(356\) −9.00000 + 15.5885i −0.476999 + 0.826187i
\(357\) 0 0
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i \(-0.730769\pi\)
0.979791 + 0.200026i \(0.0641026\pi\)
\(360\) −4.00000 −0.210819
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) −2.00000 −0.105118
\(363\) −3.50000 + 6.06218i −0.183702 + 0.318182i
\(364\) −10.5000 + 18.1865i −0.550350 + 0.953233i
\(365\) −6.00000 10.3923i −0.314054 0.543958i
\(366\) −0.500000 + 0.866025i −0.0261354 + 0.0452679i
\(367\) −9.50000 16.4545i −0.495896 0.858917i 0.504093 0.863649i \(-0.331827\pi\)
−0.999989 + 0.00473247i \(0.998494\pi\)
\(368\) −4.00000 −0.208514
\(369\) 4.00000 0.208232
\(370\) 14.0000 + 24.2487i 0.727825 + 1.26063i
\(371\) −6.00000 10.3923i −0.311504 0.539542i
\(372\) −1.00000 −0.0518476
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) −12.0000 + 20.7846i −0.619677 + 1.07331i
\(376\) −1.00000 1.73205i −0.0515711 0.0893237i
\(377\) 14.0000 24.2487i 0.721037 1.24887i
\(378\) −1.50000 + 2.59808i −0.0771517 + 0.133631i
\(379\) −21.0000 −1.07870 −0.539349 0.842082i \(-0.681330\pi\)
−0.539349 + 0.842082i \(0.681330\pi\)
\(380\) 16.0000 6.92820i 0.820783 0.355409i
\(381\) 0 0
\(382\) 10.0000 17.3205i 0.511645 0.886194i
\(383\) 7.00000 12.1244i 0.357683 0.619526i −0.629890 0.776684i \(-0.716900\pi\)
0.987573 + 0.157159i \(0.0502334\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) −12.0000 + 20.7846i −0.611577 + 1.05928i
\(386\) 10.5000 + 18.1865i 0.534436 + 0.925670i
\(387\) 7.00000 0.355830
\(388\) 10.0000 0.507673
\(389\) 12.0000 + 20.7846i 0.608424 + 1.05382i 0.991500 + 0.130105i \(0.0415314\pi\)
−0.383076 + 0.923717i \(0.625135\pi\)
\(390\) 14.0000 + 24.2487i 0.708918 + 1.22788i
\(391\) 0 0
\(392\) 2.00000 0.101015
\(393\) −9.00000 15.5885i −0.453990 0.786334i
\(394\) 5.00000 8.66025i 0.251896 0.436297i
\(395\) 10.0000 + 17.3205i 0.503155 + 0.871489i
\(396\) −1.00000 + 1.73205i −0.0502519 + 0.0870388i
\(397\) 6.50000 11.2583i 0.326226 0.565039i −0.655534 0.755166i \(-0.727556\pi\)
0.981760 + 0.190126i \(0.0608897\pi\)
\(398\) −7.00000 −0.350878
\(399\) 1.50000 12.9904i 0.0750939 0.650332i
\(400\) 11.0000 0.550000
\(401\) −5.00000 + 8.66025i −0.249688 + 0.432472i −0.963439 0.267927i \(-0.913661\pi\)
0.713751 + 0.700399i \(0.246995\pi\)
\(402\) 1.50000 2.59808i 0.0748132 0.129580i
\(403\) 3.50000 + 6.06218i 0.174347 + 0.301979i
\(404\) −1.00000 + 1.73205i −0.0497519 + 0.0861727i
\(405\) 2.00000 + 3.46410i 0.0993808 + 0.172133i
\(406\) −12.0000 −0.595550
\(407\) 14.0000 0.693954
\(408\) 0 0
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) −16.0000 −0.790184
\(411\) 2.00000 0.0986527
\(412\) −4.50000 7.79423i −0.221699 0.383994i
\(413\) −9.00000 + 15.5885i −0.442861 + 0.767058i
\(414\) 2.00000 + 3.46410i 0.0982946 + 0.170251i
\(415\) −24.0000 + 41.5692i −1.17811 + 2.04055i
\(416\) 3.50000 6.06218i 0.171602 0.297223i
\(417\) −21.0000 −1.02837
\(418\) 1.00000 8.66025i 0.0489116 0.423587i
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 6.00000 10.3923i 0.292770 0.507093i
\(421\) −13.0000 + 22.5167i −0.633581 + 1.09739i 0.353233 + 0.935536i \(0.385082\pi\)
−0.986814 + 0.161859i \(0.948251\pi\)
\(422\) −4.50000 7.79423i −0.219057 0.379417i
\(423\) −1.00000 + 1.73205i −0.0486217 + 0.0842152i
\(424\) 2.00000 + 3.46410i 0.0971286 + 0.168232i
\(425\) 0 0
\(426\) −2.00000 −0.0969003
\(427\) −1.50000 2.59808i −0.0725901 0.125730i
\(428\) −1.00000 1.73205i −0.0483368 0.0837218i
\(429\) 14.0000 0.675926
\(430\) −28.0000 −1.35028
\(431\) −3.00000 5.19615i −0.144505 0.250290i 0.784683 0.619897i \(-0.212826\pi\)
−0.929188 + 0.369607i \(0.879492\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −11.5000 19.9186i −0.552655 0.957226i −0.998082 0.0619079i \(-0.980282\pi\)
0.445427 0.895318i \(-0.353052\pi\)
\(434\) 1.50000 2.59808i 0.0720023 0.124712i
\(435\) −8.00000 + 13.8564i −0.383571 + 0.664364i
\(436\) 6.00000 0.287348
\(437\) −14.0000 10.3923i −0.669711 0.497131i
\(438\) 3.00000 0.143346
\(439\) −11.5000 + 19.9186i −0.548865 + 0.950662i 0.449488 + 0.893287i \(0.351607\pi\)
−0.998353 + 0.0573756i \(0.981727\pi\)
\(440\) 4.00000 6.92820i 0.190693 0.330289i
\(441\) −1.00000 1.73205i −0.0476190 0.0824786i
\(442\) 0 0
\(443\) −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) −7.00000 −0.332205
\(445\) −72.0000 −3.41313
\(446\) −2.50000 4.33013i −0.118378 0.205037i
\(447\) −9.00000 15.5885i −0.425685 0.737309i
\(448\) −3.00000 −0.141737
\(449\) 16.0000 0.755087 0.377543 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) −5.50000 9.52628i −0.259272 0.449073i
\(451\) −4.00000 + 6.92820i −0.188353 + 0.326236i
\(452\) −1.00000 1.73205i −0.0470360 0.0814688i
\(453\) 10.0000 17.3205i 0.469841 0.813788i
\(454\) −2.00000 + 3.46410i −0.0938647 + 0.162578i
\(455\) −84.0000 −3.93798
\(456\) −0.500000 + 4.33013i −0.0234146 + 0.202777i
\(457\) 29.0000 1.35656 0.678281 0.734802i \(-0.262725\pi\)
0.678281 + 0.734802i \(0.262725\pi\)
\(458\) 3.50000 6.06218i 0.163544 0.283267i
\(459\) 0 0
\(460\) −8.00000 13.8564i −0.373002 0.646058i
\(461\) 17.0000 29.4449i 0.791769 1.37138i −0.133102 0.991102i \(-0.542494\pi\)
0.924871 0.380282i \(-0.124173\pi\)
\(462\) −3.00000 5.19615i −0.139573 0.241747i
\(463\) 19.0000 0.883005 0.441502 0.897260i \(-0.354446\pi\)
0.441502 + 0.897260i \(0.354446\pi\)
\(464\) 4.00000 0.185695
\(465\) −2.00000 3.46410i −0.0927478 0.160644i
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) −7.00000 −0.323575
\(469\) 4.50000 + 7.79423i 0.207791 + 0.359904i
\(470\) 4.00000 6.92820i 0.184506 0.319574i
\(471\) 3.50000 + 6.06218i 0.161271 + 0.279330i
\(472\) 3.00000 5.19615i 0.138086 0.239172i
\(473\) −7.00000 + 12.1244i −0.321860 + 0.557478i
\(474\) −5.00000 −0.229658
\(475\) 38.5000 + 28.5788i 1.76650 + 1.31129i
\(476\) 0 0
\(477\) 2.00000 3.46410i 0.0915737 0.158610i
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) −17.0000 29.4449i −0.776750 1.34537i −0.933806 0.357780i \(-0.883534\pi\)
0.157056 0.987590i \(-0.449800\pi\)
\(480\) −2.00000 + 3.46410i −0.0912871 + 0.158114i
\(481\) 24.5000 + 42.4352i 1.11710 + 1.93488i
\(482\) 1.00000 0.0455488
\(483\) −12.0000 −0.546019
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 20.0000 + 34.6410i 0.908153 + 1.57297i
\(486\) −1.00000 −0.0453609
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 0.500000 + 0.866025i 0.0226339 + 0.0392031i
\(489\) 5.50000 9.52628i 0.248719 0.430793i
\(490\) 4.00000 + 6.92820i 0.180702 + 0.312984i
\(491\) −13.0000 + 22.5167i −0.586682 + 1.01616i 0.407982 + 0.912990i \(0.366233\pi\)
−0.994663 + 0.103173i \(0.967101\pi\)
\(492\) 2.00000 3.46410i 0.0901670 0.156174i
\(493\) 0 0
\(494\) 28.0000 12.1244i 1.25978 0.545501i
\(495\) −8.00000 −0.359573
\(496\) −0.500000 + 0.866025i −0.0224507 + 0.0388857i
\(497\) 3.00000 5.19615i 0.134568 0.233079i
\(498\) −6.00000 10.3923i −0.268866 0.465690i
\(499\) 5.50000 9.52628i 0.246214 0.426455i −0.716258 0.697835i \(-0.754147\pi\)
0.962472 + 0.271380i \(0.0874801\pi\)
\(500\) 12.0000 + 20.7846i 0.536656 + 0.929516i
\(501\) −6.00000 −0.268060
\(502\) 14.0000 0.624851
\(503\) 6.00000 + 10.3923i 0.267527 + 0.463370i 0.968223 0.250090i \(-0.0804603\pi\)
−0.700696 + 0.713460i \(0.747127\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) −8.00000 −0.355995
\(506\) −8.00000 −0.355643
\(507\) 18.0000 + 31.1769i 0.799408 + 1.38462i
\(508\) 0 0
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 0 0
\(511\) −4.50000 + 7.79423i −0.199068 + 0.344796i
\(512\) 1.00000 0.0441942
\(513\) 4.00000 1.73205i 0.176604 0.0764719i
\(514\) −28.0000 −1.23503
\(515\) 18.0000 31.1769i 0.793175 1.37382i
\(516\) 3.50000 6.06218i 0.154079 0.266872i
\(517\) −2.00000 3.46410i −0.0879599 0.152351i
\(518\) 10.5000 18.1865i 0.461344 0.799070i
\(519\) 6.00000 + 10.3923i 0.263371 + 0.456172i
\(520\) 28.0000 1.22788
\(521\) 38.0000 1.66481 0.832405 0.554168i \(-0.186963\pi\)
0.832405 + 0.554168i \(0.186963\pi\)
\(522\) −2.00000 3.46410i −0.0875376 0.151620i
\(523\) −14.5000 25.1147i −0.634041 1.09819i −0.986718 0.162446i \(-0.948062\pi\)
0.352677 0.935745i \(-0.385272\pi\)
\(524\) −18.0000 −0.786334
\(525\) 33.0000 1.44024
\(526\) 9.00000 + 15.5885i 0.392419 + 0.679689i
\(527\) 0 0
\(528\) 1.00000 + 1.73205i 0.0435194 + 0.0753778i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −8.00000 + 13.8564i −0.347498 + 0.601884i
\(531\) −6.00000 −0.260378
\(532\) −10.5000 7.79423i −0.455233 0.337923i
\(533\) −28.0000 −1.21281
\(534\) 9.00000 15.5885i 0.389468 0.674579i
\(535\) 4.00000 6.92820i 0.172935 0.299532i
\(536\) −1.50000 2.59808i −0.0647901 0.112220i
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) −9.00000 15.5885i −0.388018 0.672066i
\(539\) 4.00000 0.172292
\(540\) 4.00000 0.172133
\(541\) 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i \(-0.0327407\pi\)
−0.586278 + 0.810110i \(0.699407\pi\)
\(542\) 4.00000 + 6.92820i 0.171815 + 0.297592i
\(543\) 2.00000 0.0858282
\(544\) 0 0
\(545\) 12.0000 + 20.7846i 0.514024 + 0.890315i
\(546\) 10.5000 18.1865i 0.449359 0.778312i
\(547\) 14.5000 + 25.1147i 0.619975 + 1.07383i 0.989490 + 0.144604i \(0.0461907\pi\)
−0.369514 + 0.929225i \(0.620476\pi\)
\(548\) 1.00000 1.73205i 0.0427179 0.0739895i
\(549\) 0.500000 0.866025i 0.0213395 0.0369611i
\(550\) 22.0000 0.938083
\(551\) 14.0000 + 10.3923i 0.596420 + 0.442727i
\(552\) 4.00000 0.170251
\(553\) 7.50000 12.9904i 0.318932 0.552407i
\(554\) 13.0000 22.5167i 0.552317 0.956641i
\(555\) −14.0000 24.2487i −0.594267 1.02930i
\(556\) −10.5000 + 18.1865i −0.445299 + 0.771281i
\(557\) −11.0000 19.0526i −0.466085 0.807283i 0.533165 0.846011i \(-0.321003\pi\)
−0.999250 + 0.0387286i \(0.987669\pi\)
\(558\) 1.00000 0.0423334
\(559\) −49.0000 −2.07248
\(560\) −6.00000 10.3923i −0.253546 0.439155i
\(561\) 0 0
\(562\) 4.00000 0.168730
\(563\) −42.0000 −1.77009 −0.885044 0.465506i \(-0.845872\pi\)
−0.885044 + 0.465506i \(0.845872\pi\)
\(564\) 1.00000 + 1.73205i 0.0421076 + 0.0729325i
\(565\) 4.00000 6.92820i 0.168281 0.291472i
\(566\) 6.00000 + 10.3923i 0.252199 + 0.436821i
\(567\) 1.50000 2.59808i 0.0629941 0.109109i
\(568\) −1.00000 + 1.73205i −0.0419591 + 0.0726752i
\(569\) 16.0000 0.670755 0.335377 0.942084i \(-0.391136\pi\)
0.335377 + 0.942084i \(0.391136\pi\)
\(570\) −16.0000 + 6.92820i −0.670166 + 0.290191i
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) 7.00000 12.1244i 0.292685 0.506945i
\(573\) −10.0000 + 17.3205i −0.417756 + 0.723575i
\(574\) 6.00000 + 10.3923i 0.250435 + 0.433766i
\(575\) 22.0000 38.1051i 0.917463 1.58909i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −17.0000 −0.707107
\(579\) −10.5000 18.1865i −0.436365 0.755807i
\(580\) 8.00000 + 13.8564i 0.332182 + 0.575356i
\(581\) 36.0000 1.49353
\(582\) −10.0000 −0.414513
\(583\) 4.00000 + 6.92820i 0.165663 + 0.286937i
\(584\) 1.50000 2.59808i 0.0620704 0.107509i
\(585\) −14.0000 24.2487i −0.578829 1.00256i
\(586\) 9.00000 15.5885i 0.371787 0.643953i
\(587\) 9.00000 15.5885i 0.371470 0.643404i −0.618322 0.785925i \(-0.712187\pi\)
0.989792 + 0.142520i \(0.0455206\pi\)
\(588\) −2.00000 −0.0824786
\(589\) −4.00000 + 1.73205i −0.164817 + 0.0713679i
\(590\) 24.0000 0.988064
\(591\) −5.00000 + 8.66025i −0.205673 + 0.356235i
\(592\) −3.50000 + 6.06218i −0.143849 + 0.249154i
\(593\) −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
\(596\) −18.0000 −0.737309
\(597\) 7.00000 0.286491
\(598\) −14.0000 24.2487i −0.572503 0.991604i
\(599\) −15.0000 25.9808i −0.612883 1.06155i −0.990752 0.135686i \(-0.956676\pi\)
0.377869 0.925859i \(-0.376657\pi\)
\(600\) −11.0000 −0.449073
\(601\) 19.0000 0.775026 0.387513 0.921864i \(-0.373334\pi\)
0.387513 + 0.921864i \(0.373334\pi\)
\(602\) 10.5000 + 18.1865i 0.427948 + 0.741228i
\(603\) −1.50000 + 2.59808i −0.0610847 + 0.105802i
\(604\) −10.0000 17.3205i −0.406894 0.704761i
\(605\) −14.0000 + 24.2487i −0.569181 + 0.985850i
\(606\) 1.00000 1.73205i 0.0406222 0.0703598i
\(607\) 41.0000 1.66414 0.832069 0.554672i \(-0.187156\pi\)
0.832069 + 0.554672i \(0.187156\pi\)
\(608\) 3.50000 + 2.59808i 0.141944 + 0.105366i
\(609\) 12.0000 0.486265
\(610\) −2.00000 + 3.46410i −0.0809776 + 0.140257i
\(611\) 7.00000 12.1244i 0.283190 0.490499i
\(612\) 0 0
\(613\) 19.0000 32.9090i 0.767403 1.32918i −0.171564 0.985173i \(-0.554882\pi\)
0.938967 0.344008i \(-0.111785\pi\)
\(614\) −6.00000 10.3923i −0.242140 0.419399i
\(615\) 16.0000 0.645182
\(616\) −6.00000 −0.241747
\(617\) −9.00000 15.5885i −0.362326 0.627568i 0.626017 0.779809i \(-0.284684\pi\)
−0.988343 + 0.152242i \(0.951351\pi\)
\(618\) 4.50000 + 7.79423i 0.181017 + 0.313530i
\(619\) −23.0000 −0.924448 −0.462224 0.886763i \(-0.652948\pi\)
−0.462224 + 0.886763i \(0.652948\pi\)
\(620\) −4.00000 −0.160644
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) −17.0000 + 29.4449i −0.681638 + 1.18063i
\(623\) 27.0000 + 46.7654i 1.08173 + 1.87362i
\(624\) −3.50000 + 6.06218i −0.140112 + 0.242681i
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) 14.0000 0.559553
\(627\) −1.00000 + 8.66025i −0.0399362 + 0.345857i
\(628\) 7.00000 0.279330
\(629\) 0 0
\(630\) −6.00000 + 10.3923i −0.239046 + 0.414039i
\(631\) 9.50000 + 16.4545i 0.378189 + 0.655043i 0.990799 0.135343i \(-0.0432136\pi\)
−0.612610 + 0.790386i \(0.709880\pi\)
\(632\) −2.50000 + 4.33013i −0.0994447 + 0.172243i
\(633\) 4.50000 + 7.79423i 0.178859 + 0.309793i
\(634\) −24.0000 −0.953162
\(635\) 0 0
\(636\) −2.00000 3.46410i −0.0793052 0.137361i
\(637\) 7.00000 + 12.1244i 0.277350 + 0.480384i
\(638\) 8.00000 0.316723
\(639\) 2.00000 0.0791188
\(640\) 2.00000 + 3.46410i 0.0790569 + 0.136931i
\(641\) −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) 1.00000 + 1.73205i 0.0394669 + 0.0683586i
\(643\) −6.50000 + 11.2583i −0.256335 + 0.443985i −0.965257 0.261301i \(-0.915848\pi\)
0.708922 + 0.705287i \(0.249182\pi\)
\(644\) −6.00000 + 10.3923i −0.236433 + 0.409514i
\(645\) 28.0000 1.10250
\(646\) 0 0
\(647\) −28.0000 −1.10079 −0.550397 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 6.00000 10.3923i 0.235521 0.407934i
\(650\) 38.5000 + 66.6840i 1.51009 + 2.61556i
\(651\) −1.50000 + 2.59808i −0.0587896 + 0.101827i
\(652\) −5.50000 9.52628i −0.215397 0.373078i
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) −6.00000 −0.234619
\(655\) −36.0000 62.3538i −1.40664 2.43637i
\(656\) −2.00000 3.46410i −0.0780869 0.135250i
\(657\) −3.00000 −0.117041
\(658\) −6.00000 −0.233904
\(659\) 5.00000 + 8.66025i 0.194772 + 0.337356i 0.946826 0.321746i \(-0.104270\pi\)
−0.752054 + 0.659102i \(0.770937\pi\)
\(660\) −4.00000 + 6.92820i −0.155700 + 0.269680i
\(661\) −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i \(-0.228968\pi\)
−0.946729 + 0.322031i \(0.895634\pi\)
\(662\) −11.5000 + 19.9186i −0.446960 + 0.774158i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 6.00000 51.9615i 0.232670 2.01498i
\(666\) 7.00000 0.271244
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) −3.00000 + 5.19615i −0.116073 + 0.201045i
\(669\) 2.50000 + 4.33013i 0.0966556 + 0.167412i
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) 1.00000 + 1.73205i 0.0386046 + 0.0668651i
\(672\) 3.00000 0.115728
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) −6.50000 11.2583i −0.250371 0.433655i
\(675\) 5.50000 + 9.52628i 0.211695 + 0.366667i
\(676\) 36.0000 1.38462
\(677\) −38.0000 −1.46046 −0.730229 0.683202i \(-0.760587\pi\)
−0.730229 + 0.683202i \(0.760587\pi\)
\(678\) 1.00000 + 1.73205i 0.0384048 + 0.0665190i
\(679\) 15.0000 25.9808i 0.575647 0.997050i
\(680\) 0 0
\(681\) 2.00000 3.46410i 0.0766402 0.132745i
\(682\) −1.00000 + 1.73205i −0.0382920 + 0.0663237i
\(683\) 40.0000 1.53056 0.765279 0.643699i \(-0.222601\pi\)
0.765279 + 0.643699i \(0.222601\pi\)
\(684\) 0.500000 4.33013i 0.0191180 0.165567i
\(685\) 8.00000 0.305664
\(686\) −7.50000 + 12.9904i −0.286351 + 0.495975i
\(687\) −3.50000 + 6.06218i −0.133533 + 0.231287i
\(688\) −3.50000 6.06218i −0.133436 0.231118i
\(689\) −14.0000 + 24.2487i −0.533358 + 0.923802i
\(690\) 8.00000 + 13.8564i 0.304555 + 0.527504i
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) 12.0000 0.456172
\(693\) 3.00000 + 5.19615i 0.113961 + 0.197386i
\(694\) −14.0000 24.2487i −0.531433 0.920468i
\(695\) −84.0000 −3.18630
\(696\) −4.00000 −0.151620
\(697\) 0 0
\(698\) −15.5000 + 26.8468i −0.586684 + 1.01617i
\(699\) 3.00000 + 5.19615i 0.113470 + 0.196537i
\(700\) 16.5000 28.5788i 0.623641 1.08018i
\(701\) −4.00000 + 6.92820i −0.151078 + 0.261675i −0.931624 0.363424i \(-0.881608\pi\)
0.780546 + 0.625098i \(0.214941\pi\)
\(702\) 7.00000 0.264198
\(703\) −28.0000 + 12.1244i −1.05604 + 0.457279i
\(704\) 2.00000 0.0753778
\(705\) −4.00000 + 6.92820i −0.150649 + 0.260931i
\(706\) 0 0
\(707\) 3.00000 + 5.19615i 0.112827 + 0.195421i
\(708\) −3.00000 + 5.19615i −0.112747 + 0.195283i
\(709\) 1.50000 + 2.59808i 0.0563337 + 0.0975728i 0.892817 0.450420i \(-0.148726\pi\)
−0.836483 + 0.547992i \(0.815392\pi\)
\(710\) −8.00000 −0.300235
\(711\) 5.00000 0.187515
\(712\) −9.00000 15.5885i −0.337289 0.584202i
\(713\) 2.00000 + 3.46410i 0.0749006 + 0.129732i
\(714\) 0 0
\(715\) 56.0000 2.09428
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 12.0000 20.7846i 0.448148 0.776215i
\(718\) 6.00000 + 10.3923i 0.223918 + 0.387837i
\(719\) −8.00000 + 13.8564i −0.298350 + 0.516757i −0.975759 0.218850i \(-0.929769\pi\)
0.677409 + 0.735607i \(0.263103\pi\)
\(720\) 2.00000 3.46410i 0.0745356 0.129099i
\(721\) −27.0000 −1.00553
\(722\) 5.50000 + 18.1865i 0.204689 + 0.676833i
\(723\) −1.00000 −0.0371904
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) −22.0000 + 38.1051i −0.817059 + 1.41519i
\(726\) −3.50000 6.06218i −0.129897 0.224989i
\(727\) −18.5000 + 32.0429i −0.686127 + 1.18841i 0.286954 + 0.957944i \(0.407357\pi\)
−0.973081 + 0.230463i \(0.925976\pi\)
\(728\) −10.5000 18.1865i −0.389156 0.674038i
\(729\) 1.00000 0.0370370
\(730\) 12.0000 0.444140
\(731\) 0 0
\(732\) −0.500000 0.866025i −0.0184805 0.0320092i
\(733\) 30.0000 1.10808 0.554038 0.832492i \(-0.313086\pi\)
0.554038 + 0.832492i \(0.313086\pi\)
\(734\) 19.0000 0.701303
\(735\) −4.00000 6.92820i −0.147542 0.255551i
\(736\) 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
\(739\) −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) −28.0000 −1.02930
\(741\) −28.0000 + 12.1244i −1.02861 + 0.445399i
\(742\) 12.0000 0.440534
\(743\) −13.0000 + 22.5167i −0.476924 + 0.826056i −0.999650 0.0264443i \(-0.991582\pi\)
0.522727 + 0.852500i \(0.324915\pi\)
\(744\) 0.500000 0.866025i 0.0183309 0.0317500i
\(745\) −36.0000 62.3538i −1.31894 2.28447i
\(746\) 11.0000 19.0526i 0.402739 0.697564i
\(747\) 6.00000 + 10.3923i 0.219529 + 0.380235i
\(748\) 0 0
\(749\) −6.00000 −0.219235
\(750\) −12.0000 20.7846i −0.438178 0.758947i
\(751\) 15.5000 + 26.8468i 0.565603 + 0.979653i 0.996993 + 0.0774878i \(0.0246899\pi\)
−0.431390 + 0.902165i \(0.641977\pi\)
\(752\) 2.00000 0.0729325
\(753\) −14.0000 −0.510188
\(754\) 14.0000 + 24.2487i 0.509850 + 0.883086i
\(755\) 40.0000 69.2820i 1.45575 2.52143i
\(756\) −1.50000 2.59808i −0.0545545 0.0944911i
\(757\) 11.5000 19.9186i 0.417975 0.723953i −0.577761 0.816206i \(-0.696073\pi\)
0.995736 + 0.0922527i \(0.0294068\pi\)
\(758\) 10.5000 18.1865i 0.381377 0.660565i
\(759\) 8.00000 0.290382
\(760\) −2.00000 + 17.3205i −0.0725476 + 0.628281i
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) 9.00000 15.5885i 0.325822 0.564340i
\(764\) 10.0000 + 17.3205i 0.361787 + 0.626634i
\(765\) 0 0
\(766\) 7.00000 + 12.1244i 0.252920 + 0.438071i
\(767\) 42.0000 1.51653
\(768\) −1.00000 −0.0360844
\(769\) 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) −12.0000 20.7846i −0.432450 0.749025i
\(771\) 28.0000 1.00840
\(772\) −21.0000 −0.755807
\(773\) −3.00000 5.19615i −0.107903 0.186893i 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) −3.50000 + 6.06218i −0.125805 + 0.217900i
\(775\) −5.50000 9.52628i −0.197566 0.342194i
\(776\) −5.00000 + 8.66025i −0.179490 + 0.310885i
\(777\) −10.5000 + 18.1865i −0.376685 + 0.652438i
\(778\) −24.0000 −0.860442
\(779\) 2.00000 17.3205i 0.0716574 0.620572i