Properties

Label 570.2.i.e.391.1
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $2$
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: \(2\)
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 391.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.e.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} -5.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} -5.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +1.00000 q^{11} -1.00000 q^{12} +(-3.00000 - 5.19615i) q^{13} +(-2.50000 + 4.33013i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} +1.00000 q^{20} +(-2.50000 + 4.33013i) q^{21} +(0.500000 - 0.866025i) q^{22} +(-3.50000 - 6.06218i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -6.00000 q^{26} -1.00000 q^{27} +(2.50000 + 4.33013i) q^{28} +(-3.00000 - 5.19615i) q^{29} +1.00000 q^{30} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +(2.00000 + 3.46410i) q^{34} +(2.50000 - 4.33013i) q^{35} +(-0.500000 + 0.866025i) q^{36} +7.00000 q^{37} +(3.50000 + 2.59808i) q^{38} -6.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(2.50000 - 4.33013i) q^{41} +(2.50000 + 4.33013i) q^{42} +(-3.00000 + 5.19615i) q^{43} +(-0.500000 - 0.866025i) q^{44} +1.00000 q^{45} -7.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(0.500000 + 0.866025i) q^{48} +18.0000 q^{49} -1.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-5.50000 - 9.52628i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.500000 + 0.866025i) q^{55} +5.00000 q^{56} +(3.50000 + 2.59808i) q^{57} -6.00000 q^{58} +(4.00000 - 6.92820i) q^{59} +(0.500000 - 0.866025i) q^{60} +(2.00000 + 3.46410i) q^{61} +(2.50000 + 4.33013i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(-0.500000 - 0.866025i) q^{66} +(-6.00000 - 10.3923i) q^{67} +4.00000 q^{68} -7.00000 q^{69} +(-2.50000 - 4.33013i) q^{70} +(-1.00000 + 1.73205i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(3.50000 - 6.06218i) q^{74} -1.00000 q^{75} +(4.00000 - 1.73205i) q^{76} -5.00000 q^{77} +(-3.00000 + 5.19615i) q^{78} +(-5.00000 + 8.66025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} -10.0000 q^{83} +5.00000 q^{84} +(-2.00000 - 3.46410i) q^{85} +(3.00000 + 5.19615i) q^{86} -6.00000 q^{87} -1.00000 q^{88} +(-6.50000 - 11.2583i) q^{89} +(0.500000 - 0.866025i) q^{90} +(15.0000 + 25.9808i) q^{91} +(-3.50000 + 6.06218i) q^{92} +8.00000 q^{94} +(-3.50000 - 2.59808i) q^{95} +1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(9.00000 - 15.5885i) q^{98} +(-0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 10q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 10q^{7} - 2q^{8} - q^{9} + q^{10} + 2q^{11} - 2q^{12} - 6q^{13} - 5q^{14} + q^{15} - q^{16} - 4q^{17} - 2q^{18} - q^{19} + 2q^{20} - 5q^{21} + q^{22} - 7q^{23} - q^{24} - q^{25} - 12q^{26} - 2q^{27} + 5q^{28} - 6q^{29} + 2q^{30} + q^{32} + q^{33} + 4q^{34} + 5q^{35} - q^{36} + 14q^{37} + 7q^{38} - 12q^{39} + q^{40} + 5q^{41} + 5q^{42} - 6q^{43} - q^{44} + 2q^{45} - 14q^{46} + 8q^{47} + q^{48} + 36q^{49} - 2q^{50} + 4q^{51} - 6q^{52} - 11q^{53} - q^{54} - q^{55} + 10q^{56} + 7q^{57} - 12q^{58} + 8q^{59} + q^{60} + 4q^{61} + 5q^{63} + 2q^{64} + 12q^{65} - q^{66} - 12q^{67} + 8q^{68} - 14q^{69} - 5q^{70} - 2q^{71} + q^{72} + 2q^{73} + 7q^{74} - 2q^{75} + 8q^{76} - 10q^{77} - 6q^{78} - 10q^{79} - q^{80} - q^{81} - 5q^{82} - 20q^{83} + 10q^{84} - 4q^{85} + 6q^{86} - 12q^{87} - 2q^{88} - 13q^{89} + q^{90} + 30q^{91} - 7q^{92} + 16q^{94} - 7q^{95} + 2q^{96} - 2q^{97} + 18q^{98} - q^{99} + O(q^{100}) \)

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
\(7\) −5.00000 −1.88982 −0.944911 0.327327i \(-0.893852\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) −1.00000 −0.288675
\(13\) −3.00000 5.19615i −0.832050 1.44115i −0.896410 0.443227i \(-0.853834\pi\)
0.0643593 0.997927i \(-0.479500\pi\)
\(14\) −2.50000 + 4.33013i −0.668153 + 1.15728i
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) −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
\(19\) −0.500000 + 4.33013i −0.114708 + 0.993399i
\(20\) 1.00000 0.223607
\(21\) −2.50000 + 4.33013i −0.545545 + 0.944911i
\(22\) 0.500000 0.866025i 0.106600 0.184637i
\(23\) −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i \(-0.906280\pi\)
0.227167 0.973856i \(-0.427054\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −6.00000 −1.17670
\(27\) −1.00000 −0.192450
\(28\) 2.50000 + 4.33013i 0.472456 + 0.818317i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 1.00000 0.182574
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.500000 0.866025i 0.0870388 0.150756i
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) 2.50000 4.33013i 0.422577 0.731925i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 3.50000 + 2.59808i 0.567775 + 0.421464i
\(39\) −6.00000 −0.960769
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 2.50000 4.33013i 0.390434 0.676252i −0.602072 0.798441i \(-0.705658\pi\)
0.992507 + 0.122189i \(0.0389915\pi\)
\(42\) 2.50000 + 4.33013i 0.385758 + 0.668153i
\(43\) −3.00000 + 5.19615i −0.457496 + 0.792406i −0.998828 0.0484030i \(-0.984587\pi\)
0.541332 + 0.840809i \(0.317920\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 1.00000 0.149071
\(46\) −7.00000 −1.03209
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 18.0000 2.57143
\(50\) −1.00000 −0.141421
\(51\) 2.00000 + 3.46410i 0.280056 + 0.485071i
\(52\) −3.00000 + 5.19615i −0.416025 + 0.720577i
\(53\) −5.50000 9.52628i −0.755483 1.30854i −0.945134 0.326683i \(-0.894069\pi\)
0.189651 0.981852i \(-0.439264\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −0.500000 + 0.866025i −0.0674200 + 0.116775i
\(56\) 5.00000 0.668153
\(57\) 3.50000 + 2.59808i 0.463586 + 0.344124i
\(58\) −6.00000 −0.787839
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) 0 0
\(63\) 2.50000 + 4.33013i 0.314970 + 0.545545i
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) −0.500000 0.866025i −0.0615457 0.106600i
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) 4.00000 0.485071
\(69\) −7.00000 −0.842701
\(70\) −2.50000 4.33013i −0.298807 0.517549i
\(71\) −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
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) 3.50000 6.06218i 0.406867 0.704714i
\(75\) −1.00000 −0.115470
\(76\) 4.00000 1.73205i 0.458831 0.198680i
\(77\) −5.00000 −0.569803
\(78\) −3.00000 + 5.19615i −0.339683 + 0.588348i
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.50000 4.33013i −0.276079 0.478183i
\(83\) −10.0000 −1.09764 −0.548821 0.835940i \(-0.684923\pi\)
−0.548821 + 0.835940i \(0.684923\pi\)
\(84\) 5.00000 0.545545
\(85\) −2.00000 3.46410i −0.216930 0.375735i
\(86\) 3.00000 + 5.19615i 0.323498 + 0.560316i
\(87\) −6.00000 −0.643268
\(88\) −1.00000 −0.106600
\(89\) −6.50000 11.2583i −0.688999 1.19338i −0.972162 0.234309i \(-0.924717\pi\)
0.283164 0.959072i \(-0.408616\pi\)
\(90\) 0.500000 0.866025i 0.0527046 0.0912871i
\(91\) 15.0000 + 25.9808i 1.57243 + 2.72352i
\(92\) −3.50000 + 6.06218i −0.364900 + 0.632026i
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) −3.50000 2.59808i −0.359092 0.266557i
\(96\) 1.00000 0.102062
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 9.00000 15.5885i 0.909137 1.57467i
\(99\) −0.500000 0.866025i −0.0502519 0.0870388i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 4.00000 0.396059
\(103\) 15.0000 1.47799 0.738997 0.673709i \(-0.235300\pi\)
0.738997 + 0.673709i \(0.235300\pi\)
\(104\) 3.00000 + 5.19615i 0.294174 + 0.509525i
\(105\) −2.50000 4.33013i −0.243975 0.422577i
\(106\) −11.0000 −1.06841
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 8.00000 13.8564i 0.766261 1.32720i −0.173316 0.984866i \(-0.555448\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(110\) 0.500000 + 0.866025i 0.0476731 + 0.0825723i
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 2.50000 4.33013i 0.236228 0.409159i
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 4.00000 1.73205i 0.374634 0.162221i
\(115\) 7.00000 0.652753
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) −3.00000 + 5.19615i −0.277350 + 0.480384i
\(118\) −4.00000 6.92820i −0.368230 0.637793i
\(119\) 10.0000 17.3205i 0.916698 1.58777i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) −10.0000 −0.909091
\(122\) 4.00000 0.362143
\(123\) −2.50000 4.33013i −0.225417 0.390434i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 5.00000 0.445435
\(127\) 2.50000 + 4.33013i 0.221839 + 0.384237i 0.955366 0.295423i \(-0.0954607\pi\)
−0.733527 + 0.679660i \(0.762127\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 3.00000 + 5.19615i 0.264135 + 0.457496i
\(130\) 3.00000 5.19615i 0.263117 0.455733i
\(131\) 1.50000 2.59808i 0.131056 0.226995i −0.793028 0.609185i \(-0.791497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 2.50000 21.6506i 0.216777 1.87735i
\(134\) −12.0000 −1.03664
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) −3.50000 + 6.06218i −0.297940 + 0.516047i
\(139\) 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) −5.00000 −0.422577
\(141\) 8.00000 0.673722
\(142\) 1.00000 + 1.73205i 0.0839181 + 0.145350i
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 9.00000 15.5885i 0.742307 1.28571i
\(148\) −3.50000 6.06218i −0.287698 0.498308i
\(149\) 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i \(-0.780943\pi\)
0.936245 + 0.351348i \(0.114277\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0.500000 4.33013i 0.0405554 0.351220i
\(153\) 4.00000 0.323381
\(154\) −2.50000 + 4.33013i −0.201456 + 0.348932i
\(155\) 0 0
\(156\) 3.00000 + 5.19615i 0.240192 + 0.416025i
\(157\) −4.50000 + 7.79423i −0.359139 + 0.622047i −0.987817 0.155618i \(-0.950263\pi\)
0.628678 + 0.777666i \(0.283596\pi\)
\(158\) 5.00000 + 8.66025i 0.397779 + 0.688973i
\(159\) −11.0000 −0.872357
\(160\) −1.00000 −0.0790569
\(161\) 17.5000 + 30.3109i 1.37919 + 2.38883i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0.500000 + 0.866025i 0.0389249 + 0.0674200i
\(166\) −5.00000 + 8.66025i −0.388075 + 0.672166i
\(167\) −10.5000 18.1865i −0.812514 1.40732i −0.911099 0.412188i \(-0.864765\pi\)
0.0985846 0.995129i \(-0.468568\pi\)
\(168\) 2.50000 4.33013i 0.192879 0.334077i
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) −4.00000 −0.306786
\(171\) 4.00000 1.73205i 0.305888 0.132453i
\(172\) 6.00000 0.457496
\(173\) 4.50000 7.79423i 0.342129 0.592584i −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) −3.00000 + 5.19615i −0.227429 + 0.393919i
\(175\) 2.50000 + 4.33013i 0.188982 + 0.327327i
\(176\) −0.500000 + 0.866025i −0.0376889 + 0.0652791i
\(177\) −4.00000 6.92820i −0.300658 0.520756i
\(178\) −13.0000 −0.974391
\(179\) 7.00000 0.523205 0.261602 0.965176i \(-0.415749\pi\)
0.261602 + 0.965176i \(0.415749\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −9.00000 15.5885i −0.668965 1.15868i −0.978194 0.207693i \(-0.933404\pi\)
0.309229 0.950988i \(-0.399929\pi\)
\(182\) 30.0000 2.22375
\(183\) 4.00000 0.295689
\(184\) 3.50000 + 6.06218i 0.258023 + 0.446910i
\(185\) −3.50000 + 6.06218i −0.257325 + 0.445700i
\(186\) 0 0
\(187\) −2.00000 + 3.46410i −0.146254 + 0.253320i
\(188\) 4.00000 6.92820i 0.291730 0.505291i
\(189\) 5.00000 0.363696
\(190\) −4.00000 + 1.73205i −0.290191 + 0.125656i
\(191\) −14.0000 −1.01300 −0.506502 0.862239i \(-0.669062\pi\)
−0.506502 + 0.862239i \(0.669062\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 3.00000 5.19615i 0.214834 0.372104i
\(196\) −9.00000 15.5885i −0.642857 1.11346i
\(197\) 1.00000 0.0712470 0.0356235 0.999365i \(-0.488658\pi\)
0.0356235 + 0.999365i \(0.488658\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) −12.0000 −0.846415
\(202\) −2.00000 −0.140720
\(203\) 15.0000 + 25.9808i 1.05279 + 1.82349i
\(204\) 2.00000 3.46410i 0.140028 0.242536i
\(205\) 2.50000 + 4.33013i 0.174608 + 0.302429i
\(206\) 7.50000 12.9904i 0.522550 0.905083i
\(207\) −3.50000 + 6.06218i −0.243267 + 0.421350i
\(208\) 6.00000 0.416025
\(209\) −0.500000 + 4.33013i −0.0345857 + 0.299521i
\(210\) −5.00000 −0.345033
\(211\) −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) −5.50000 + 9.52628i −0.377742 + 0.654268i
\(213\) 1.00000 + 1.73205i 0.0685189 + 0.118678i
\(214\) −2.00000 + 3.46410i −0.136717 + 0.236801i
\(215\) −3.00000 5.19615i −0.204598 0.354375i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −8.00000 13.8564i −0.541828 0.938474i
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) 1.00000 0.0674200
\(221\) 24.0000 1.61441
\(222\) −3.50000 6.06218i −0.234905 0.406867i
\(223\) 10.5000 18.1865i 0.703132 1.21786i −0.264229 0.964460i \(-0.585118\pi\)
0.967361 0.253401i \(-0.0815490\pi\)
\(224\) −2.50000 4.33013i −0.167038 0.289319i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 2.00000 3.46410i 0.133038 0.230429i
\(227\) 2.00000 0.132745 0.0663723 0.997795i \(-0.478857\pi\)
0.0663723 + 0.997795i \(0.478857\pi\)
\(228\) 0.500000 4.33013i 0.0331133 0.286770i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 3.50000 6.06218i 0.230783 0.399728i
\(231\) −2.50000 + 4.33013i −0.164488 + 0.284901i
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 9.00000 15.5885i 0.589610 1.02123i −0.404674 0.914461i \(-0.632615\pi\)
0.994283 0.106773i \(-0.0340517\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) −8.00000 −0.521862
\(236\) −8.00000 −0.520756
\(237\) 5.00000 + 8.66025i 0.324785 + 0.562544i
\(238\) −10.0000 17.3205i −0.648204 1.12272i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 13.0000 + 22.5167i 0.837404 + 1.45043i 0.892058 + 0.451920i \(0.149261\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) −5.00000 + 8.66025i −0.321412 + 0.556702i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 2.00000 3.46410i 0.128037 0.221766i
\(245\) −9.00000 + 15.5885i −0.574989 + 0.995910i
\(246\) −5.00000 −0.318788
\(247\) 24.0000 10.3923i 1.52708 0.661247i
\(248\) 0 0
\(249\) −5.00000 + 8.66025i −0.316862 + 0.548821i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) −6.00000 10.3923i −0.378717 0.655956i 0.612159 0.790735i \(-0.290301\pi\)
−0.990876 + 0.134778i \(0.956968\pi\)
\(252\) 2.50000 4.33013i 0.157485 0.272772i
\(253\) −3.50000 6.06218i −0.220043 0.381126i
\(254\) 5.00000 0.313728
\(255\) −4.00000 −0.250490
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 6.00000 0.373544
\(259\) −35.0000 −2.17479
\(260\) −3.00000 5.19615i −0.186052 0.322252i
\(261\) −3.00000 + 5.19615i −0.185695 + 0.321634i
\(262\) −1.50000 2.59808i −0.0926703 0.160510i
\(263\) −10.5000 + 18.1865i −0.647458 + 1.12143i 0.336270 + 0.941766i \(0.390834\pi\)
−0.983728 + 0.179664i \(0.942499\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 11.0000 0.675725
\(266\) −17.5000 12.9904i −1.07299 0.796491i
\(267\) −13.0000 −0.795587
\(268\) −6.00000 + 10.3923i −0.366508 + 0.634811i
\(269\) −16.0000 + 27.7128i −0.975537 + 1.68968i −0.297386 + 0.954757i \(0.596115\pi\)
−0.678151 + 0.734923i \(0.737218\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −1.00000 + 1.73205i −0.0607457 + 0.105215i −0.894799 0.446469i \(-0.852681\pi\)
0.834053 + 0.551684i \(0.186015\pi\)
\(272\) −2.00000 3.46410i −0.121268 0.210042i
\(273\) 30.0000 1.81568
\(274\) 12.0000 0.724947
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) 3.50000 + 6.06218i 0.210675 + 0.364900i
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) 16.0000 0.959616
\(279\) 0 0
\(280\) −2.50000 + 4.33013i −0.149404 + 0.258775i
\(281\) 5.50000 + 9.52628i 0.328102 + 0.568290i 0.982135 0.188176i \(-0.0602575\pi\)
−0.654033 + 0.756466i \(0.726924\pi\)
\(282\) 4.00000 6.92820i 0.238197 0.412568i
\(283\) −11.0000 + 19.0526i −0.653882 + 1.13256i 0.328291 + 0.944577i \(0.393527\pi\)
−0.982173 + 0.187980i \(0.939806\pi\)
\(284\) 2.00000 0.118678
\(285\) −4.00000 + 1.73205i −0.236940 + 0.102598i
\(286\) −6.00000 −0.354787
\(287\) −12.5000 + 21.6506i −0.737852 + 1.27800i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 3.00000 5.19615i 0.176166 0.305129i
\(291\) 1.00000 + 1.73205i 0.0586210 + 0.101535i
\(292\) −2.00000 −0.117041
\(293\) 5.00000 0.292103 0.146052 0.989277i \(-0.453343\pi\)
0.146052 + 0.989277i \(0.453343\pi\)
\(294\) −9.00000 15.5885i −0.524891 0.909137i
\(295\) 4.00000 + 6.92820i 0.232889 + 0.403376i
\(296\) −7.00000 −0.406867
\(297\) −1.00000 −0.0580259
\(298\) −2.00000 3.46410i −0.115857 0.200670i
\(299\) −21.0000 + 36.3731i −1.21446 + 2.10351i
\(300\) 0.500000 + 0.866025i 0.0288675 + 0.0500000i
\(301\) 15.0000 25.9808i 0.864586 1.49751i
\(302\) −10.0000 + 17.3205i −0.575435 + 0.996683i
\(303\) −2.00000 −0.114897
\(304\) −3.50000 2.59808i −0.200739 0.149010i
\(305\) −4.00000 −0.229039
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) −9.00000 + 15.5885i −0.513657 + 0.889680i 0.486217 + 0.873838i \(0.338376\pi\)
−0.999875 + 0.0158424i \(0.994957\pi\)
\(308\) 2.50000 + 4.33013i 0.142451 + 0.246732i
\(309\) 7.50000 12.9904i 0.426660 0.738997i
\(310\) 0 0
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 6.00000 0.339683
\(313\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(314\) 4.50000 + 7.79423i 0.253950 + 0.439854i
\(315\) −5.00000 −0.281718
\(316\) 10.0000 0.562544
\(317\) −1.50000 2.59808i −0.0842484 0.145922i 0.820822 0.571184i \(-0.193516\pi\)
−0.905071 + 0.425261i \(0.860182\pi\)
\(318\) −5.50000 + 9.52628i −0.308425 + 0.534207i
\(319\) −3.00000 5.19615i −0.167968 0.290929i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −2.00000 + 3.46410i −0.111629 + 0.193347i
\(322\) 35.0000 1.95047
\(323\) −14.0000 10.3923i −0.778981 0.578243i
\(324\) 1.00000 0.0555556
\(325\) −3.00000 + 5.19615i −0.166410 + 0.288231i
\(326\) −5.00000 + 8.66025i −0.276924 + 0.479647i
\(327\) −8.00000 13.8564i −0.442401 0.766261i
\(328\) −2.50000 + 4.33013i −0.138039 + 0.239091i
\(329\) −20.0000 34.6410i −1.10264 1.90982i
\(330\) 1.00000 0.0550482
\(331\) 15.0000 0.824475 0.412237 0.911077i \(-0.364747\pi\)
0.412237 + 0.911077i \(0.364747\pi\)
\(332\) 5.00000 + 8.66025i 0.274411 + 0.475293i
\(333\) −3.50000 6.06218i −0.191799 0.332205i
\(334\) −21.0000 −1.14907
\(335\) 12.0000 0.655630
\(336\) −2.50000 4.33013i −0.136386 0.236228i
\(337\) −1.00000 + 1.73205i −0.0544735 + 0.0943508i −0.891976 0.452082i \(-0.850681\pi\)
0.837503 + 0.546433i \(0.184015\pi\)
\(338\) 11.5000 + 19.9186i 0.625518 + 1.08343i
\(339\) 2.00000 3.46410i 0.108625 0.188144i
\(340\) −2.00000 + 3.46410i −0.108465 + 0.187867i
\(341\) 0 0
\(342\) 0.500000 4.33013i 0.0270369 0.234146i
\(343\) −55.0000 −2.96972
\(344\) 3.00000 5.19615i 0.161749 0.280158i
\(345\) 3.50000 6.06218i 0.188434 0.326377i
\(346\) −4.50000 7.79423i −0.241921 0.419020i
\(347\) 1.00000 1.73205i 0.0536828 0.0929814i −0.837935 0.545770i \(-0.816237\pi\)
0.891618 + 0.452788i \(0.149571\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 5.00000 0.267261
\(351\) 3.00000 + 5.19615i 0.160128 + 0.277350i
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 36.0000 1.91609 0.958043 0.286623i \(-0.0925328\pi\)
0.958043 + 0.286623i \(0.0925328\pi\)
\(354\) −8.00000 −0.425195
\(355\) −1.00000 1.73205i −0.0530745 0.0919277i
\(356\) −6.50000 + 11.2583i −0.344499 + 0.596690i
\(357\) −10.0000 17.3205i −0.529256 0.916698i
\(358\) 3.50000 6.06218i 0.184981 0.320396i
\(359\) 9.00000 15.5885i 0.475002 0.822727i −0.524588 0.851356i \(-0.675781\pi\)
0.999590 + 0.0286287i \(0.00911406\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −18.5000 4.33013i −0.973684 0.227901i
\(362\) −18.0000 −0.946059
\(363\) −5.00000 + 8.66025i −0.262432 + 0.454545i
\(364\) 15.0000 25.9808i 0.786214 1.36176i
\(365\) 1.00000 + 1.73205i 0.0523424 + 0.0906597i
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 7.00000 0.364900
\(369\) −5.00000 −0.260290
\(370\) 3.50000 + 6.06218i 0.181956 + 0.315158i
\(371\) 27.5000 + 47.6314i 1.42773 + 2.47290i
\(372\) 0 0
\(373\) 5.00000 0.258890 0.129445 0.991587i \(-0.458680\pi\)
0.129445 + 0.991587i \(0.458680\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) −4.00000 6.92820i −0.206284 0.357295i
\(377\) −18.0000 + 31.1769i −0.927047 + 1.60569i
\(378\) 2.50000 4.33013i 0.128586 0.222718i
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) −0.500000 + 4.33013i −0.0256495 + 0.222131i
\(381\) 5.00000 0.256158
\(382\) −7.00000 + 12.1244i −0.358151 + 0.620336i
\(383\) −16.0000 + 27.7128i −0.817562 + 1.41606i 0.0899119 + 0.995950i \(0.471341\pi\)
−0.907474 + 0.420109i \(0.861992\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 2.50000 4.33013i 0.127412 0.220684i
\(386\) −2.00000 3.46410i −0.101797 0.176318i
\(387\) 6.00000 0.304997
\(388\) 2.00000 0.101535
\(389\) 5.00000 + 8.66025i 0.253510 + 0.439092i 0.964490 0.264120i \(-0.0850816\pi\)
−0.710980 + 0.703213i \(0.751748\pi\)
\(390\) −3.00000 5.19615i −0.151911 0.263117i
\(391\) 28.0000 1.41602
\(392\) −18.0000 −0.909137
\(393\) −1.50000 2.59808i −0.0756650 0.131056i
\(394\) 0.500000 0.866025i 0.0251896 0.0436297i
\(395\) −5.00000 8.66025i −0.251577 0.435745i
\(396\) −0.500000 + 0.866025i −0.0251259 + 0.0435194i
\(397\) 16.5000 28.5788i 0.828111 1.43433i −0.0714068 0.997447i \(-0.522749\pi\)
0.899518 0.436884i \(-0.143918\pi\)
\(398\) 4.00000 0.200502
\(399\) −17.5000 12.9904i −0.876096 0.650332i
\(400\) 1.00000 0.0500000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) −6.00000 + 10.3923i −0.299253 + 0.518321i
\(403\) 0 0
\(404\) −1.00000 + 1.73205i −0.0497519 + 0.0861727i
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) 30.0000 1.48888
\(407\) 7.00000 0.346977
\(408\) −2.00000 3.46410i −0.0990148 0.171499i
\(409\) 1.50000 + 2.59808i 0.0741702 + 0.128467i 0.900725 0.434389i \(-0.143036\pi\)
−0.826555 + 0.562856i \(0.809703\pi\)
\(410\) 5.00000 0.246932
\(411\) 12.0000 0.591916
\(412\) −7.50000 12.9904i −0.369498 0.639990i
\(413\) −20.0000 + 34.6410i −0.984136 + 1.70457i
\(414\) 3.50000 + 6.06218i 0.172016 + 0.297940i
\(415\) 5.00000 8.66025i 0.245440 0.425115i
\(416\) 3.00000 5.19615i 0.147087 0.254762i
\(417\) 16.0000 0.783523
\(418\) 3.50000 + 2.59808i 0.171191 + 0.127076i
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) −2.50000 + 4.33013i −0.121988 + 0.211289i
\(421\) 4.00000 6.92820i 0.194948 0.337660i −0.751935 0.659237i \(-0.770879\pi\)
0.946883 + 0.321577i \(0.104213\pi\)
\(422\) 6.50000 + 11.2583i 0.316415 + 0.548047i
\(423\) 4.00000 6.92820i 0.194487 0.336861i
\(424\) 5.50000 + 9.52628i 0.267104 + 0.462637i
\(425\) 4.00000 0.194029
\(426\) 2.00000 0.0969003
\(427\) −10.0000 17.3205i −0.483934 0.838198i
\(428\) 2.00000 + 3.46410i 0.0966736 + 0.167444i
\(429\) −6.00000 −0.289683
\(430\) −6.00000 −0.289346
\(431\) 2.00000 + 3.46410i 0.0963366 + 0.166860i 0.910166 0.414244i \(-0.135954\pi\)
−0.813829 + 0.581104i \(0.802621\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −3.00000 5.19615i −0.144171 0.249711i 0.784892 0.619632i \(-0.212718\pi\)
−0.929063 + 0.369921i \(0.879385\pi\)
\(434\) 0 0
\(435\) 3.00000 5.19615i 0.143839 0.249136i
\(436\) −16.0000 −0.766261
\(437\) 28.0000 12.1244i 1.33942 0.579987i
\(438\) −2.00000 −0.0955637
\(439\) 16.0000 27.7128i 0.763638 1.32266i −0.177325 0.984152i \(-0.556744\pi\)
0.940963 0.338508i \(-0.109922\pi\)
\(440\) 0.500000 0.866025i 0.0238366 0.0412861i
\(441\) −9.00000 15.5885i −0.428571 0.742307i
\(442\) 12.0000 20.7846i 0.570782 0.988623i
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) −7.00000 −0.332205
\(445\) 13.0000 0.616259
\(446\) −10.5000 18.1865i −0.497189 0.861157i
\(447\) −2.00000 3.46410i −0.0945968 0.163846i
\(448\) −5.00000 −0.236228
\(449\) −39.0000 −1.84052 −0.920262 0.391303i \(-0.872024\pi\)
−0.920262 + 0.391303i \(0.872024\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) 2.50000 4.33013i 0.117720 0.203898i
\(452\) −2.00000 3.46410i −0.0940721 0.162938i
\(453\) −10.0000 + 17.3205i −0.469841 + 0.813788i
\(454\) 1.00000 1.73205i 0.0469323 0.0812892i
\(455\) −30.0000 −1.40642
\(456\) −3.50000 2.59808i −0.163903 0.121666i
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 5.00000 8.66025i 0.233635 0.404667i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) −3.50000 6.06218i −0.163188 0.282650i
\(461\) 3.00000 5.19615i 0.139724 0.242009i −0.787668 0.616100i \(-0.788712\pi\)
0.927392 + 0.374091i \(0.122045\pi\)
\(462\) 2.50000 + 4.33013i 0.116311 + 0.201456i
\(463\) −9.00000 −0.418265 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −9.00000 15.5885i −0.416917 0.722121i
\(467\) 38.0000 1.75843 0.879215 0.476425i \(-0.158068\pi\)
0.879215 + 0.476425i \(0.158068\pi\)
\(468\) 6.00000 0.277350
\(469\) 30.0000 + 51.9615i 1.38527 + 2.39936i
\(470\) −4.00000 + 6.92820i −0.184506 + 0.319574i
\(471\) 4.50000 + 7.79423i 0.207349 + 0.359139i
\(472\) −4.00000 + 6.92820i −0.184115 + 0.318896i
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) 10.0000 0.459315
\(475\) 4.00000 1.73205i 0.183533 0.0794719i
\(476\) −20.0000 −0.916698
\(477\) −5.50000 + 9.52628i −0.251828 + 0.436178i
\(478\) 0 0
\(479\) −21.0000 36.3731i −0.959514 1.66193i −0.723681 0.690134i \(-0.757551\pi\)
−0.235833 0.971794i \(-0.575782\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) −21.0000 36.3731i −0.957518 1.65847i
\(482\) 26.0000 1.18427
\(483\) 35.0000 1.59256
\(484\) 5.00000 + 8.66025i 0.227273 + 0.393648i
\(485\) −1.00000 1.73205i −0.0454077 0.0786484i
\(486\) 1.00000 0.0453609
\(487\) −13.0000 −0.589086 −0.294543 0.955638i \(-0.595167\pi\)
−0.294543 + 0.955638i \(0.595167\pi\)
\(488\) −2.00000 3.46410i −0.0905357 0.156813i
\(489\) −5.00000 + 8.66025i −0.226108 + 0.391630i
\(490\) 9.00000 + 15.5885i 0.406579 + 0.704215i
\(491\) 16.5000 28.5788i 0.744635 1.28974i −0.205731 0.978609i \(-0.565957\pi\)
0.950365 0.311136i \(-0.100710\pi\)
\(492\) −2.50000 + 4.33013i −0.112709 + 0.195217i
\(493\) 24.0000 1.08091
\(494\) 3.00000 25.9808i 0.134976 1.16893i
\(495\) 1.00000 0.0449467
\(496\) 0 0
\(497\) 5.00000 8.66025i 0.224281 0.388465i
\(498\) 5.00000 + 8.66025i 0.224055 + 0.388075i
\(499\) 3.50000 6.06218i 0.156682 0.271380i −0.776989 0.629515i \(-0.783254\pi\)
0.933670 + 0.358134i \(0.116587\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) −21.0000 −0.938211
\(502\) −12.0000 −0.535586
\(503\) −0.500000 0.866025i −0.0222939 0.0386142i 0.854663 0.519183i \(-0.173764\pi\)
−0.876957 + 0.480569i \(0.840430\pi\)
\(504\) −2.50000 4.33013i −0.111359 0.192879i
\(505\) 2.00000 0.0889988
\(506\) −7.00000 −0.311188
\(507\) 11.5000 + 19.9186i 0.510733 + 0.884615i
\(508\) 2.50000 4.33013i 0.110920 0.192118i
\(509\) −1.00000 1.73205i −0.0443242 0.0767718i 0.843012 0.537895i \(-0.180780\pi\)
−0.887336 + 0.461123i \(0.847447\pi\)
\(510\) −2.00000 + 3.46410i −0.0885615 + 0.153393i
\(511\) −5.00000 + 8.66025i −0.221187 + 0.383107i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 4.33013i 0.0220755 0.191180i
\(514\) −18.0000 −0.793946
\(515\) −7.50000 + 12.9904i −0.330489 + 0.572425i
\(516\) 3.00000 5.19615i 0.132068 0.228748i
\(517\) 4.00000 + 6.92820i 0.175920 + 0.304702i
\(518\) −17.5000 + 30.3109i −0.768906 + 1.33178i
\(519\) −4.50000 7.79423i −0.197528 0.342129i
\(520\) −6.00000 −0.263117
\(521\) −14.0000 −0.613351 −0.306676 0.951814i \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) 3.00000 + 5.19615i 0.131306 + 0.227429i
\(523\) 7.00000 + 12.1244i 0.306089 + 0.530161i 0.977503 0.210921i \(-0.0676463\pi\)
−0.671414 + 0.741082i \(0.734313\pi\)
\(524\) −3.00000 −0.131056
\(525\) 5.00000 0.218218
\(526\) 10.5000 + 18.1865i 0.457822 + 0.792971i
\(527\) 0 0
\(528\) 0.500000 + 0.866025i 0.0217597 + 0.0376889i
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) 5.50000 9.52628i 0.238905 0.413795i
\(531\) −8.00000 −0.347170
\(532\) −20.0000 + 8.66025i −0.867110 + 0.375470i
\(533\) −30.0000 −1.29944
\(534\) −6.50000 + 11.2583i −0.281283 + 0.487196i
\(535\) 2.00000 3.46410i 0.0864675 0.149766i
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 3.50000 6.06218i 0.151036 0.261602i
\(538\) 16.0000 + 27.7128i 0.689809 + 1.19478i
\(539\) 18.0000 0.775315
\(540\) −1.00000 −0.0430331
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) 1.00000 + 1.73205i 0.0429537 + 0.0743980i
\(543\) −18.0000 −0.772454
\(544\) −4.00000 −0.171499
\(545\) 8.00000 + 13.8564i 0.342682 + 0.593543i
\(546\) 15.0000 25.9808i 0.641941 1.11187i
\(547\) −7.00000 12.1244i −0.299298 0.518400i 0.676677 0.736280i \(-0.263419\pi\)
−0.975976 + 0.217880i \(0.930086\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) 2.00000 3.46410i 0.0853579 0.147844i
\(550\) −1.00000 −0.0426401
\(551\) 24.0000 10.3923i 1.02243 0.442727i
\(552\) 7.00000 0.297940
\(553\) 25.0000 43.3013i 1.06311 1.84136i
\(554\) −7.00000 + 12.1244i −0.297402 + 0.515115i
\(555\) 3.50000 + 6.06218i 0.148567 + 0.257325i
\(556\) 8.00000 13.8564i 0.339276 0.587643i
\(557\) −0.500000 0.866025i −0.0211857 0.0366947i 0.855238 0.518235i \(-0.173411\pi\)
−0.876424 + 0.481540i \(0.840077\pi\)
\(558\) 0 0
\(559\) 36.0000 1.52264
\(560\) 2.50000 + 4.33013i 0.105644 + 0.182981i
\(561\) 2.00000 + 3.46410i 0.0844401 + 0.146254i
\(562\) 11.0000 0.464007
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −4.00000 6.92820i −0.168430 0.291730i
\(565\) −2.00000 + 3.46410i −0.0841406 + 0.145736i
\(566\) 11.0000 + 19.0526i 0.462364 + 0.800839i
\(567\) 2.50000 4.33013i 0.104990 0.181848i
\(568\) 1.00000 1.73205i 0.0419591 0.0726752i
\(569\) 33.0000 1.38343 0.691716 0.722170i \(-0.256855\pi\)
0.691716 + 0.722170i \(0.256855\pi\)
\(570\) −0.500000 + 4.33013i −0.0209427 + 0.181369i
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) −3.00000 + 5.19615i −0.125436 + 0.217262i
\(573\) −7.00000 + 12.1244i −0.292429 + 0.506502i
\(574\) 12.5000 + 21.6506i 0.521740 + 0.903680i
\(575\) −3.50000 + 6.06218i −0.145960 + 0.252810i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −32.0000 −1.33218 −0.666089 0.745873i \(-0.732033\pi\)
−0.666089 + 0.745873i \(0.732033\pi\)
\(578\) 1.00000 0.0415945
\(579\) −2.00000 3.46410i −0.0831172 0.143963i
\(580\) −3.00000 5.19615i −0.124568 0.215758i
\(581\) 50.0000 2.07435
\(582\) 2.00000 0.0829027
\(583\) −5.50000 9.52628i −0.227787 0.394538i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) −3.00000 5.19615i −0.124035 0.214834i
\(586\) 2.50000 4.33013i 0.103274 0.178876i
\(587\) 10.0000 17.3205i 0.412744 0.714894i −0.582445 0.812870i \(-0.697904\pi\)
0.995189 + 0.0979766i \(0.0312370\pi\)
\(588\) −18.0000 −0.742307
\(589\) 0 0
\(590\) 8.00000 0.329355
\(591\) 0.500000 0.866025i 0.0205673 0.0356235i
\(592\) −3.50000 + 6.06218i −0.143849 + 0.249154i
\(593\) −11.0000 19.0526i −0.451716 0.782395i 0.546777 0.837278i \(-0.315855\pi\)
−0.998493 + 0.0548835i \(0.982521\pi\)
\(594\) −0.500000 + 0.866025i −0.0205152 + 0.0355335i
\(595\) 10.0000 + 17.3205i 0.409960 + 0.710072i
\(596\) −4.00000 −0.163846
\(597\) 4.00000 0.163709
\(598\) 21.0000 + 36.3731i 0.858754 + 1.48741i
\(599\) −4.00000 6.92820i −0.163436 0.283079i 0.772663 0.634816i \(-0.218924\pi\)
−0.936099 + 0.351738i \(0.885591\pi\)
\(600\) 1.00000 0.0408248
\(601\) −3.00000 −0.122373 −0.0611863 0.998126i \(-0.519488\pi\)
−0.0611863 + 0.998126i \(0.519488\pi\)
\(602\) −15.0000 25.9808i −0.611354 1.05890i
\(603\) −6.00000 + 10.3923i −0.244339 + 0.423207i
\(604\) 10.0000 + 17.3205i 0.406894 + 0.704761i
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) −1.00000 + 1.73205i −0.0406222 + 0.0703598i
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) −4.00000 + 1.73205i −0.162221 + 0.0702439i
\(609\) 30.0000 1.21566
\(610\) −2.00000 + 3.46410i −0.0809776 + 0.140257i
\(611\) 24.0000 41.5692i 0.970936 1.68171i
\(612\) −2.00000 3.46410i −0.0808452 0.140028i
\(613\) −17.5000 + 30.3109i −0.706818 + 1.22425i 0.259213 + 0.965820i \(0.416537\pi\)
−0.966031 + 0.258425i \(0.916796\pi\)
\(614\) 9.00000 + 15.5885i 0.363210 + 0.629099i
\(615\) 5.00000 0.201619
\(616\) 5.00000 0.201456
\(617\) −24.0000 41.5692i −0.966204 1.67351i −0.706346 0.707867i \(-0.749658\pi\)
−0.259858 0.965647i \(-0.583676\pi\)
\(618\) −7.50000 12.9904i −0.301694 0.522550i
\(619\) 43.0000 1.72832 0.864158 0.503221i \(-0.167852\pi\)
0.864158 + 0.503221i \(0.167852\pi\)
\(620\) 0 0
\(621\) 3.50000 + 6.06218i 0.140450 + 0.243267i
\(622\) −10.0000 + 17.3205i −0.400963 + 0.694489i
\(623\) 32.5000 + 56.2917i 1.30209 + 2.25528i
\(624\) 3.00000 5.19615i 0.120096 0.208013i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 3.50000 + 2.59808i 0.139777 + 0.103757i
\(628\) 9.00000 0.359139
\(629\) −14.0000 + 24.2487i −0.558217 + 0.966859i
\(630\) −2.50000 + 4.33013i −0.0996024 + 0.172516i
\(631\) −19.0000 32.9090i −0.756378 1.31009i −0.944686 0.327975i \(-0.893634\pi\)
0.188308 0.982110i \(-0.439700\pi\)
\(632\) 5.00000 8.66025i 0.198889 0.344486i
\(633\) 6.50000 + 11.2583i 0.258352 + 0.447478i
\(634\) −3.00000 −0.119145
\(635\) −5.00000 −0.198419
\(636\) 5.50000 + 9.52628i 0.218089 + 0.377742i
\(637\) −54.0000 93.5307i −2.13956 3.70582i
\(638\) −6.00000 −0.237542
\(639\) 2.00000 0.0791188
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 13.0000 22.5167i 0.513469 0.889355i −0.486409 0.873731i \(-0.661693\pi\)
0.999878 0.0156233i \(-0.00497325\pi\)
\(642\) 2.00000 + 3.46410i 0.0789337 + 0.136717i
\(643\) 22.0000 38.1051i 0.867595 1.50272i 0.00314839 0.999995i \(-0.498998\pi\)
0.864447 0.502724i \(-0.167669\pi\)
\(644\) 17.5000 30.3109i 0.689597 1.19442i
\(645\) −6.00000 −0.236250
\(646\) −16.0000 + 6.92820i −0.629512 + 0.272587i
\(647\) 3.00000 0.117942 0.0589711 0.998260i \(-0.481218\pi\)
0.0589711 + 0.998260i \(0.481218\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 4.00000 6.92820i 0.157014 0.271956i
\(650\) 3.00000 + 5.19615i 0.117670 + 0.203810i
\(651\) 0 0
\(652\) 5.00000 + 8.66025i 0.195815 + 0.339162i
\(653\) 9.00000 0.352197 0.176099 0.984373i \(-0.443652\pi\)
0.176099 + 0.984373i \(0.443652\pi\)
\(654\) −16.0000 −0.625650
\(655\) 1.50000 + 2.59808i 0.0586098 + 0.101515i
\(656\) 2.50000 + 4.33013i 0.0976086 + 0.169063i
\(657\) −2.00000 −0.0780274
\(658\) −40.0000 −1.55936
\(659\) 5.50000 + 9.52628i 0.214250 + 0.371091i 0.953040 0.302844i \(-0.0979361\pi\)
−0.738791 + 0.673935i \(0.764603\pi\)
\(660\) 0.500000 0.866025i 0.0194625 0.0337100i
\(661\) 10.0000 + 17.3205i 0.388955 + 0.673690i 0.992309 0.123784i \(-0.0395028\pi\)
−0.603354 + 0.797473i \(0.706170\pi\)
\(662\) 7.50000 12.9904i 0.291496 0.504885i
\(663\) 12.0000 20.7846i 0.466041 0.807207i
\(664\) 10.0000 0.388075
\(665\) 17.5000 + 12.9904i 0.678621 + 0.503745i
\(666\) −7.00000 −0.271244
\(667\) −21.0000 + 36.3731i −0.813123 + 1.40837i
\(668\) −10.5000 + 18.1865i −0.406257 + 0.703658i
\(669\) −10.5000 18.1865i −0.405953 0.703132i
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) 2.00000 + 3.46410i 0.0772091 + 0.133730i
\(672\) −5.00000 −0.192879
\(673\) −40.0000 −1.54189 −0.770943 0.636904i \(-0.780215\pi\)
−0.770943 + 0.636904i \(0.780215\pi\)
\(674\) 1.00000 + 1.73205i 0.0385186 + 0.0667161i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 23.0000 0.884615
\(677\) 21.0000 0.807096 0.403548 0.914959i \(-0.367777\pi\)
0.403548 + 0.914959i \(0.367777\pi\)
\(678\) −2.00000 3.46410i −0.0768095 0.133038i
\(679\) 5.00000 8.66025i 0.191882 0.332350i
\(680\) 2.00000 + 3.46410i 0.0766965 + 0.132842i
\(681\) 1.00000 1.73205i 0.0383201 0.0663723i
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −3.50000 2.59808i −0.133826 0.0993399i
\(685\) −12.0000 −0.458496
\(686\) −27.5000 + 47.6314i −1.04995 + 1.81858i
\(687\) 5.00000 8.66025i 0.190762 0.330409i
\(688\) −3.00000 5.19615i −0.114374 0.198101i
\(689\) −33.0000 + 57.1577i −1.25720 + 2.17753i
\(690\) −3.50000 6.06218i −0.133243 0.230783i
\(691\) 1.00000 0.0380418 0.0190209 0.999819i \(-0.493945\pi\)
0.0190209 + 0.999819i \(0.493945\pi\)
\(692\) −9.00000 −0.342129
\(693\) 2.50000 + 4.33013i 0.0949671 + 0.164488i
\(694\) −1.00000 1.73205i −0.0379595 0.0657477i
\(695\) −16.0000 −0.606915
\(696\) 6.00000 0.227429
\(697\) 10.0000 + 17.3205i 0.378777 + 0.656061i
\(698\) 8.00000 13.8564i 0.302804 0.524473i
\(699\) −9.00000 15.5885i −0.340411 0.589610i
\(700\) 2.50000 4.33013i 0.0944911 0.163663i
\(701\) −17.0000 + 29.4449i −0.642081 + 1.11212i 0.342886 + 0.939377i \(0.388595\pi\)
−0.984967 + 0.172740i \(0.944738\pi\)
\(702\) 6.00000 0.226455
\(703\) −3.50000 + 30.3109i −0.132005 + 1.14320i
\(704\) 1.00000 0.0376889
\(705\) −4.00000 + 6.92820i −0.150649 + 0.260931i
\(706\) 18.0000 31.1769i 0.677439 1.17336i
\(707\) 5.00000 + 8.66025i 0.188044 + 0.325702i
\(708\) −4.00000 + 6.92820i −0.150329 + 0.260378i
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) −2.00000 −0.0750587
\(711\) 10.0000 0.375029
\(712\) 6.50000 + 11.2583i 0.243598 + 0.421924i
\(713\) 0 0
\(714\) −20.0000 −0.748481
\(715\) 6.00000 0.224387
\(716\) −3.50000 6.06218i −0.130801 0.226554i
\(717\) 0 0
\(718\) −9.00000 15.5885i −0.335877 0.581756i
\(719\) 22.0000 38.1051i 0.820462 1.42108i −0.0848774 0.996391i \(-0.527050\pi\)
0.905339 0.424690i \(-0.139617\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) −75.0000 −2.79315
\(722\) −13.0000 + 13.8564i −0.483810 + 0.515682i
\(723\) 26.0000 0.966950
\(724\) −9.00000 + 15.5885i −0.334482 + 0.579340i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 5.00000 + 8.66025i 0.185567 + 0.321412i
\(727\) −16.0000 + 27.7128i −0.593407 + 1.02781i 0.400362 + 0.916357i \(0.368884\pi\)
−0.993770 + 0.111454i \(0.964449\pi\)
\(728\) −15.0000 25.9808i −0.555937 0.962911i
\(729\) 1.00000 0.0370370
\(730\) 2.00000 0.0740233
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) −2.00000 3.46410i −0.0739221 0.128037i
\(733\) 19.0000 0.701781 0.350891 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) 4.00000 0.147643
\(735\) 9.00000 + 15.5885i 0.331970 + 0.574989i
\(736\) 3.50000 6.06218i 0.129012 0.223455i
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) −2.50000 + 4.33013i −0.0920263 + 0.159394i
\(739\) 23.5000 40.7032i 0.864461 1.49729i −0.00311943 0.999995i \(-0.500993\pi\)
0.867581 0.497296i \(-0.165674\pi\)
\(740\) 7.00000 0.257325
\(741\) 3.00000 25.9808i 0.110208 0.954427i
\(742\) 55.0000 2.01911
\(743\) −7.50000 + 12.9904i −0.275148 + 0.476571i −0.970173 0.242415i \(-0.922060\pi\)
0.695024 + 0.718986i \(0.255394\pi\)
\(744\) 0 0
\(745\) 2.00000 + 3.46410i 0.0732743 + 0.126915i
\(746\) 2.50000 4.33013i 0.0915315 0.158537i
\(747\) 5.00000 + 8.66025i 0.182940 + 0.316862i
\(748\) 4.00000 0.146254
\(749\) 20.0000 0.730784
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) −20.0000 34.6410i −0.729810 1.26407i −0.956963 0.290209i \(-0.906275\pi\)
0.227153 0.973859i \(-0.427058\pi\)
\(752\) −8.00000 −0.291730
\(753\) −12.0000 −0.437304
\(754\) 18.0000 + 31.1769i 0.655521 + 1.13540i
\(755\) 10.0000 17.3205i 0.363937 0.630358i
\(756\) −2.50000 4.33013i −0.0909241 0.157485i
\(757\) 6.50000 11.2583i 0.236247 0.409191i −0.723388 0.690442i \(-0.757416\pi\)
0.959634 + 0.281251i \(0.0907494\pi\)
\(758\) −2.00000 + 3.46410i −0.0726433 + 0.125822i
\(759\) −7.00000 −0.254084
\(760\) 3.50000 + 2.59808i 0.126958 + 0.0942421i
\(761\) −31.0000 −1.12375 −0.561875 0.827222i \(-0.689920\pi\)
−0.561875 + 0.827222i \(0.689920\pi\)
\(762\) 2.50000 4.33013i 0.0905654 0.156864i
\(763\) −40.0000 + 69.2820i −1.44810 + 2.50818i
\(764\) 7.00000 + 12.1244i 0.253251 + 0.438644i
\(765\) −2.00000 + 3.46410i −0.0723102 + 0.125245i
\(766\) 16.0000 + 27.7128i 0.578103 + 1.00130i
\(767\) −48.0000 −1.73318
\(768\) −1.00000 −0.0360844
\(769\) −3.00000 5.19615i −0.108183 0.187378i 0.806851 0.590755i \(-0.201170\pi\)
−0.915034 + 0.403376i \(0.867837\pi\)
\(770\) −2.50000 4.33013i −0.0900937 0.156047i
\(771\) −18.0000 −0.648254
\(772\) −4.00000 −0.143963
\(773\) 10.5000 + 18.1865i 0.377659 + 0.654124i 0.990721 0.135910i \(-0.0433959\pi\)
−0.613062 + 0.790034i \(0.710063\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) 0 0
\(776\) 1.00000 1.73205i 0.0358979 0.0621770i
\(777\) −17.5000 + 30.3109i −0.627809 + 1.08740i
\(778\) 10.0000 0.358517