Properties

Label 570.2.i.g.391.2
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{73})\)
Defining polynomial: \(x^{4} - x^{3} + 19 x^{2} + 18 x + 324\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.2
Root \(-1.88600 - 3.26665i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.g.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +3.77200 q^{11} +1.00000 q^{12} +(2.38600 + 4.13267i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.00000 q^{18} +(2.88600 + 3.26665i) q^{19} +1.00000 q^{20} +(0.500000 - 0.866025i) q^{21} +(1.88600 - 3.26665i) q^{22} +(1.88600 + 3.26665i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.77200 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} -1.00000 q^{30} +2.77200 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.88600 + 3.26665i) q^{33} +(0.500000 - 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.00000 q^{37} +(4.27200 - 0.866025i) q^{38} -4.77200 q^{39} +(0.500000 - 0.866025i) q^{40} +(1.88600 - 3.26665i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.38600 + 7.59678i) q^{43} +(-1.88600 - 3.26665i) q^{44} +1.00000 q^{45} +3.77200 q^{46} +(-0.500000 - 0.866025i) q^{48} -6.00000 q^{49} -1.00000 q^{50} +(2.38600 - 4.13267i) q^{52} +(-4.88600 - 8.46280i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.88600 + 3.26665i) q^{55} +1.00000 q^{56} +(-4.27200 + 0.866025i) q^{57} +6.00000 q^{58} +(6.77200 - 11.7295i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-1.38600 - 2.40062i) q^{61} +(1.38600 - 2.40062i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} -4.77200 q^{65} +(1.88600 + 3.26665i) q^{66} +(5.38600 + 9.32883i) q^{67} -3.77200 q^{69} +(-0.500000 - 0.866025i) q^{70} +(3.77200 - 6.53330i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.61400 - 2.79553i) q^{73} +(-0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(1.38600 - 4.13267i) q^{76} -3.77200 q^{77} +(-2.38600 + 4.13267i) q^{78} +(-5.15800 + 8.93392i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.88600 - 3.26665i) q^{82} +6.00000 q^{83} -1.00000 q^{84} +(4.38600 + 7.59678i) q^{86} -6.00000 q^{87} -3.77200 q^{88} +(-8.65800 - 14.9961i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-2.38600 - 4.13267i) q^{91} +(1.88600 - 3.26665i) q^{92} +(-1.38600 + 2.40062i) q^{93} +(-4.27200 + 0.866025i) q^{95} -1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(-1.88600 - 3.26665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 4q^{7} - 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 4q^{7} - 4q^{8} - 2q^{9} + 2q^{10} - 2q^{11} + 4q^{12} + q^{13} - 2q^{14} - 2q^{15} - 2q^{16} - 4q^{18} + 3q^{19} + 4q^{20} + 2q^{21} - q^{22} - q^{23} + 2q^{24} - 2q^{25} + 2q^{26} + 4q^{27} + 2q^{28} + 12q^{29} - 4q^{30} - 6q^{31} + 2q^{32} + q^{33} + 2q^{35} - 2q^{36} - 4q^{37} - 2q^{39} + 2q^{40} - q^{41} - 2q^{42} - 9q^{43} + q^{44} + 4q^{45} - 2q^{46} - 2q^{48} - 24q^{49} - 4q^{50} + q^{52} - 11q^{53} + 2q^{54} + q^{55} + 4q^{56} + 24q^{58} + 10q^{59} - 2q^{60} + 3q^{61} - 3q^{62} + 2q^{63} + 4q^{64} - 2q^{65} - q^{66} + 13q^{67} + 2q^{69} - 2q^{70} - 2q^{71} + 2q^{72} + 15q^{73} - 2q^{74} + 4q^{75} - 3q^{76} + 2q^{77} - q^{78} + 5q^{79} - 2q^{80} - 2q^{81} + q^{82} + 24q^{83} - 4q^{84} + 9q^{86} - 24q^{87} + 2q^{88} - 9q^{89} + 2q^{90} - q^{91} - q^{92} + 3q^{93} - 4q^{96} + 20q^{97} - 12q^{98} + q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 3.77200 1.13730 0.568651 0.822579i \(-0.307466\pi\)
0.568651 + 0.822579i \(0.307466\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.38600 + 4.13267i 0.661758 + 1.14620i 0.980154 + 0.198240i \(0.0635225\pi\)
−0.318396 + 0.947958i \(0.603144\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −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
\(19\) 2.88600 + 3.26665i 0.662094 + 0.749421i
\(20\) 1.00000 0.223607
\(21\) 0.500000 0.866025i 0.109109 0.188982i
\(22\) 1.88600 3.26665i 0.402097 0.696452i
\(23\) 1.88600 + 3.26665i 0.393258 + 0.681143i 0.992877 0.119142i \(-0.0380145\pi\)
−0.599619 + 0.800286i \(0.704681\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 4.77200 0.935867
\(27\) 1.00000 0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) −1.00000 −0.182574
\(31\) 2.77200 0.497866 0.248933 0.968521i \(-0.419920\pi\)
0.248933 + 0.968521i \(0.419920\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.88600 + 3.26665i −0.328311 + 0.568651i
\(34\) 0 0
\(35\) 0.500000 0.866025i 0.0845154 0.146385i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 4.27200 0.866025i 0.693010 0.140488i
\(39\) −4.77200 −0.764132
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 1.88600 3.26665i 0.294544 0.510165i −0.680335 0.732901i \(-0.738166\pi\)
0.974879 + 0.222737i \(0.0714990\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −4.38600 + 7.59678i −0.668859 + 1.15850i 0.309365 + 0.950943i \(0.399884\pi\)
−0.978224 + 0.207554i \(0.933450\pi\)
\(44\) −1.88600 3.26665i −0.284325 0.492466i
\(45\) 1.00000 0.149071
\(46\) 3.77200 0.556151
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −6.00000 −0.857143
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 2.38600 4.13267i 0.330879 0.573099i
\(53\) −4.88600 8.46280i −0.671144 1.16246i −0.977580 0.210564i \(-0.932470\pi\)
0.306436 0.951891i \(-0.400863\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −1.88600 + 3.26665i −0.254308 + 0.440475i
\(56\) 1.00000 0.133631
\(57\) −4.27200 + 0.866025i −0.565840 + 0.114708i
\(58\) 6.00000 0.787839
\(59\) 6.77200 11.7295i 0.881640 1.52704i 0.0321221 0.999484i \(-0.489773\pi\)
0.849517 0.527561i \(-0.176893\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) −1.38600 2.40062i −0.177459 0.307368i 0.763550 0.645748i \(-0.223454\pi\)
−0.941010 + 0.338380i \(0.890121\pi\)
\(62\) 1.38600 2.40062i 0.176022 0.304880i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) −4.77200 −0.591894
\(66\) 1.88600 + 3.26665i 0.232151 + 0.402097i
\(67\) 5.38600 + 9.32883i 0.658005 + 1.13970i 0.981131 + 0.193342i \(0.0619327\pi\)
−0.323127 + 0.946356i \(0.604734\pi\)
\(68\) 0 0
\(69\) −3.77200 −0.454096
\(70\) −0.500000 0.866025i −0.0597614 0.103510i
\(71\) 3.77200 6.53330i 0.447654 0.775360i −0.550579 0.834783i \(-0.685593\pi\)
0.998233 + 0.0594234i \(0.0189262\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 1.61400 2.79553i 0.188904 0.327192i −0.755981 0.654594i \(-0.772840\pi\)
0.944885 + 0.327402i \(0.106173\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) 1.00000 0.115470
\(76\) 1.38600 4.13267i 0.158985 0.474050i
\(77\) −3.77200 −0.429860
\(78\) −2.38600 + 4.13267i −0.270161 + 0.467933i
\(79\) −5.15800 + 8.93392i −0.580321 + 1.00514i 0.415120 + 0.909766i \(0.363739\pi\)
−0.995441 + 0.0953784i \(0.969594\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.88600 3.26665i −0.208274 0.360741i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) 4.38600 + 7.59678i 0.472955 + 0.819181i
\(87\) −6.00000 −0.643268
\(88\) −3.77200 −0.402097
\(89\) −8.65800 14.9961i −0.917746 1.58958i −0.802830 0.596208i \(-0.796673\pi\)
−0.114917 0.993375i \(-0.536660\pi\)
\(90\) 0.500000 0.866025i 0.0527046 0.0912871i
\(91\) −2.38600 4.13267i −0.250121 0.433222i
\(92\) 1.88600 3.26665i 0.196629 0.340572i
\(93\) −1.38600 + 2.40062i −0.143722 + 0.248933i
\(94\) 0 0
\(95\) −4.27200 + 0.866025i −0.438298 + 0.0888523i
\(96\) −1.00000 −0.102062
\(97\) 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i \(-0.663839\pi\)
0.999961 0.00888289i \(-0.00282755\pi\)
\(98\) −3.00000 + 5.19615i −0.303046 + 0.524891i
\(99\) −1.88600 3.26665i −0.189550 0.328311i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) −2.38600 4.13267i −0.233967 0.405242i
\(105\) 0.500000 + 0.866025i 0.0487950 + 0.0845154i
\(106\) −9.77200 −0.949141
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −4.77200 + 8.26535i −0.457075 + 0.791677i −0.998805 0.0488756i \(-0.984436\pi\)
0.541730 + 0.840553i \(0.317770\pi\)
\(110\) 1.88600 + 3.26665i 0.179823 + 0.311463i
\(111\) 0.500000 0.866025i 0.0474579 0.0821995i
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) −13.5440 −1.27411 −0.637056 0.770817i \(-0.719848\pi\)
−0.637056 + 0.770817i \(0.719848\pi\)
\(114\) −1.38600 + 4.13267i −0.129811 + 0.387060i
\(115\) −3.77200 −0.351741
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 2.38600 4.13267i 0.220586 0.382066i
\(118\) −6.77200 11.7295i −0.623413 1.07978i
\(119\) 0 0
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 3.22800 0.293454
\(122\) −2.77200 −0.250965
\(123\) 1.88600 + 3.26665i 0.170055 + 0.294544i
\(124\) −1.38600 2.40062i −0.124467 0.215582i
\(125\) 1.00000 0.0894427
\(126\) 1.00000 0.0890871
\(127\) 4.65800 + 8.06790i 0.413331 + 0.715910i 0.995252 0.0973354i \(-0.0310319\pi\)
−0.581921 + 0.813246i \(0.697699\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −4.38600 7.59678i −0.386166 0.668859i
\(130\) −2.38600 + 4.13267i −0.209266 + 0.362460i
\(131\) 5.65800 9.79995i 0.494342 0.856225i −0.505637 0.862746i \(-0.668742\pi\)
0.999979 + 0.00652102i \(0.00207572\pi\)
\(132\) 3.77200 0.328311
\(133\) −2.88600 3.26665i −0.250248 0.283254i
\(134\) 10.7720 0.930559
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) 0.772002 + 1.33715i 0.0659566 + 0.114240i 0.897118 0.441791i \(-0.145657\pi\)
−0.831161 + 0.556031i \(0.812323\pi\)
\(138\) −1.88600 + 3.26665i −0.160547 + 0.278076i
\(139\) 5.38600 + 9.32883i 0.456835 + 0.791261i 0.998792 0.0491454i \(-0.0156498\pi\)
−0.541957 + 0.840406i \(0.682316\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 0 0
\(142\) −3.77200 6.53330i −0.316539 0.548262i
\(143\) 9.00000 + 15.5885i 0.752618 + 1.30357i
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) −1.61400 2.79553i −0.133576 0.231360i
\(147\) 3.00000 5.19615i 0.247436 0.428571i
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 6.77200 11.7295i 0.554784 0.960914i −0.443136 0.896454i \(-0.646134\pi\)
0.997920 0.0644598i \(-0.0205324\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −2.88600 3.26665i −0.234086 0.264960i
\(153\) 0 0
\(154\) −1.88600 + 3.26665i −0.151978 + 0.263234i
\(155\) −1.38600 + 2.40062i −0.111326 + 0.192823i
\(156\) 2.38600 + 4.13267i 0.191033 + 0.330879i
\(157\) −1.72800 + 2.99298i −0.137909 + 0.238866i −0.926705 0.375790i \(-0.877372\pi\)
0.788796 + 0.614655i \(0.210705\pi\)
\(158\) 5.15800 + 8.93392i 0.410349 + 0.710745i
\(159\) 9.77200 0.774970
\(160\) −1.00000 −0.0790569
\(161\) −1.88600 3.26665i −0.148638 0.257448i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −18.3160 −1.43462 −0.717310 0.696754i \(-0.754627\pi\)
−0.717310 + 0.696754i \(0.754627\pi\)
\(164\) −3.77200 −0.294544
\(165\) −1.88600 3.26665i −0.146825 0.254308i
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) 5.65800 + 9.79995i 0.437829 + 0.758343i 0.997522 0.0703577i \(-0.0224141\pi\)
−0.559692 + 0.828700i \(0.689081\pi\)
\(168\) −0.500000 + 0.866025i −0.0385758 + 0.0668153i
\(169\) −4.88600 + 8.46280i −0.375846 + 0.650985i
\(170\) 0 0
\(171\) 1.38600 4.13267i 0.105990 0.316034i
\(172\) 8.77200 0.668859
\(173\) −5.65800 + 9.79995i −0.430170 + 0.745076i −0.996888 0.0788358i \(-0.974880\pi\)
0.566718 + 0.823912i \(0.308213\pi\)
\(174\) −3.00000 + 5.19615i −0.227429 + 0.393919i
\(175\) 0.500000 + 0.866025i 0.0377964 + 0.0654654i
\(176\) −1.88600 + 3.26665i −0.142163 + 0.246233i
\(177\) 6.77200 + 11.7295i 0.509015 + 0.881640i
\(178\) −17.3160 −1.29789
\(179\) −0.683994 −0.0511241 −0.0255621 0.999673i \(-0.508138\pi\)
−0.0255621 + 0.999673i \(0.508138\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −8.54400 14.7986i −0.635071 1.09997i −0.986500 0.163760i \(-0.947638\pi\)
0.351429 0.936214i \(-0.385696\pi\)
\(182\) −4.77200 −0.353724
\(183\) 2.77200 0.204912
\(184\) −1.88600 3.26665i −0.139038 0.240821i
\(185\) 0.500000 0.866025i 0.0367607 0.0636715i
\(186\) 1.38600 + 2.40062i 0.101627 + 0.176022i
\(187\) 0 0
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) −1.38600 + 4.13267i −0.100551 + 0.299816i
\(191\) 7.54400 0.545865 0.272932 0.962033i \(-0.412006\pi\)
0.272932 + 0.962033i \(0.412006\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.38600 + 2.40062i −0.0997665 + 0.172801i −0.911588 0.411105i \(-0.865143\pi\)
0.811821 + 0.583906i \(0.198476\pi\)
\(194\) −5.00000 8.66025i −0.358979 0.621770i
\(195\) 2.38600 4.13267i 0.170865 0.295947i
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) −11.3160 −0.806232 −0.403116 0.915149i \(-0.632073\pi\)
−0.403116 + 0.915149i \(0.632073\pi\)
\(198\) −3.77200 −0.268065
\(199\) 0.158003 + 0.273669i 0.0112005 + 0.0193999i 0.871571 0.490269i \(-0.163101\pi\)
−0.860371 + 0.509669i \(0.829768\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) −10.7720 −0.759798
\(202\) 6.00000 0.422159
\(203\) −3.00000 5.19615i −0.210559 0.364698i
\(204\) 0 0
\(205\) 1.88600 + 3.26665i 0.131724 + 0.228153i
\(206\) −6.50000 + 11.2583i −0.452876 + 0.784405i
\(207\) 1.88600 3.26665i 0.131086 0.227048i
\(208\) −4.77200 −0.330879
\(209\) 10.8860 + 12.3218i 0.753000 + 0.852317i
\(210\) 1.00000 0.0690066
\(211\) 10.2720 17.7916i 0.707154 1.22483i −0.258755 0.965943i \(-0.583312\pi\)
0.965909 0.258883i \(-0.0833545\pi\)
\(212\) −4.88600 + 8.46280i −0.335572 + 0.581228i
\(213\) 3.77200 + 6.53330i 0.258453 + 0.447654i
\(214\) 0 0
\(215\) −4.38600 7.59678i −0.299123 0.518096i
\(216\) −1.00000 −0.0680414
\(217\) −2.77200 −0.188176
\(218\) 4.77200 + 8.26535i 0.323201 + 0.559800i
\(219\) 1.61400 + 2.79553i 0.109064 + 0.188904i
\(220\) 3.77200 0.254308
\(221\) 0 0
\(222\) −0.500000 0.866025i −0.0335578 0.0581238i
\(223\) 12.5000 21.6506i 0.837062 1.44983i −0.0552786 0.998471i \(-0.517605\pi\)
0.892341 0.451363i \(-0.149062\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) −6.77200 + 11.7295i −0.450467 + 0.780231i
\(227\) 9.08801 0.603192 0.301596 0.953436i \(-0.402481\pi\)
0.301596 + 0.953436i \(0.402481\pi\)
\(228\) 2.88600 + 3.26665i 0.191130 + 0.216339i
\(229\) 23.8600 1.57671 0.788357 0.615218i \(-0.210932\pi\)
0.788357 + 0.615218i \(0.210932\pi\)
\(230\) −1.88600 + 3.26665i −0.124359 + 0.215396i
\(231\) 1.88600 3.26665i 0.124090 0.214930i
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) 2.22800 3.85901i 0.145961 0.252812i −0.783770 0.621051i \(-0.786706\pi\)
0.929731 + 0.368239i \(0.120039\pi\)
\(234\) −2.38600 4.13267i −0.155978 0.270161i
\(235\) 0 0
\(236\) −13.5440 −0.881640
\(237\) −5.15800 8.93392i −0.335048 0.580321i
\(238\) 0 0
\(239\) 13.5440 0.876089 0.438044 0.898953i \(-0.355671\pi\)
0.438044 + 0.898953i \(0.355671\pi\)
\(240\) 1.00000 0.0645497
\(241\) −11.1580 19.3262i −0.718750 1.24491i −0.961495 0.274822i \(-0.911381\pi\)
0.242745 0.970090i \(-0.421952\pi\)
\(242\) 1.61400 2.79553i 0.103752 0.179703i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −1.38600 + 2.40062i −0.0887296 + 0.153684i
\(245\) 3.00000 5.19615i 0.191663 0.331970i
\(246\) 3.77200 0.240494
\(247\) −6.61400 + 19.7211i −0.420839 + 1.25483i
\(248\) −2.77200 −0.176022
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) −0.772002 1.33715i −0.0487283 0.0843999i 0.840632 0.541606i \(-0.182184\pi\)
−0.889361 + 0.457206i \(0.848850\pi\)
\(252\) 0.500000 0.866025i 0.0314970 0.0545545i
\(253\) 7.11400 + 12.3218i 0.447253 + 0.774665i
\(254\) 9.31601 0.584538
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.0000 + 25.9808i 0.935674 + 1.62064i 0.773427 + 0.633885i \(0.218541\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(258\) −8.77200 −0.546121
\(259\) 1.00000 0.0621370
\(260\) 2.38600 + 4.13267i 0.147973 + 0.256298i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) −5.65800 9.79995i −0.349553 0.605443i
\(263\) −7.88600 + 13.6590i −0.486272 + 0.842247i −0.999875 0.0157802i \(-0.994977\pi\)
0.513604 + 0.858027i \(0.328310\pi\)
\(264\) 1.88600 3.26665i 0.116075 0.201048i
\(265\) 9.77200 0.600289
\(266\) −4.27200 + 0.866025i −0.261933 + 0.0530994i
\(267\) 17.3160 1.05972
\(268\) 5.38600 9.32883i 0.329002 0.569849i
\(269\) 12.7720 22.1218i 0.778723 1.34879i −0.153956 0.988078i \(-0.549201\pi\)
0.932678 0.360709i \(-0.117465\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) −6.22800 + 10.7872i −0.378324 + 0.655276i −0.990819 0.135198i \(-0.956833\pi\)
0.612495 + 0.790475i \(0.290166\pi\)
\(272\) 0 0
\(273\) 4.77200 0.288815
\(274\) 1.54400 0.0932767
\(275\) −1.88600 3.26665i −0.113730 0.196986i
\(276\) 1.88600 + 3.26665i 0.113524 + 0.196629i
\(277\) 5.08801 0.305709 0.152854 0.988249i \(-0.451153\pi\)
0.152854 + 0.988249i \(0.451153\pi\)
\(278\) 10.7720 0.646062
\(279\) −1.38600 2.40062i −0.0829777 0.143722i
\(280\) −0.500000 + 0.866025i −0.0298807 + 0.0517549i
\(281\) −13.8860 24.0513i −0.828369 1.43478i −0.899317 0.437298i \(-0.855936\pi\)
0.0709474 0.997480i \(-0.477398\pi\)
\(282\) 0 0
\(283\) 13.3160 23.0640i 0.791554 1.37101i −0.133450 0.991056i \(-0.542606\pi\)
0.925004 0.379957i \(-0.124061\pi\)
\(284\) −7.54400 −0.447654
\(285\) 1.38600 4.13267i 0.0820996 0.244799i
\(286\) 18.0000 1.06436
\(287\) −1.88600 + 3.26665i −0.111327 + 0.192824i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −3.00000 + 5.19615i −0.176166 + 0.305129i
\(291\) 5.00000 + 8.66025i 0.293105 + 0.507673i
\(292\) −3.22800 −0.188904
\(293\) −20.2280 −1.18173 −0.590866 0.806770i \(-0.701214\pi\)
−0.590866 + 0.806770i \(0.701214\pi\)
\(294\) −3.00000 5.19615i −0.174964 0.303046i
\(295\) 6.77200 + 11.7295i 0.394281 + 0.682915i
\(296\) 1.00000 0.0581238
\(297\) 3.77200 0.218874
\(298\) −6.77200 11.7295i −0.392292 0.679469i
\(299\) −9.00000 + 15.5885i −0.520483 + 0.901504i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) 4.38600 7.59678i 0.252805 0.437871i
\(302\) 4.00000 6.92820i 0.230174 0.398673i
\(303\) −6.00000 −0.344691
\(304\) −4.27200 + 0.866025i −0.245016 + 0.0496700i
\(305\) 2.77200 0.158724
\(306\) 0 0
\(307\) 11.7720 20.3897i 0.671864 1.16370i −0.305511 0.952188i \(-0.598827\pi\)
0.977375 0.211514i \(-0.0678392\pi\)
\(308\) 1.88600 + 3.26665i 0.107465 + 0.186135i
\(309\) 6.50000 11.2583i 0.369772 0.640464i
\(310\) 1.38600 + 2.40062i 0.0787196 + 0.136346i
\(311\) 25.5440 1.44847 0.724234 0.689555i \(-0.242194\pi\)
0.724234 + 0.689555i \(0.242194\pi\)
\(312\) 4.77200 0.270161
\(313\) 1.22800 + 2.12696i 0.0694106 + 0.120223i 0.898642 0.438683i \(-0.144555\pi\)
−0.829231 + 0.558905i \(0.811221\pi\)
\(314\) 1.72800 + 2.99298i 0.0975166 + 0.168904i
\(315\) −1.00000 −0.0563436
\(316\) 10.3160 0.580321
\(317\) −10.1140 17.5180i −0.568059 0.983907i −0.996758 0.0804593i \(-0.974361\pi\)
0.428699 0.903447i \(-0.358972\pi\)
\(318\) 4.88600 8.46280i 0.273993 0.474570i
\(319\) 11.3160 + 19.5999i 0.633575 + 1.09738i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) −3.77200 −0.210205
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 2.38600 4.13267i 0.132352 0.229240i
\(326\) −9.15800 + 15.8621i −0.507215 + 0.878522i
\(327\) −4.77200 8.26535i −0.263892 0.457075i
\(328\) −1.88600 + 3.26665i −0.104137 + 0.180371i
\(329\) 0 0
\(330\) −3.77200 −0.207642
\(331\) −26.5440 −1.45899 −0.729495 0.683986i \(-0.760245\pi\)
−0.729495 + 0.683986i \(0.760245\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 0.500000 + 0.866025i 0.0273998 + 0.0474579i
\(334\) 11.3160 0.619184
\(335\) −10.7720 −0.588537
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) 15.1580 26.2544i 0.825709 1.43017i −0.0756672 0.997133i \(-0.524109\pi\)
0.901376 0.433037i \(-0.142558\pi\)
\(338\) 4.88600 + 8.46280i 0.265763 + 0.460316i
\(339\) 6.77200 11.7295i 0.367805 0.637056i
\(340\) 0 0
\(341\) 10.4560 0.566224
\(342\) −2.88600 3.26665i −0.156057 0.176640i
\(343\) 13.0000 0.701934
\(344\) 4.38600 7.59678i 0.236477 0.409591i
\(345\) 1.88600 3.26665i 0.101539 0.175870i
\(346\) 5.65800 + 9.79995i 0.304176 + 0.526848i
\(347\) 3.77200 6.53330i 0.202492 0.350726i −0.746839 0.665005i \(-0.768429\pi\)
0.949331 + 0.314279i \(0.101763\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) −9.22800 −0.493963 −0.246982 0.969020i \(-0.579439\pi\)
−0.246982 + 0.969020i \(0.579439\pi\)
\(350\) 1.00000 0.0534522
\(351\) 2.38600 + 4.13267i 0.127355 + 0.220586i
\(352\) 1.88600 + 3.26665i 0.100524 + 0.174113i
\(353\) −13.5440 −0.720875 −0.360437 0.932783i \(-0.617373\pi\)
−0.360437 + 0.932783i \(0.617373\pi\)
\(354\) 13.5440 0.719856
\(355\) 3.77200 + 6.53330i 0.200197 + 0.346752i
\(356\) −8.65800 + 14.9961i −0.458873 + 0.794792i
\(357\) 0 0
\(358\) −0.341997 + 0.592357i −0.0180751 + 0.0313070i
\(359\) −10.5440 + 18.2628i −0.556491 + 0.963871i 0.441295 + 0.897362i \(0.354519\pi\)
−0.997786 + 0.0665088i \(0.978814\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −2.34200 + 18.8551i −0.123263 + 0.992374i
\(362\) −17.0880 −0.898126
\(363\) −1.61400 + 2.79553i −0.0847130 + 0.146727i
\(364\) −2.38600 + 4.13267i −0.125060 + 0.216611i
\(365\) 1.61400 + 2.79553i 0.0844806 + 0.146325i
\(366\) 1.38600 2.40062i 0.0724474 0.125483i
\(367\) 4.61400 + 7.99168i 0.240849 + 0.417162i 0.960956 0.276700i \(-0.0892409\pi\)
−0.720108 + 0.693862i \(0.755908\pi\)
\(368\) −3.77200 −0.196629
\(369\) −3.77200 −0.196363
\(370\) −0.500000 0.866025i −0.0259938 0.0450225i
\(371\) 4.88600 + 8.46280i 0.253669 + 0.439367i
\(372\) 2.77200 0.143722
\(373\) −0.227998 −0.0118053 −0.00590265 0.999983i \(-0.501879\pi\)
−0.00590265 + 0.999983i \(0.501879\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) −14.3160 + 24.7960i −0.737312 + 1.27706i
\(378\) −0.500000 + 0.866025i −0.0257172 + 0.0445435i
\(379\) −9.22800 −0.474010 −0.237005 0.971508i \(-0.576166\pi\)
−0.237005 + 0.971508i \(0.576166\pi\)
\(380\) 2.88600 + 3.26665i 0.148049 + 0.167576i
\(381\) −9.31601 −0.477273
\(382\) 3.77200 6.53330i 0.192992 0.334273i
\(383\) 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i \(-0.623227\pi\)
0.990702 0.136047i \(-0.0434398\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 1.88600 3.26665i 0.0961195 0.166484i
\(386\) 1.38600 + 2.40062i 0.0705456 + 0.122189i
\(387\) 8.77200 0.445906
\(388\) −10.0000 −0.507673
\(389\) 4.54400 + 7.87045i 0.230390 + 0.399047i 0.957923 0.287025i \(-0.0926664\pi\)
−0.727533 + 0.686073i \(0.759333\pi\)
\(390\) −2.38600 4.13267i −0.120820 0.209266i
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) 5.65800 + 9.79995i 0.285408 + 0.494342i
\(394\) −5.65800 + 9.79995i −0.285046 + 0.493714i
\(395\) −5.15800 8.93392i −0.259527 0.449514i
\(396\) −1.88600 + 3.26665i −0.0947751 + 0.164155i
\(397\) −1.04400 + 1.80827i −0.0523970 + 0.0907543i −0.891034 0.453936i \(-0.850019\pi\)
0.838637 + 0.544690i \(0.183353\pi\)
\(398\) 0.316006 0.0158399
\(399\) 4.27200 0.866025i 0.213868 0.0433555i
\(400\) 1.00000 0.0500000
\(401\) −4.54400 + 7.87045i −0.226917 + 0.393031i −0.956893 0.290441i \(-0.906198\pi\)
0.729976 + 0.683473i \(0.239531\pi\)
\(402\) −5.38600 + 9.32883i −0.268629 + 0.465280i
\(403\) 6.61400 + 11.4558i 0.329467 + 0.570653i
\(404\) 3.00000 5.19615i 0.149256 0.258518i
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) −6.00000 −0.297775
\(407\) −3.77200 −0.186971
\(408\) 0 0
\(409\) 15.2020 + 26.3306i 0.751691 + 1.30197i 0.947003 + 0.321226i \(0.104095\pi\)
−0.195312 + 0.980741i \(0.562572\pi\)
\(410\) 3.77200 0.186286
\(411\) −1.54400 −0.0761601
\(412\) 6.50000 + 11.2583i 0.320232 + 0.554658i
\(413\) −6.77200 + 11.7295i −0.333228 + 0.577169i
\(414\) −1.88600 3.26665i −0.0926919 0.160547i
\(415\) −3.00000 + 5.19615i −0.147264 + 0.255069i
\(416\) −2.38600 + 4.13267i −0.116983 + 0.202621i
\(417\) −10.7720 −0.527507
\(418\) 16.1140 3.26665i 0.788161 0.159777i
\(419\) −24.8600 −1.21449 −0.607245 0.794514i \(-0.707726\pi\)
−0.607245 + 0.794514i \(0.707726\pi\)
\(420\) 0.500000 0.866025i 0.0243975 0.0422577i
\(421\) 8.77200 15.1936i 0.427521 0.740488i −0.569131 0.822247i \(-0.692720\pi\)
0.996652 + 0.0817584i \(0.0260536\pi\)
\(422\) −10.2720 17.7916i −0.500033 0.866083i
\(423\) 0 0
\(424\) 4.88600 + 8.46280i 0.237285 + 0.410990i
\(425\) 0 0
\(426\) 7.54400 0.365508
\(427\) 1.38600 + 2.40062i 0.0670733 + 0.116174i
\(428\) 0 0
\(429\) −18.0000 −0.869048
\(430\) −8.77200 −0.423023
\(431\) 1.54400 + 2.67429i 0.0743720 + 0.128816i 0.900813 0.434207i \(-0.142971\pi\)
−0.826441 + 0.563023i \(0.809638\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −5.15800 8.93392i −0.247878 0.429337i 0.715059 0.699064i \(-0.246400\pi\)
−0.962937 + 0.269727i \(0.913066\pi\)
\(434\) −1.38600 + 2.40062i −0.0665302 + 0.115234i
\(435\) 3.00000 5.19615i 0.143839 0.249136i
\(436\) 9.54400 0.457075
\(437\) −5.22800 + 15.5885i −0.250089 + 0.745697i
\(438\) 3.22800 0.154240
\(439\) −2.15800 + 3.73777i −0.102996 + 0.178394i −0.912918 0.408144i \(-0.866176\pi\)
0.809922 + 0.586538i \(0.199510\pi\)
\(440\) 1.88600 3.26665i 0.0899116 0.155731i
\(441\) 3.00000 + 5.19615i 0.142857 + 0.247436i
\(442\) 0 0
\(443\) −19.5440 33.8512i −0.928564 1.60832i −0.785727 0.618573i \(-0.787711\pi\)
−0.142836 0.989746i \(-0.545622\pi\)
\(444\) −1.00000 −0.0474579
\(445\) 17.3160 0.820857
\(446\) −12.5000 21.6506i −0.591892 1.02519i
\(447\) 6.77200 + 11.7295i 0.320305 + 0.554784i
\(448\) −1.00000 −0.0472456
\(449\) 2.22800 0.105146 0.0525729 0.998617i \(-0.483258\pi\)
0.0525729 + 0.998617i \(0.483258\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) 7.11400 12.3218i 0.334985 0.580211i
\(452\) 6.77200 + 11.7295i 0.318528 + 0.551707i
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) 4.54400 7.87045i 0.213261 0.369378i
\(455\) 4.77200 0.223715
\(456\) 4.27200 0.866025i 0.200055 0.0405554i
\(457\) −25.8600 −1.20968 −0.604840 0.796347i \(-0.706763\pi\)
−0.604840 + 0.796347i \(0.706763\pi\)
\(458\) 11.9300 20.6634i 0.557453 0.965536i
\(459\) 0 0
\(460\) 1.88600 + 3.26665i 0.0879352 + 0.152308i
\(461\) −17.3160 + 29.9922i −0.806487 + 1.39688i 0.108796 + 0.994064i \(0.465300\pi\)
−0.915283 + 0.402812i \(0.868033\pi\)
\(462\) −1.88600 3.26665i −0.0877447 0.151978i
\(463\) 27.6320 1.28417 0.642084 0.766634i \(-0.278070\pi\)
0.642084 + 0.766634i \(0.278070\pi\)
\(464\) −6.00000 −0.278543
\(465\) −1.38600 2.40062i −0.0642743 0.111326i
\(466\) −2.22800 3.85901i −0.103210 0.178765i
\(467\) −9.08801 −0.420543 −0.210271 0.977643i \(-0.567435\pi\)
−0.210271 + 0.977643i \(0.567435\pi\)
\(468\) −4.77200 −0.220586
\(469\) −5.38600 9.32883i −0.248702 0.430765i
\(470\) 0 0
\(471\) −1.72800 2.99298i −0.0796220 0.137909i
\(472\) −6.77200 + 11.7295i −0.311707 + 0.539892i
\(473\) −16.5440 + 28.6551i −0.760694 + 1.31756i
\(474\) −10.3160 −0.473830
\(475\) 1.38600 4.13267i 0.0635941 0.189620i
\(476\) 0 0
\(477\) −4.88600 + 8.46280i −0.223715 + 0.387485i
\(478\) 6.77200 11.7295i 0.309744 0.536493i
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 0.500000 0.866025i 0.0228218 0.0395285i
\(481\) −2.38600 4.13267i −0.108792 0.188434i
\(482\) −22.3160 −1.01647
\(483\) 3.77200 0.171632
\(484\) −1.61400 2.79553i −0.0733636 0.127069i
\(485\) 5.00000 + 8.66025i 0.227038 + 0.393242i
\(486\) −1.00000 −0.0453609
\(487\) −9.31601 −0.422149 −0.211074 0.977470i \(-0.567696\pi\)
−0.211074 + 0.977470i \(0.567696\pi\)
\(488\) 1.38600 + 2.40062i 0.0627413 + 0.108671i
\(489\) 9.15800 15.8621i 0.414139 0.717310i
\(490\) −3.00000 5.19615i −0.135526 0.234738i
\(491\) −3.34200 + 5.78851i −0.150822 + 0.261232i −0.931530 0.363665i \(-0.881525\pi\)
0.780708 + 0.624896i \(0.214859\pi\)
\(492\) 1.88600 3.26665i 0.0850275 0.147272i
\(493\) 0 0
\(494\) 13.7720 + 15.5885i 0.619632 + 0.701358i
\(495\) 3.77200 0.169539
\(496\) −1.38600 + 2.40062i −0.0622333 + 0.107791i
\(497\) −3.77200 + 6.53330i −0.169197 + 0.293059i
\(498\) 3.00000 + 5.19615i 0.134433 + 0.232845i
\(499\) −10.8160 + 18.7339i −0.484191 + 0.838643i −0.999835 0.0181596i \(-0.994219\pi\)
0.515644 + 0.856803i \(0.327553\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) −11.3160 −0.505562
\(502\) −1.54400 −0.0689123
\(503\) −8.65800 14.9961i −0.386041 0.668643i 0.605872 0.795562i \(-0.292824\pi\)
−0.991913 + 0.126919i \(0.959491\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) −6.00000 −0.266996
\(506\) 14.2280 0.632512
\(507\) −4.88600 8.46280i −0.216995 0.375846i
\(508\) 4.65800 8.06790i 0.206665 0.357955i
\(509\) −17.3160 29.9922i −0.767518 1.32938i −0.938905 0.344177i \(-0.888158\pi\)
0.171386 0.985204i \(-0.445175\pi\)
\(510\) 0 0
\(511\) −1.61400 + 2.79553i −0.0713991 + 0.123667i
\(512\) −1.00000 −0.0441942
\(513\) 2.88600 + 3.26665i 0.127420 + 0.144226i
\(514\) 30.0000 1.32324
\(515\) 6.50000 11.2583i 0.286424 0.496101i
\(516\) −4.38600 + 7.59678i −0.193083 + 0.334429i
\(517\) 0 0
\(518\) 0.500000 0.866025i 0.0219687 0.0380510i
\(519\) −5.65800 9.79995i −0.248359 0.430170i
\(520\) 4.77200 0.209266
\(521\) −16.4560 −0.720950 −0.360475 0.932769i \(-0.617385\pi\)
−0.360475 + 0.932769i \(0.617385\pi\)
\(522\) −3.00000 5.19615i −0.131306 0.227429i
\(523\) −11.1580 19.3262i −0.487905 0.845077i 0.511998 0.858987i \(-0.328906\pi\)
−0.999903 + 0.0139098i \(0.995572\pi\)
\(524\) −11.3160 −0.494342
\(525\) −1.00000 −0.0436436
\(526\) 7.88600 + 13.6590i 0.343846 + 0.595559i
\(527\) 0 0
\(528\) −1.88600 3.26665i −0.0820777 0.142163i
\(529\) 4.38600 7.59678i 0.190696 0.330295i
\(530\) 4.88600 8.46280i 0.212234 0.367601i
\(531\) −13.5440 −0.587760
\(532\) −1.38600 + 4.13267i −0.0600908 + 0.179174i
\(533\) 18.0000 0.779667
\(534\) 8.65800 14.9961i 0.374668 0.648945i
\(535\) 0 0
\(536\) −5.38600 9.32883i −0.232640 0.402944i
\(537\) 0.341997 0.592357i 0.0147583 0.0255621i
\(538\) −12.7720 22.1218i −0.550640 0.953737i
\(539\) −22.6320 −0.974830
\(540\) 1.00000 0.0430331
\(541\) −8.15800 14.1301i −0.350740 0.607499i 0.635639 0.771986i \(-0.280737\pi\)
−0.986379 + 0.164487i \(0.947403\pi\)
\(542\) 6.22800 + 10.7872i 0.267515 + 0.463350i
\(543\) 17.0880 0.733317
\(544\) 0 0
\(545\) −4.77200 8.26535i −0.204410 0.354049i
\(546\) 2.38600 4.13267i 0.102111 0.176862i
\(547\) −5.93000 10.2711i −0.253549 0.439159i 0.710952 0.703241i \(-0.248264\pi\)
−0.964500 + 0.264082i \(0.914931\pi\)
\(548\) 0.772002 1.33715i 0.0329783 0.0571201i
\(549\) −1.38600 + 2.40062i −0.0591531 + 0.102456i
\(550\) −3.77200 −0.160839
\(551\) −8.31601 + 24.7960i −0.354274 + 1.05635i
\(552\) 3.77200 0.160547
\(553\) 5.15800 8.93392i 0.219341 0.379909i
\(554\) 2.54400 4.40634i 0.108084 0.187208i
\(555\) 0.500000 + 0.866025i 0.0212238 + 0.0367607i
\(556\) 5.38600 9.32883i 0.228417 0.395630i
\(557\) −1.11400 1.92950i −0.0472017 0.0817557i 0.841459 0.540321i \(-0.181697\pi\)
−0.888661 + 0.458565i \(0.848364\pi\)
\(558\) −2.77200 −0.117348
\(559\) −41.8600 −1.77049
\(560\) 0.500000 + 0.866025i 0.0211289 + 0.0365963i
\(561\) 0 0
\(562\) −27.7720 −1.17149
\(563\) 37.5440 1.58229 0.791146 0.611628i \(-0.209485\pi\)
0.791146 + 0.611628i \(0.209485\pi\)
\(564\) 0 0
\(565\) 6.77200 11.7295i 0.284900 0.493462i
\(566\) −13.3160 23.0640i −0.559713 0.969452i
\(567\) 0.500000 0.866025i 0.0209980 0.0363696i
\(568\) −3.77200 + 6.53330i −0.158270 + 0.274131i
\(569\) 2.22800 0.0934025 0.0467013 0.998909i \(-0.485129\pi\)
0.0467013 + 0.998909i \(0.485129\pi\)
\(570\) −2.88600 3.26665i −0.120881 0.136825i
\(571\) −1.86001 −0.0778390 −0.0389195 0.999242i \(-0.512392\pi\)
−0.0389195 + 0.999242i \(0.512392\pi\)
\(572\) 9.00000 15.5885i 0.376309 0.651786i
\(573\) −3.77200 + 6.53330i −0.157578 + 0.272932i
\(574\) 1.88600 + 3.26665i 0.0787202 + 0.136347i
\(575\) 1.88600 3.26665i 0.0786517 0.136229i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 9.54400 0.397322 0.198661 0.980068i \(-0.436341\pi\)
0.198661 + 0.980068i \(0.436341\pi\)
\(578\) 17.0000 0.707107
\(579\) −1.38600 2.40062i −0.0576002 0.0997665i
\(580\) 3.00000 + 5.19615i 0.124568 + 0.215758i
\(581\) −6.00000 −0.248922
\(582\) 10.0000 0.414513
\(583\) −18.4300 31.9217i −0.763293 1.32206i
\(584\) −1.61400 + 2.79553i −0.0667878 + 0.115680i
\(585\) 2.38600 + 4.13267i 0.0986490 + 0.170865i
\(586\) −10.1140 + 17.5180i −0.417805 + 0.723660i
\(587\) 12.7720 22.1218i 0.527157 0.913063i −0.472342 0.881415i \(-0.656591\pi\)
0.999499 0.0316473i \(-0.0100753\pi\)
\(588\) −6.00000 −0.247436
\(589\) 8.00000 + 9.05516i 0.329634 + 0.373111i
\(590\) 13.5440 0.557598
\(591\) 5.65800 9.79995i 0.232739 0.403116i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) −3.77200 6.53330i −0.154898 0.268290i 0.778124 0.628110i \(-0.216171\pi\)
−0.933022 + 0.359820i \(0.882838\pi\)
\(594\) 1.88600 3.26665i 0.0773836 0.134032i
\(595\) 0 0
\(596\) −13.5440 −0.554784
\(597\) −0.316006 −0.0129332
\(598\) 9.00000 + 15.5885i 0.368037 + 0.637459i
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −35.6320 −1.45346 −0.726730 0.686923i \(-0.758961\pi\)
−0.726730 + 0.686923i \(0.758961\pi\)
\(602\) −4.38600 7.59678i −0.178760 0.309621i
\(603\) 5.38600 9.32883i 0.219335 0.379899i
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) −1.61400 + 2.79553i −0.0656184 + 0.113654i
\(606\) −3.00000 + 5.19615i −0.121867 + 0.211079i
\(607\) −40.0880 −1.62712 −0.813561 0.581480i \(-0.802474\pi\)
−0.813561 + 0.581480i \(0.802474\pi\)
\(608\) −1.38600 + 4.13267i −0.0562098 + 0.167602i
\(609\) 6.00000 0.243132
\(610\) 1.38600 2.40062i 0.0561175 0.0971984i
\(611\) 0 0
\(612\) 0 0
\(613\) 17.4300 30.1897i 0.703991 1.21935i −0.263063 0.964779i \(-0.584733\pi\)
0.967054 0.254570i \(-0.0819339\pi\)
\(614\) −11.7720 20.3897i −0.475079 0.822862i
\(615\) −3.77200 −0.152102
\(616\) 3.77200 0.151978
\(617\) 1.54400 + 2.67429i 0.0621593 + 0.107663i 0.895430 0.445202i \(-0.146868\pi\)
−0.833271 + 0.552865i \(0.813535\pi\)
\(618\) −6.50000 11.2583i −0.261468 0.452876i
\(619\) −31.1760 −1.25307 −0.626535 0.779393i \(-0.715527\pi\)
−0.626535 + 0.779393i \(0.715527\pi\)
\(620\) 2.77200 0.111326
\(621\) 1.88600 + 3.26665i 0.0756826 + 0.131086i
\(622\) 12.7720 22.1218i 0.512111 0.887002i
\(623\) 8.65800 + 14.9961i 0.346876 + 0.600806i
\(624\) 2.38600 4.13267i 0.0955165 0.165439i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 2.45600 0.0981614
\(627\) −16.1140 + 3.26665i −0.643531 + 0.130457i
\(628\) 3.45600 0.137909
\(629\) 0 0
\(630\) −0.500000 + 0.866025i −0.0199205 + 0.0345033i
\(631\) 21.9300 + 37.9839i 0.873020 + 1.51211i 0.858857 + 0.512215i \(0.171175\pi\)
0.0141623 + 0.999900i \(0.495492\pi\)
\(632\) 5.15800 8.93392i 0.205174 0.355372i
\(633\) 10.2720 + 17.7916i 0.408275 + 0.707154i
\(634\) −20.2280 −0.803356
\(635\) −9.31601 −0.369694
\(636\) −4.88600 8.46280i −0.193743 0.335572i
\(637\) −14.3160 24.7960i −0.567221 0.982455i
\(638\) 22.6320 0.896010
\(639\) −7.54400 −0.298436
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −9.77200 + 16.9256i −0.385971 + 0.668521i −0.991903 0.126995i \(-0.959467\pi\)
0.605933 + 0.795516i \(0.292800\pi\)
\(642\) 0 0
\(643\) 0.158003 0.273669i 0.00623102 0.0107924i −0.862893 0.505387i \(-0.831350\pi\)
0.869124 + 0.494594i \(0.164683\pi\)
\(644\) −1.88600 + 3.26665i −0.0743188 + 0.128724i
\(645\) 8.77200 0.345397
\(646\) 0 0
\(647\) −12.6840 −0.498659 −0.249330 0.968419i \(-0.580210\pi\)
−0.249330 + 0.968419i \(0.580210\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 25.5440 44.2435i 1.00269 1.73671i
\(650\) −2.38600 4.13267i −0.0935867 0.162097i
\(651\) 1.38600 2.40062i 0.0543217 0.0940879i
\(652\) 9.15800 + 15.8621i 0.358655 + 0.621209i
\(653\) 29.3160 1.14722 0.573612 0.819127i \(-0.305542\pi\)
0.573612 + 0.819127i \(0.305542\pi\)
\(654\) −9.54400 −0.373200
\(655\) 5.65800 + 9.79995i 0.221076 + 0.382916i
\(656\) 1.88600 + 3.26665i 0.0736360 + 0.127541i
\(657\) −3.22800 −0.125936
\(658\) 0 0
\(659\) −6.34200 10.9847i −0.247049 0.427902i 0.715657 0.698452i \(-0.246128\pi\)
−0.962706 + 0.270551i \(0.912794\pi\)
\(660\) −1.88600 + 3.26665i −0.0734125 + 0.127154i
\(661\) 22.3160 + 38.6525i 0.867992 + 1.50341i 0.864045 + 0.503414i \(0.167923\pi\)
0.00394672 + 0.999992i \(0.498744\pi\)
\(662\) −13.2720 + 22.9878i −0.515831 + 0.893446i
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 4.27200 0.866025i 0.165661 0.0335830i
\(666\) 1.00000 0.0387492
\(667\) −11.3160 + 19.5999i −0.438157 + 0.758911i
\(668\) 5.65800 9.79995i 0.218915 0.379171i
\(669\) 12.5000 + 21.6506i 0.483278 + 0.837062i
\(670\) −5.38600 + 9.32883i −0.208079 + 0.360404i
\(671\) −5.22800 9.05516i −0.201825 0.349571i
\(672\) 1.00000 0.0385758
\(673\) −21.2280 −0.818279 −0.409140 0.912472i \(-0.634171\pi\)
−0.409140 + 0.912472i \(0.634171\pi\)
\(674\) −15.1580 26.2544i −0.583864 1.01128i
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 9.77200 0.375846
\(677\) 17.3160 0.665508 0.332754 0.943014i \(-0.392022\pi\)
0.332754 + 0.943014i \(0.392022\pi\)
\(678\) −6.77200 11.7295i −0.260077 0.450467i
\(679\) −5.00000 + 8.66025i −0.191882 + 0.332350i
\(680\) 0 0
\(681\) −4.54400 + 7.87045i −0.174127 + 0.301596i
\(682\) 5.22800 9.05516i 0.200190 0.346740i
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) −4.27200 + 0.866025i −0.163344 + 0.0331133i
\(685\) −1.54400 −0.0589934
\(686\) 6.50000 11.2583i 0.248171 0.429845i
\(687\) −11.9300 + 20.6634i −0.455158 + 0.788357i
\(688\) −4.38600 7.59678i −0.167215 0.289624i
\(689\) 23.3160 40.3845i 0.888269 1.53853i
\(690\) −1.88600 3.26665i −0.0717988 0.124359i
\(691\) 7.13999 0.271618 0.135809 0.990735i \(-0.456637\pi\)
0.135809 + 0.990735i \(0.456637\pi\)
\(692\) 11.3160 0.430170
\(693\) 1.88600 + 3.26665i 0.0716433 + 0.124090i
\(694\) −3.77200 6.53330i −0.143183 0.248001i
\(695\) −10.7720 −0.408605
\(696\) 6.00000 0.227429
\(697\) 0 0
\(698\) −4.61400 + 7.99168i −0.174642 + 0.302490i
\(699\) 2.22800 + 3.85901i 0.0842706 + 0.145961i
\(700\) 0.500000 0.866025i 0.0188982 0.0327327i
\(701\) −17.3160 + 29.9922i −0.654017 + 1.13279i 0.328123 + 0.944635i \(0.393584\pi\)
−0.982139 + 0.188155i \(0.939749\pi\)
\(702\) 4.77200 0.180108
\(703\) −2.88600 3.26665i −0.108848 0.123204i
\(704\) 3.77200 0.142163
\(705\) 0 0
\(706\) −6.77200 + 11.7295i −0.254868 + 0.441444i
\(707\) −3.00000 5.19615i −0.112827 0.195421i
\(708\) 6.77200 11.7295i 0.254507 0.440820i
\(709\) 17.3860 + 30.1134i 0.652945 + 1.13093i 0.982405 + 0.186764i \(0.0598001\pi\)
−0.329460 + 0.944170i \(0.606867\pi\)
\(710\) 7.54400 0.283121
\(711\) 10.3160 0.386880
\(712\) 8.65800 + 14.9961i 0.324472 + 0.562003i
\(713\) 5.22800 + 9.05516i 0.195790 + 0.339118i
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) 0.341997 + 0.592357i 0.0127810 + 0.0221374i
\(717\) −6.77200 + 11.7295i −0.252905 + 0.438044i
\(718\) 10.5440 + 18.2628i 0.393499 + 0.681560i
\(719\) −14.3160 + 24.7960i −0.533897 + 0.924737i 0.465319 + 0.885143i \(0.345940\pi\)
−0.999216 + 0.0395935i \(0.987394\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) 13.0000 0.484145
\(722\) 15.1580 + 11.4558i 0.564122 + 0.426340i
\(723\) 22.3160 0.829941
\(724\) −8.54400 + 14.7986i −0.317535 + 0.549987i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 1.61400 + 2.79553i 0.0599011 + 0.103752i
\(727\) −21.7020 + 37.5890i −0.804883 + 1.39410i 0.111487 + 0.993766i \(0.464439\pi\)
−0.916370 + 0.400332i \(0.868895\pi\)
\(728\) 2.38600 + 4.13267i 0.0884311 + 0.153167i
\(729\) 1.00000 0.0370370
\(730\) 3.22800 0.119474
\(731\) 0 0
\(732\) −1.38600 2.40062i −0.0512281 0.0887296i
\(733\) 22.4040 0.827511 0.413756 0.910388i \(-0.364217\pi\)
0.413756 + 0.910388i \(0.364217\pi\)
\(734\) 9.22800 0.340612
\(735\) 3.00000 + 5.19615i 0.110657 + 0.191663i
\(736\) −1.88600 + 3.26665i −0.0695189 + 0.120410i
\(737\) 20.3160 + 35.1884i 0.748350 + 1.29618i
\(738\) −1.88600 + 3.26665i −0.0694247 + 0.120247i
\(739\) −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i \(-0.862648\pi\)
0.816373 + 0.577524i \(0.195981\pi\)
\(740\) −1.00000 −0.0367607
\(741\) −13.7720 15.5885i −0.505927 0.572656i
\(742\) 9.77200 0.358741
\(743\) −10.1140 + 17.5180i −0.371047 + 0.642672i −0.989727 0.142971i \(-0.954334\pi\)
0.618680 + 0.785643i \(0.287668\pi\)
\(744\) 1.38600 2.40062i 0.0508133 0.0880111i
\(745\) 6.77200 + 11.7295i 0.248107 + 0.429734i
\(746\) −0.113999 + 0.197452i −0.00417380 + 0.00722924i
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) 0 0
\(749\) 0 0
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) −25.3860 43.9698i −0.926348 1.60448i −0.789378 0.613907i \(-0.789597\pi\)
−0.136970 0.990575i \(-0.543736\pi\)
\(752\) 0 0
\(753\) 1.54400 0.0562666
\(754\) 14.3160 + 24.7960i 0.521358 + 0.903019i
\(755\) −4.00000 + 6.92820i −0.145575 + 0.252143i
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) 14.8160 25.6621i 0.538497 0.932704i −0.460488 0.887666i \(-0.652326\pi\)
0.998985 0.0450382i \(-0.0143410\pi\)
\(758\) −4.61400 + 7.99168i −0.167588 + 0.290271i
\(759\) −14.2280 −0.516444
\(760\) 4.27200 0.866025i 0.154962 0.0314140i
\(761\) 21.9480 0.795615 0.397807 0.917469i \(-0.369771\pi\)
0.397807 + 0.917469i \(0.369771\pi\)
\(762\) −4.65800 + 8.06790i −0.168742 + 0.292269i
\(763\) 4.77200 8.26535i 0.172758 0.299226i
\(764\) −3.77200 6.53330i −0.136466 0.236366i
\(765\) 0 0
\(766\) −12.0000 20.7846i −0.433578 0.750978i
\(767\) 64.6320 2.33373
\(768\) 1.00000 0.0360844
\(769\) −17.9300 31.0557i −0.646573 1.11990i −0.983936 0.178522i \(-0.942868\pi\)
0.337363 0.941374i \(-0.390465\pi\)
\(770\) −1.88600 3.26665i −0.0679668 0.117722i
\(771\) −30.0000 −1.08042
\(772\) 2.77200 0.0997665
\(773\) 1.88600 + 3.26665i 0.0678347 + 0.117493i 0.897948 0.440102i \(-0.145058\pi\)
−0.830113 + 0.557595i \(0.811724\pi\)
\(774\) 4.38600 7.59678i 0.157652 0.273060i
\(775\) −1.38600 2.40062i −0.0497866 0.0862330i
\(776\) −5.00000 + 8.66025i −0.179490 + 0.310885i
\(777\) −0.500000 + 0.866025i −0.0179374 + 0.0310685i
\(778\) 9.08801 0.325821
\(779\) 16.1140 3.26665i 0.577344 0.117040i
\(780\) −4.77200 −0.170865