Properties

Label 60.3.f.a.19.4
Level $60$
Weight $3$
Character 60.19
Analytic conductor $1.635$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.63488158616\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.4
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 60.19
Dual form 60.3.f.a.19.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73205 + 1.00000i) q^{2} +1.73205 q^{3} +(2.00000 + 3.46410i) q^{4} -5.00000i q^{5} +(3.00000 + 1.73205i) q^{6} -10.3923 q^{7} +8.00000i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(1.73205 + 1.00000i) q^{2} +1.73205 q^{3} +(2.00000 + 3.46410i) q^{4} -5.00000i q^{5} +(3.00000 + 1.73205i) q^{6} -10.3923 q^{7} +8.00000i q^{8} +3.00000 q^{9} +(5.00000 - 8.66025i) q^{10} +10.3923i q^{11} +(3.46410 + 6.00000i) q^{12} -18.0000i q^{13} +(-18.0000 - 10.3923i) q^{14} -8.66025i q^{15} +(-8.00000 + 13.8564i) q^{16} +10.0000i q^{17} +(5.19615 + 3.00000i) q^{18} -13.8564i q^{19} +(17.3205 - 10.0000i) q^{20} -18.0000 q^{21} +(-10.3923 + 18.0000i) q^{22} +6.92820 q^{23} +13.8564i q^{24} -25.0000 q^{25} +(18.0000 - 31.1769i) q^{26} +5.19615 q^{27} +(-20.7846 - 36.0000i) q^{28} +36.0000 q^{29} +(8.66025 - 15.0000i) q^{30} -6.92820i q^{31} +(-27.7128 + 16.0000i) q^{32} +18.0000i q^{33} +(-10.0000 + 17.3205i) q^{34} +51.9615i q^{35} +(6.00000 + 10.3923i) q^{36} +54.0000i q^{37} +(13.8564 - 24.0000i) q^{38} -31.1769i q^{39} +40.0000 q^{40} +18.0000 q^{41} +(-31.1769 - 18.0000i) q^{42} +20.7846 q^{43} +(-36.0000 + 20.7846i) q^{44} -15.0000i q^{45} +(12.0000 + 6.92820i) q^{46} +(-13.8564 + 24.0000i) q^{48} +59.0000 q^{49} +(-43.3013 - 25.0000i) q^{50} +17.3205i q^{51} +(62.3538 - 36.0000i) q^{52} +26.0000i q^{53} +(9.00000 + 5.19615i) q^{54} +51.9615 q^{55} -83.1384i q^{56} -24.0000i q^{57} +(62.3538 + 36.0000i) q^{58} +31.1769i q^{59} +(30.0000 - 17.3205i) q^{60} -74.0000 q^{61} +(6.92820 - 12.0000i) q^{62} -31.1769 q^{63} -64.0000 q^{64} -90.0000 q^{65} +(-18.0000 + 31.1769i) q^{66} -41.5692 q^{67} +(-34.6410 + 20.0000i) q^{68} +12.0000 q^{69} +(-51.9615 + 90.0000i) q^{70} -103.923i q^{71} +24.0000i q^{72} -36.0000i q^{73} +(-54.0000 + 93.5307i) q^{74} -43.3013 q^{75} +(48.0000 - 27.7128i) q^{76} -108.000i q^{77} +(31.1769 - 54.0000i) q^{78} -90.0666i q^{79} +(69.2820 + 40.0000i) q^{80} +9.00000 q^{81} +(31.1769 + 18.0000i) q^{82} -90.0666 q^{83} +(-36.0000 - 62.3538i) q^{84} +50.0000 q^{85} +(36.0000 + 20.7846i) q^{86} +62.3538 q^{87} -83.1384 q^{88} +18.0000 q^{89} +(15.0000 - 25.9808i) q^{90} +187.061i q^{91} +(13.8564 + 24.0000i) q^{92} -12.0000i q^{93} -69.2820 q^{95} +(-48.0000 + 27.7128i) q^{96} -72.0000i q^{97} +(102.191 + 59.0000i) q^{98} +31.1769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{4} + 12q^{6} + 12q^{9} + O(q^{10}) \) \( 4q + 8q^{4} + 12q^{6} + 12q^{9} + 20q^{10} - 72q^{14} - 32q^{16} - 72q^{21} - 100q^{25} + 72q^{26} + 144q^{29} - 40q^{34} + 24q^{36} + 160q^{40} + 72q^{41} - 144q^{44} + 48q^{46} + 236q^{49} + 36q^{54} + 120q^{60} - 296q^{61} - 256q^{64} - 360q^{65} - 72q^{66} + 48q^{69} - 216q^{74} + 192q^{76} + 36q^{81} - 144q^{84} + 200q^{85} + 144q^{86} + 72q^{89} + 60q^{90} - 192q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(3\) 1.73205 0.577350
\(4\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(5\) 5.00000i 1.00000i
\(6\) 3.00000 + 1.73205i 0.500000 + 0.288675i
\(7\) −10.3923 −1.48461 −0.742307 0.670059i \(-0.766269\pi\)
−0.742307 + 0.670059i \(0.766269\pi\)
\(8\) 8.00000i 1.00000i
\(9\) 3.00000 0.333333
\(10\) 5.00000 8.66025i 0.500000 0.866025i
\(11\) 10.3923i 0.944755i 0.881396 + 0.472377i \(0.156604\pi\)
−0.881396 + 0.472377i \(0.843396\pi\)
\(12\) 3.46410 + 6.00000i 0.288675 + 0.500000i
\(13\) 18.0000i 1.38462i −0.721602 0.692308i \(-0.756594\pi\)
0.721602 0.692308i \(-0.243406\pi\)
\(14\) −18.0000 10.3923i −1.28571 0.742307i
\(15\) 8.66025i 0.577350i
\(16\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(17\) 10.0000i 0.588235i 0.955769 + 0.294118i \(0.0950258\pi\)
−0.955769 + 0.294118i \(0.904974\pi\)
\(18\) 5.19615 + 3.00000i 0.288675 + 0.166667i
\(19\) 13.8564i 0.729285i −0.931148 0.364642i \(-0.881191\pi\)
0.931148 0.364642i \(-0.118809\pi\)
\(20\) 17.3205 10.0000i 0.866025 0.500000i
\(21\) −18.0000 −0.857143
\(22\) −10.3923 + 18.0000i −0.472377 + 0.818182i
\(23\) 6.92820 0.301226 0.150613 0.988593i \(-0.451875\pi\)
0.150613 + 0.988593i \(0.451875\pi\)
\(24\) 13.8564i 0.577350i
\(25\) −25.0000 −1.00000
\(26\) 18.0000 31.1769i 0.692308 1.19911i
\(27\) 5.19615 0.192450
\(28\) −20.7846 36.0000i −0.742307 1.28571i
\(29\) 36.0000 1.24138 0.620690 0.784056i \(-0.286853\pi\)
0.620690 + 0.784056i \(0.286853\pi\)
\(30\) 8.66025 15.0000i 0.288675 0.500000i
\(31\) 6.92820i 0.223490i −0.993737 0.111745i \(-0.964356\pi\)
0.993737 0.111745i \(-0.0356441\pi\)
\(32\) −27.7128 + 16.0000i −0.866025 + 0.500000i
\(33\) 18.0000i 0.545455i
\(34\) −10.0000 + 17.3205i −0.294118 + 0.509427i
\(35\) 51.9615i 1.48461i
\(36\) 6.00000 + 10.3923i 0.166667 + 0.288675i
\(37\) 54.0000i 1.45946i 0.683736 + 0.729730i \(0.260354\pi\)
−0.683736 + 0.729730i \(0.739646\pi\)
\(38\) 13.8564 24.0000i 0.364642 0.631579i
\(39\) 31.1769i 0.799408i
\(40\) 40.0000 1.00000
\(41\) 18.0000 0.439024 0.219512 0.975610i \(-0.429553\pi\)
0.219512 + 0.975610i \(0.429553\pi\)
\(42\) −31.1769 18.0000i −0.742307 0.428571i
\(43\) 20.7846 0.483363 0.241682 0.970356i \(-0.422301\pi\)
0.241682 + 0.970356i \(0.422301\pi\)
\(44\) −36.0000 + 20.7846i −0.818182 + 0.472377i
\(45\) 15.0000i 0.333333i
\(46\) 12.0000 + 6.92820i 0.260870 + 0.150613i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −13.8564 + 24.0000i −0.288675 + 0.500000i
\(49\) 59.0000 1.20408
\(50\) −43.3013 25.0000i −0.866025 0.500000i
\(51\) 17.3205i 0.339618i
\(52\) 62.3538 36.0000i 1.19911 0.692308i
\(53\) 26.0000i 0.490566i 0.969452 + 0.245283i \(0.0788809\pi\)
−0.969452 + 0.245283i \(0.921119\pi\)
\(54\) 9.00000 + 5.19615i 0.166667 + 0.0962250i
\(55\) 51.9615 0.944755
\(56\) 83.1384i 1.48461i
\(57\) 24.0000i 0.421053i
\(58\) 62.3538 + 36.0000i 1.07507 + 0.620690i
\(59\) 31.1769i 0.528422i 0.964465 + 0.264211i \(0.0851116\pi\)
−0.964465 + 0.264211i \(0.914888\pi\)
\(60\) 30.0000 17.3205i 0.500000 0.288675i
\(61\) −74.0000 −1.21311 −0.606557 0.795040i \(-0.707450\pi\)
−0.606557 + 0.795040i \(0.707450\pi\)
\(62\) 6.92820 12.0000i 0.111745 0.193548i
\(63\) −31.1769 −0.494872
\(64\) −64.0000 −1.00000
\(65\) −90.0000 −1.38462
\(66\) −18.0000 + 31.1769i −0.272727 + 0.472377i
\(67\) −41.5692 −0.620436 −0.310218 0.950665i \(-0.600402\pi\)
−0.310218 + 0.950665i \(0.600402\pi\)
\(68\) −34.6410 + 20.0000i −0.509427 + 0.294118i
\(69\) 12.0000 0.173913
\(70\) −51.9615 + 90.0000i −0.742307 + 1.28571i
\(71\) 103.923i 1.46370i −0.681463 0.731852i \(-0.738656\pi\)
0.681463 0.731852i \(-0.261344\pi\)
\(72\) 24.0000i 0.333333i
\(73\) 36.0000i 0.493151i −0.969124 0.246575i \(-0.920695\pi\)
0.969124 0.246575i \(-0.0793053\pi\)
\(74\) −54.0000 + 93.5307i −0.729730 + 1.26393i
\(75\) −43.3013 −0.577350
\(76\) 48.0000 27.7128i 0.631579 0.364642i
\(77\) 108.000i 1.40260i
\(78\) 31.1769 54.0000i 0.399704 0.692308i
\(79\) 90.0666i 1.14008i −0.821616 0.570042i \(-0.806927\pi\)
0.821616 0.570042i \(-0.193073\pi\)
\(80\) 69.2820 + 40.0000i 0.866025 + 0.500000i
\(81\) 9.00000 0.111111
\(82\) 31.1769 + 18.0000i 0.380206 + 0.219512i
\(83\) −90.0666 −1.08514 −0.542570 0.840011i \(-0.682549\pi\)
−0.542570 + 0.840011i \(0.682549\pi\)
\(84\) −36.0000 62.3538i −0.428571 0.742307i
\(85\) 50.0000 0.588235
\(86\) 36.0000 + 20.7846i 0.418605 + 0.241682i
\(87\) 62.3538 0.716711
\(88\) −83.1384 −0.944755
\(89\) 18.0000 0.202247 0.101124 0.994874i \(-0.467756\pi\)
0.101124 + 0.994874i \(0.467756\pi\)
\(90\) 15.0000 25.9808i 0.166667 0.288675i
\(91\) 187.061i 2.05562i
\(92\) 13.8564 + 24.0000i 0.150613 + 0.260870i
\(93\) 12.0000i 0.129032i
\(94\) 0 0
\(95\) −69.2820 −0.729285
\(96\) −48.0000 + 27.7128i −0.500000 + 0.288675i
\(97\) 72.0000i 0.742268i −0.928579 0.371134i \(-0.878969\pi\)
0.928579 0.371134i \(-0.121031\pi\)
\(98\) 102.191 + 59.0000i 1.04277 + 0.602041i
\(99\) 31.1769i 0.314918i
\(100\) −50.0000 86.6025i −0.500000 0.866025i
\(101\) 36.0000 0.356436 0.178218 0.983991i \(-0.442967\pi\)
0.178218 + 0.983991i \(0.442967\pi\)
\(102\) −17.3205 + 30.0000i −0.169809 + 0.294118i
\(103\) 10.3923 0.100896 0.0504481 0.998727i \(-0.483935\pi\)
0.0504481 + 0.998727i \(0.483935\pi\)
\(104\) 144.000 1.38462
\(105\) 90.0000i 0.857143i
\(106\) −26.0000 + 45.0333i −0.245283 + 0.424843i
\(107\) 187.061 1.74824 0.874119 0.485712i \(-0.161439\pi\)
0.874119 + 0.485712i \(0.161439\pi\)
\(108\) 10.3923 + 18.0000i 0.0962250 + 0.166667i
\(109\) 26.0000 0.238532 0.119266 0.992862i \(-0.461946\pi\)
0.119266 + 0.992862i \(0.461946\pi\)
\(110\) 90.0000 + 51.9615i 0.818182 + 0.472377i
\(111\) 93.5307i 0.842619i
\(112\) 83.1384 144.000i 0.742307 1.28571i
\(113\) 10.0000i 0.0884956i 0.999021 + 0.0442478i \(0.0140891\pi\)
−0.999021 + 0.0442478i \(0.985911\pi\)
\(114\) 24.0000 41.5692i 0.210526 0.364642i
\(115\) 34.6410i 0.301226i
\(116\) 72.0000 + 124.708i 0.620690 + 1.07507i
\(117\) 54.0000i 0.461538i
\(118\) −31.1769 + 54.0000i −0.264211 + 0.457627i
\(119\) 103.923i 0.873303i
\(120\) 69.2820 0.577350
\(121\) 13.0000 0.107438
\(122\) −128.172 74.0000i −1.05059 0.606557i
\(123\) 31.1769 0.253471
\(124\) 24.0000 13.8564i 0.193548 0.111745i
\(125\) 125.000i 1.00000i
\(126\) −54.0000 31.1769i −0.428571 0.247436i
\(127\) −218.238 −1.71841 −0.859206 0.511629i \(-0.829042\pi\)
−0.859206 + 0.511629i \(0.829042\pi\)
\(128\) −110.851 64.0000i −0.866025 0.500000i
\(129\) 36.0000 0.279070
\(130\) −155.885 90.0000i −1.19911 0.692308i
\(131\) 135.100i 1.03130i −0.856800 0.515649i \(-0.827551\pi\)
0.856800 0.515649i \(-0.172449\pi\)
\(132\) −62.3538 + 36.0000i −0.472377 + 0.272727i
\(133\) 144.000i 1.08271i
\(134\) −72.0000 41.5692i −0.537313 0.310218i
\(135\) 25.9808i 0.192450i
\(136\) −80.0000 −0.588235
\(137\) 110.000i 0.802920i 0.915877 + 0.401460i \(0.131497\pi\)
−0.915877 + 0.401460i \(0.868503\pi\)
\(138\) 20.7846 + 12.0000i 0.150613 + 0.0869565i
\(139\) 187.061i 1.34577i 0.739749 + 0.672883i \(0.234944\pi\)
−0.739749 + 0.672883i \(0.765056\pi\)
\(140\) −180.000 + 103.923i −1.28571 + 0.742307i
\(141\) 0 0
\(142\) 103.923 180.000i 0.731852 1.26761i
\(143\) 187.061 1.30812
\(144\) −24.0000 + 41.5692i −0.166667 + 0.288675i
\(145\) 180.000i 1.24138i
\(146\) 36.0000 62.3538i 0.246575 0.427081i
\(147\) 102.191 0.695177
\(148\) −187.061 + 108.000i −1.26393 + 0.729730i
\(149\) −288.000 −1.93289 −0.966443 0.256881i \(-0.917305\pi\)
−0.966443 + 0.256881i \(0.917305\pi\)
\(150\) −75.0000 43.3013i −0.500000 0.288675i
\(151\) 187.061i 1.23882i −0.785069 0.619409i \(-0.787372\pi\)
0.785069 0.619409i \(-0.212628\pi\)
\(152\) 110.851 0.729285
\(153\) 30.0000i 0.196078i
\(154\) 108.000 187.061i 0.701299 1.21468i
\(155\) −34.6410 −0.223490
\(156\) 108.000 62.3538i 0.692308 0.399704i
\(157\) 234.000i 1.49045i 0.666815 + 0.745223i \(0.267657\pi\)
−0.666815 + 0.745223i \(0.732343\pi\)
\(158\) 90.0666 156.000i 0.570042 0.987342i
\(159\) 45.0333i 0.283228i
\(160\) 80.0000 + 138.564i 0.500000 + 0.866025i
\(161\) −72.0000 −0.447205
\(162\) 15.5885 + 9.00000i 0.0962250 + 0.0555556i
\(163\) 124.708 0.765078 0.382539 0.923939i \(-0.375050\pi\)
0.382539 + 0.923939i \(0.375050\pi\)
\(164\) 36.0000 + 62.3538i 0.219512 + 0.380206i
\(165\) 90.0000 0.545455
\(166\) −156.000 90.0666i −0.939759 0.542570i
\(167\) −131.636 −0.788239 −0.394119 0.919059i \(-0.628950\pi\)
−0.394119 + 0.919059i \(0.628950\pi\)
\(168\) 144.000i 0.857143i
\(169\) −155.000 −0.917160
\(170\) 86.6025 + 50.0000i 0.509427 + 0.294118i
\(171\) 41.5692i 0.243095i
\(172\) 41.5692 + 72.0000i 0.241682 + 0.418605i
\(173\) 146.000i 0.843931i −0.906612 0.421965i \(-0.861340\pi\)
0.906612 0.421965i \(-0.138660\pi\)
\(174\) 108.000 + 62.3538i 0.620690 + 0.358355i
\(175\) 259.808 1.48461
\(176\) −144.000 83.1384i −0.818182 0.472377i
\(177\) 54.0000i 0.305085i
\(178\) 31.1769 + 18.0000i 0.175151 + 0.101124i
\(179\) 72.7461i 0.406403i 0.979137 + 0.203201i \(0.0651346\pi\)
−0.979137 + 0.203201i \(0.934865\pi\)
\(180\) 51.9615 30.0000i 0.288675 0.166667i
\(181\) 262.000 1.44751 0.723757 0.690055i \(-0.242414\pi\)
0.723757 + 0.690055i \(0.242414\pi\)
\(182\) −187.061 + 324.000i −1.02781 + 1.78022i
\(183\) −128.172 −0.700392
\(184\) 55.4256i 0.301226i
\(185\) 270.000 1.45946
\(186\) 12.0000 20.7846i 0.0645161 0.111745i
\(187\) −103.923 −0.555738
\(188\) 0 0
\(189\) −54.0000 −0.285714
\(190\) −120.000 69.2820i −0.631579 0.364642i
\(191\) 187.061i 0.979380i 0.871897 + 0.489690i \(0.162890\pi\)
−0.871897 + 0.489690i \(0.837110\pi\)
\(192\) −110.851 −0.577350
\(193\) 180.000i 0.932642i −0.884615 0.466321i \(-0.845579\pi\)
0.884615 0.466321i \(-0.154421\pi\)
\(194\) 72.0000 124.708i 0.371134 0.642823i
\(195\) −155.885 −0.799408
\(196\) 118.000 + 204.382i 0.602041 + 1.04277i
\(197\) 154.000i 0.781726i −0.920449 0.390863i \(-0.872177\pi\)
0.920449 0.390863i \(-0.127823\pi\)
\(198\) −31.1769 + 54.0000i −0.157459 + 0.272727i
\(199\) 187.061i 0.940007i 0.882664 + 0.470004i \(0.155747\pi\)
−0.882664 + 0.470004i \(0.844253\pi\)
\(200\) 200.000i 1.00000i
\(201\) −72.0000 −0.358209
\(202\) 62.3538 + 36.0000i 0.308682 + 0.178218i
\(203\) −374.123 −1.84297
\(204\) −60.0000 + 34.6410i −0.294118 + 0.169809i
\(205\) 90.0000i 0.439024i
\(206\) 18.0000 + 10.3923i 0.0873786 + 0.0504481i
\(207\) 20.7846 0.100409
\(208\) 249.415 + 144.000i 1.19911 + 0.692308i
\(209\) 144.000 0.688995
\(210\) −90.0000 + 155.885i −0.428571 + 0.742307i
\(211\) 242.487i 1.14923i −0.818425 0.574614i \(-0.805152\pi\)
0.818425 0.574614i \(-0.194848\pi\)
\(212\) −90.0666 + 52.0000i −0.424843 + 0.245283i
\(213\) 180.000i 0.845070i
\(214\) 324.000 + 187.061i 1.51402 + 0.874119i
\(215\) 103.923i 0.483363i
\(216\) 41.5692i 0.192450i
\(217\) 72.0000i 0.331797i
\(218\) 45.0333 + 26.0000i 0.206575 + 0.119266i
\(219\) 62.3538i 0.284721i
\(220\) 103.923 + 180.000i 0.472377 + 0.818182i
\(221\) 180.000 0.814480
\(222\) −93.5307 + 162.000i −0.421310 + 0.729730i
\(223\) 93.5307 0.419420 0.209710 0.977764i \(-0.432748\pi\)
0.209710 + 0.977764i \(0.432748\pi\)
\(224\) 288.000 166.277i 1.28571 0.742307i
\(225\) −75.0000 −0.333333
\(226\) −10.0000 + 17.3205i −0.0442478 + 0.0766394i
\(227\) 214.774 0.946142 0.473071 0.881024i \(-0.343145\pi\)
0.473071 + 0.881024i \(0.343145\pi\)
\(228\) 83.1384 48.0000i 0.364642 0.210526i
\(229\) −338.000 −1.47598 −0.737991 0.674810i \(-0.764225\pi\)
−0.737991 + 0.674810i \(0.764225\pi\)
\(230\) 34.6410 60.0000i 0.150613 0.260870i
\(231\) 187.061i 0.809790i
\(232\) 288.000i 1.24138i
\(233\) 182.000i 0.781116i 0.920578 + 0.390558i \(0.127718\pi\)
−0.920578 + 0.390558i \(0.872282\pi\)
\(234\) 54.0000 93.5307i 0.230769 0.399704i
\(235\) 0 0
\(236\) −108.000 + 62.3538i −0.457627 + 0.264211i
\(237\) 156.000i 0.658228i
\(238\) 103.923 180.000i 0.436651 0.756303i
\(239\) 353.338i 1.47840i 0.673484 + 0.739202i \(0.264797\pi\)
−0.673484 + 0.739202i \(0.735203\pi\)
\(240\) 120.000 + 69.2820i 0.500000 + 0.288675i
\(241\) −106.000 −0.439834 −0.219917 0.975519i \(-0.570579\pi\)
−0.219917 + 0.975519i \(0.570579\pi\)
\(242\) 22.5167 + 13.0000i 0.0930441 + 0.0537190i
\(243\) 15.5885 0.0641500
\(244\) −148.000 256.344i −0.606557 1.05059i
\(245\) 295.000i 1.20408i
\(246\) 54.0000 + 31.1769i 0.219512 + 0.126735i
\(247\) −249.415 −1.00978
\(248\) 55.4256 0.223490
\(249\) −156.000 −0.626506
\(250\) −125.000 + 216.506i −0.500000 + 0.866025i
\(251\) 322.161i 1.28351i 0.766909 + 0.641756i \(0.221794\pi\)
−0.766909 + 0.641756i \(0.778206\pi\)
\(252\) −62.3538 108.000i −0.247436 0.428571i
\(253\) 72.0000i 0.284585i
\(254\) −378.000 218.238i −1.48819 0.859206i
\(255\) 86.6025 0.339618
\(256\) −128.000 221.703i −0.500000 0.866025i
\(257\) 14.0000i 0.0544747i 0.999629 + 0.0272374i \(0.00867099\pi\)
−0.999629 + 0.0272374i \(0.991329\pi\)
\(258\) 62.3538 + 36.0000i 0.241682 + 0.139535i
\(259\) 561.184i 2.16674i
\(260\) −180.000 311.769i −0.692308 1.19911i
\(261\) 108.000 0.413793
\(262\) 135.100 234.000i 0.515649 0.893130i
\(263\) 187.061 0.711260 0.355630 0.934627i \(-0.384266\pi\)
0.355630 + 0.934627i \(0.384266\pi\)
\(264\) −144.000 −0.545455
\(265\) 130.000 0.490566
\(266\) −144.000 + 249.415i −0.541353 + 0.937652i
\(267\) 31.1769 0.116767
\(268\) −83.1384 144.000i −0.310218 0.537313i
\(269\) 108.000 0.401487 0.200743 0.979644i \(-0.435664\pi\)
0.200743 + 0.979644i \(0.435664\pi\)
\(270\) 25.9808 45.0000i 0.0962250 0.166667i
\(271\) 325.626i 1.20157i 0.799411 + 0.600785i \(0.205145\pi\)
−0.799411 + 0.600785i \(0.794855\pi\)
\(272\) −138.564 80.0000i −0.509427 0.294118i
\(273\) 324.000i 1.18681i
\(274\) −110.000 + 190.526i −0.401460 + 0.695349i
\(275\) 259.808i 0.944755i
\(276\) 24.0000 + 41.5692i 0.0869565 + 0.150613i
\(277\) 270.000i 0.974729i 0.873199 + 0.487365i \(0.162042\pi\)
−0.873199 + 0.487365i \(0.837958\pi\)
\(278\) −187.061 + 324.000i −0.672883 + 1.16547i
\(279\) 20.7846i 0.0744968i
\(280\) −415.692 −1.48461
\(281\) −234.000 −0.832740 −0.416370 0.909195i \(-0.636698\pi\)
−0.416370 + 0.909195i \(0.636698\pi\)
\(282\) 0 0
\(283\) −83.1384 −0.293775 −0.146888 0.989153i \(-0.546926\pi\)
−0.146888 + 0.989153i \(0.546926\pi\)
\(284\) 360.000 207.846i 1.26761 0.731852i
\(285\) −120.000 −0.421053
\(286\) 324.000 + 187.061i 1.13287 + 0.654061i
\(287\) −187.061 −0.651782
\(288\) −83.1384 + 48.0000i −0.288675 + 0.166667i
\(289\) 189.000 0.653979
\(290\) 180.000 311.769i 0.620690 1.07507i
\(291\) 124.708i 0.428549i
\(292\) 124.708 72.0000i 0.427081 0.246575i
\(293\) 58.0000i 0.197952i 0.995090 + 0.0989761i \(0.0315567\pi\)
−0.995090 + 0.0989761i \(0.968443\pi\)
\(294\) 177.000 + 102.191i 0.602041 + 0.347588i
\(295\) 155.885 0.528422
\(296\) −432.000 −1.45946
\(297\) 54.0000i 0.181818i
\(298\) −498.831 288.000i −1.67393 0.966443i
\(299\) 124.708i 0.417082i
\(300\) −86.6025 150.000i −0.288675 0.500000i
\(301\) −216.000 −0.717608
\(302\) 187.061 324.000i 0.619409 1.07285i
\(303\) 62.3538 0.205788
\(304\) 192.000 + 110.851i 0.631579 + 0.364642i
\(305\) 370.000i 1.21311i
\(306\) −30.0000 + 51.9615i −0.0980392 + 0.169809i
\(307\) 270.200 0.880130 0.440065 0.897966i \(-0.354955\pi\)
0.440065 + 0.897966i \(0.354955\pi\)
\(308\) 374.123 216.000i 1.21468 0.701299i
\(309\) 18.0000 0.0582524
\(310\) −60.0000 34.6410i −0.193548 0.111745i
\(311\) 270.200i 0.868810i 0.900718 + 0.434405i \(0.143041\pi\)
−0.900718 + 0.434405i \(0.856959\pi\)
\(312\) 249.415 0.799408
\(313\) 468.000i 1.49521i −0.664145 0.747604i \(-0.731204\pi\)
0.664145 0.747604i \(-0.268796\pi\)
\(314\) −234.000 + 405.300i −0.745223 + 1.29076i
\(315\) 155.885i 0.494872i
\(316\) 312.000 180.133i 0.987342 0.570042i
\(317\) 250.000i 0.788644i 0.918972 + 0.394322i \(0.129020\pi\)
−0.918972 + 0.394322i \(0.870980\pi\)
\(318\) −45.0333 + 78.0000i −0.141614 + 0.245283i
\(319\) 374.123i 1.17280i
\(320\) 320.000i 1.00000i
\(321\) 324.000 1.00935
\(322\) −124.708 72.0000i −0.387291 0.223602i
\(323\) 138.564 0.428991
\(324\) 18.0000 + 31.1769i 0.0555556 + 0.0962250i
\(325\) 450.000i 1.38462i
\(326\) 216.000 + 124.708i 0.662577 + 0.382539i
\(327\) 45.0333 0.137717
\(328\) 144.000i 0.439024i
\(329\) 0 0
\(330\) 155.885 + 90.0000i 0.472377 + 0.272727i
\(331\) 374.123i 1.13028i −0.824995 0.565140i \(-0.808822\pi\)
0.824995 0.565140i \(-0.191178\pi\)
\(332\) −180.133 312.000i −0.542570 0.939759i
\(333\) 162.000i 0.486486i
\(334\) −228.000 131.636i −0.682635 0.394119i
\(335\) 207.846i 0.620436i
\(336\) 144.000 249.415i 0.428571 0.742307i
\(337\) 468.000i 1.38872i −0.719626 0.694362i \(-0.755687\pi\)
0.719626 0.694362i \(-0.244313\pi\)
\(338\) −268.468 155.000i −0.794284 0.458580i
\(339\) 17.3205i 0.0510929i
\(340\) 100.000 + 173.205i 0.294118 + 0.509427i
\(341\) 72.0000 0.211144
\(342\) 41.5692 72.0000i 0.121547 0.210526i
\(343\) −103.923 −0.302983
\(344\) 166.277i 0.483363i
\(345\) 60.0000i 0.173913i
\(346\) 146.000 252.879i 0.421965 0.730865i
\(347\) 561.184 1.61725 0.808623 0.588327i \(-0.200213\pi\)
0.808623 + 0.588327i \(0.200213\pi\)
\(348\) 124.708 + 216.000i 0.358355 + 0.620690i
\(349\) 434.000 1.24355 0.621777 0.783195i \(-0.286411\pi\)
0.621777 + 0.783195i \(0.286411\pi\)
\(350\) 450.000 + 259.808i 1.28571 + 0.742307i
\(351\) 93.5307i 0.266469i
\(352\) −166.277 288.000i −0.472377 0.818182i
\(353\) 158.000i 0.447592i 0.974636 + 0.223796i \(0.0718449\pi\)
−0.974636 + 0.223796i \(0.928155\pi\)
\(354\) −54.0000 + 93.5307i −0.152542 + 0.264211i
\(355\) −519.615 −1.46370
\(356\) 36.0000 + 62.3538i 0.101124 + 0.175151i
\(357\) 180.000i 0.504202i
\(358\) −72.7461 + 126.000i −0.203201 + 0.351955i
\(359\) 457.261i 1.27371i −0.770984 0.636854i \(-0.780235\pi\)
0.770984 0.636854i \(-0.219765\pi\)
\(360\) 120.000 0.333333
\(361\) 169.000 0.468144
\(362\) 453.797 + 262.000i 1.25358 + 0.723757i
\(363\) 22.5167 0.0620294
\(364\) −648.000 + 374.123i −1.78022 + 1.02781i
\(365\) −180.000 −0.493151
\(366\) −222.000 128.172i −0.606557 0.350196i
\(367\) −218.238 −0.594655 −0.297328 0.954776i \(-0.596095\pi\)
−0.297328 + 0.954776i \(0.596095\pi\)
\(368\) −55.4256 + 96.0000i −0.150613 + 0.260870i
\(369\) 54.0000 0.146341
\(370\) 467.654 + 270.000i 1.26393 + 0.729730i
\(371\) 270.200i 0.728302i
\(372\) 41.5692 24.0000i 0.111745 0.0645161i
\(373\) 270.000i 0.723861i 0.932205 + 0.361930i \(0.117882\pi\)
−0.932205 + 0.361930i \(0.882118\pi\)
\(374\) −180.000 103.923i −0.481283 0.277869i
\(375\) 216.506i 0.577350i
\(376\) 0 0
\(377\) 648.000i 1.71883i
\(378\) −93.5307 54.0000i −0.247436 0.142857i
\(379\) 325.626i 0.859170i 0.903026 + 0.429585i \(0.141340\pi\)
−0.903026 + 0.429585i \(0.858660\pi\)
\(380\) −138.564 240.000i −0.364642 0.631579i
\(381\) −378.000 −0.992126
\(382\) −187.061 + 324.000i −0.489690 + 0.848168i
\(383\) −55.4256 −0.144714 −0.0723572 0.997379i \(-0.523052\pi\)
−0.0723572 + 0.997379i \(0.523052\pi\)
\(384\) −192.000 110.851i −0.500000 0.288675i
\(385\) −540.000 −1.40260
\(386\) 180.000 311.769i 0.466321 0.807692i
\(387\) 62.3538 0.161121
\(388\) 249.415 144.000i 0.642823 0.371134i
\(389\) 288.000 0.740360 0.370180 0.928960i \(-0.379296\pi\)
0.370180 + 0.928960i \(0.379296\pi\)
\(390\) −270.000 155.885i −0.692308 0.399704i
\(391\) 69.2820i 0.177192i
\(392\) 472.000i 1.20408i
\(393\) 234.000i 0.595420i
\(394\) 154.000 266.736i 0.390863 0.676994i
\(395\) −450.333 −1.14008
\(396\) −108.000 + 62.3538i −0.272727 + 0.157459i
\(397\) 306.000i 0.770781i −0.922754 0.385390i \(-0.874067\pi\)
0.922754 0.385390i \(-0.125933\pi\)
\(398\) −187.061 + 324.000i −0.470004 + 0.814070i
\(399\) 249.415i 0.625101i
\(400\) 200.000 346.410i 0.500000 0.866025i
\(401\) −450.000 −1.12219 −0.561097 0.827750i \(-0.689621\pi\)
−0.561097 + 0.827750i \(0.689621\pi\)
\(402\) −124.708 72.0000i −0.310218 0.179104i
\(403\) −124.708 −0.309448
\(404\) 72.0000 + 124.708i 0.178218 + 0.308682i
\(405\) 45.0000i 0.111111i
\(406\) −648.000 374.123i −1.59606 0.921485i
\(407\) −561.184 −1.37883
\(408\) −138.564 −0.339618
\(409\) 50.0000 0.122249 0.0611247 0.998130i \(-0.480531\pi\)
0.0611247 + 0.998130i \(0.480531\pi\)
\(410\) 90.0000 155.885i 0.219512 0.380206i
\(411\) 190.526i 0.463566i
\(412\) 20.7846 + 36.0000i 0.0504481 + 0.0873786i
\(413\) 324.000i 0.784504i
\(414\) 36.0000 + 20.7846i 0.0869565 + 0.0502044i
\(415\) 450.333i 1.08514i
\(416\) 288.000 + 498.831i 0.692308 + 1.19911i
\(417\) 324.000i 0.776978i
\(418\) 249.415 + 144.000i 0.596687 + 0.344498i
\(419\) 737.854i 1.76099i −0.474058 0.880494i \(-0.657211\pi\)
0.474058 0.880494i \(-0.342789\pi\)
\(420\) −311.769 + 180.000i −0.742307 + 0.428571i
\(421\) −286.000 −0.679335 −0.339667 0.940546i \(-0.610315\pi\)
−0.339667 + 0.940546i \(0.610315\pi\)
\(422\) 242.487 420.000i 0.574614 0.995261i
\(423\) 0 0
\(424\) −208.000 −0.490566
\(425\) 250.000i 0.588235i
\(426\) 180.000 311.769i 0.422535 0.731852i
\(427\) 769.031 1.80101
\(428\) 374.123 + 648.000i 0.874119 + 1.51402i
\(429\) 324.000 0.755245
\(430\) 103.923 180.000i 0.241682 0.418605i
\(431\) 124.708i 0.289345i −0.989480 0.144672i \(-0.953787\pi\)
0.989480 0.144672i \(-0.0462128\pi\)
\(432\) −41.5692 + 72.0000i −0.0962250 + 0.166667i
\(433\) 36.0000i 0.0831409i 0.999136 + 0.0415704i \(0.0132361\pi\)
−0.999136 + 0.0415704i \(0.986764\pi\)
\(434\) −72.0000 + 124.708i −0.165899 + 0.287345i
\(435\) 311.769i 0.716711i
\(436\) 52.0000 + 90.0666i 0.119266 + 0.206575i
\(437\) 96.0000i 0.219680i
\(438\) 62.3538 108.000i 0.142360 0.246575i
\(439\) 782.887i 1.78334i −0.452684 0.891671i \(-0.649534\pi\)
0.452684 0.891671i \(-0.350466\pi\)
\(440\) 415.692i 0.944755i
\(441\) 177.000 0.401361
\(442\) 311.769 + 180.000i 0.705360 + 0.407240i
\(443\) −214.774 −0.484818 −0.242409 0.970174i \(-0.577938\pi\)
−0.242409 + 0.970174i \(0.577938\pi\)
\(444\) −324.000 + 187.061i −0.729730 + 0.421310i
\(445\) 90.0000i 0.202247i
\(446\) 162.000 + 93.5307i 0.363229 + 0.209710i
\(447\) −498.831 −1.11595
\(448\) 665.108 1.48461
\(449\) −54.0000 −0.120267 −0.0601336 0.998190i \(-0.519153\pi\)
−0.0601336 + 0.998190i \(0.519153\pi\)
\(450\) −129.904 75.0000i −0.288675 0.166667i
\(451\) 187.061i 0.414770i
\(452\) −34.6410 + 20.0000i −0.0766394 + 0.0442478i
\(453\) 324.000i 0.715232i
\(454\) 372.000 + 214.774i 0.819383 + 0.473071i
\(455\) 935.307 2.05562
\(456\) 192.000 0.421053
\(457\) 288.000i 0.630197i 0.949059 + 0.315098i \(0.102038\pi\)
−0.949059 + 0.315098i \(0.897962\pi\)
\(458\) −585.433 338.000i −1.27824 0.737991i
\(459\) 51.9615i 0.113206i
\(460\) 120.000 69.2820i 0.260870 0.150613i
\(461\) −288.000 −0.624729 −0.312364 0.949962i \(-0.601121\pi\)
−0.312364 + 0.949962i \(0.601121\pi\)
\(462\) 187.061 324.000i 0.404895 0.701299i
\(463\) 405.300 0.875378 0.437689 0.899126i \(-0.355797\pi\)
0.437689 + 0.899126i \(0.355797\pi\)
\(464\) −288.000 + 498.831i −0.620690 + 1.07507i
\(465\) −60.0000 −0.129032
\(466\) −182.000 + 315.233i −0.390558 + 0.676466i
\(467\) −575.041 −1.23135 −0.615675 0.788000i \(-0.711117\pi\)
−0.615675 + 0.788000i \(0.711117\pi\)
\(468\) 187.061 108.000i 0.399704 0.230769i
\(469\) 432.000 0.921109
\(470\) 0 0
\(471\) 405.300i 0.860509i
\(472\) −249.415 −0.528422
\(473\) 216.000i 0.456660i
\(474\) 156.000 270.200i 0.329114 0.570042i
\(475\) 346.410i 0.729285i
\(476\) 360.000 207.846i 0.756303 0.436651i
\(477\) 78.0000i 0.163522i
\(478\) −353.338 + 612.000i −0.739202 + 1.28033i
\(479\) 145.492i 0.303742i 0.988400 + 0.151871i \(0.0485298\pi\)
−0.988400 + 0.151871i \(0.951470\pi\)
\(480\) 138.564 + 240.000i 0.288675 + 0.500000i
\(481\) 972.000 2.02079
\(482\) −183.597 106.000i −0.380907 0.219917i
\(483\) −124.708 −0.258194
\(484\) 26.0000 + 45.0333i 0.0537190 + 0.0930441i
\(485\) −360.000 −0.742268
\(486\) 27.0000 + 15.5885i 0.0555556 + 0.0320750i
\(487\) 259.808 0.533486 0.266743 0.963768i \(-0.414053\pi\)
0.266743 + 0.963768i \(0.414053\pi\)
\(488\) 592.000i 1.21311i
\(489\) 216.000 0.441718
\(490\) 295.000 510.955i 0.602041 1.04277i
\(491\) 72.7461i 0.148159i 0.997252 + 0.0740796i \(0.0236019\pi\)
−0.997252 + 0.0740796i \(0.976398\pi\)
\(492\) 62.3538 + 108.000i 0.126735 + 0.219512i
\(493\) 360.000i 0.730223i
\(494\) −432.000 249.415i −0.874494 0.504889i
\(495\) 155.885 0.314918
\(496\) 96.0000 + 55.4256i 0.193548 + 0.111745i
\(497\) 1080.00i 2.17304i
\(498\) −270.200 156.000i −0.542570 0.313253i
\(499\) 443.405i 0.888587i 0.895881 + 0.444294i \(0.146545\pi\)
−0.895881 + 0.444294i \(0.853455\pi\)
\(500\) −433.013 + 250.000i −0.866025 + 0.500000i
\(501\) −228.000 −0.455090
\(502\) −322.161 + 558.000i −0.641756 + 1.11155i
\(503\) 110.851 0.220380 0.110190 0.993911i \(-0.464854\pi\)
0.110190 + 0.993911i \(0.464854\pi\)
\(504\) 249.415i 0.494872i
\(505\) 180.000i 0.356436i
\(506\) −72.0000 + 124.708i −0.142292 + 0.246458i
\(507\) −268.468 −0.529522
\(508\) −436.477 756.000i −0.859206 1.48819i
\(509\) 252.000 0.495088 0.247544 0.968877i \(-0.420376\pi\)
0.247544 + 0.968877i \(0.420376\pi\)
\(510\) 150.000 + 86.6025i 0.294118 + 0.169809i
\(511\) 374.123i 0.732139i
\(512\) 512.000i 1.00000i
\(513\) 72.0000i 0.140351i
\(514\) −14.0000 + 24.2487i −0.0272374 + 0.0471765i
\(515\) 51.9615i 0.100896i
\(516\) 72.0000 + 124.708i 0.139535 + 0.241682i
\(517\) 0 0
\(518\) 561.184 972.000i 1.08337 1.87645i
\(519\) 252.879i 0.487244i
\(520\) 720.000i 1.38462i
\(521\) 54.0000 0.103647 0.0518234 0.998656i \(-0.483497\pi\)
0.0518234 + 0.998656i \(0.483497\pi\)
\(522\) 187.061 + 108.000i 0.358355 + 0.206897i
\(523\) −623.538 −1.19223 −0.596117 0.802898i \(-0.703291\pi\)
−0.596117 + 0.802898i \(0.703291\pi\)
\(524\) 468.000 270.200i 0.893130 0.515649i
\(525\) 450.000 0.857143
\(526\) 324.000 + 187.061i 0.615970 + 0.355630i
\(527\) 69.2820 0.131465
\(528\) −249.415 144.000i −0.472377 0.272727i
\(529\) −481.000 −0.909263
\(530\) 225.167 + 130.000i 0.424843 + 0.245283i
\(531\) 93.5307i 0.176141i
\(532\) −498.831 + 288.000i −0.937652 + 0.541353i
\(533\) 324.000i 0.607880i
\(534\) 54.0000 + 31.1769i 0.101124 + 0.0583837i
\(535\) 935.307i 1.74824i
\(536\) 332.554i 0.620436i
\(537\) 126.000i 0.234637i
\(538\) 187.061 + 108.000i 0.347698 + 0.200743i
\(539\) 613.146i 1.13756i
\(540\) 90.0000 51.9615i 0.166667 0.0962250i
\(541\) −650.000 −1.20148 −0.600739 0.799445i \(-0.705127\pi\)
−0.600739 + 0.799445i \(0.705127\pi\)
\(542\) −325.626 + 564.000i −0.600785 + 1.04059i
\(543\) 453.797 0.835722
\(544\) −160.000 277.128i −0.294118 0.509427i
\(545\) 130.000i 0.238532i
\(546\) −324.000 + 561.184i −0.593407 + 1.02781i
\(547\) 685.892 1.25392 0.626958 0.779053i \(-0.284300\pi\)
0.626958 + 0.779053i \(0.284300\pi\)
\(548\) −381.051 + 220.000i −0.695349 + 0.401460i
\(549\) −222.000 −0.404372
\(550\) 259.808 450.000i 0.472377 0.818182i
\(551\) 498.831i 0.905319i
\(552\) 96.0000i 0.173913i
\(553\) 936.000i 1.69259i
\(554\) −270.000 + 467.654i −0.487365 + 0.844140i
\(555\) 467.654 0.842619
\(556\) −648.000 + 374.123i −1.16547 + 0.672883i
\(557\) 574.000i 1.03052i 0.857034 + 0.515260i \(0.172305\pi\)
−0.857034 + 0.515260i \(0.827695\pi\)
\(558\) 20.7846 36.0000i 0.0372484 0.0645161i
\(559\) 374.123i 0.669272i
\(560\) −720.000 415.692i −1.28571 0.742307i
\(561\) −180.000 −0.320856
\(562\) −405.300 234.000i −0.721174 0.416370i
\(563\) 561.184 0.996775 0.498388 0.866954i \(-0.333926\pi\)
0.498388 + 0.866954i \(0.333926\pi\)
\(564\) 0 0
\(565\) 50.0000 0.0884956
\(566\) −144.000 83.1384i −0.254417 0.146888i
\(567\) −93.5307 −0.164957
\(568\) 831.384 1.46370
\(569\) −198.000 −0.347979 −0.173989 0.984748i \(-0.555666\pi\)
−0.173989 + 0.984748i \(0.555666\pi\)
\(570\) −207.846 120.000i −0.364642 0.210526i
\(571\) 180.133i 0.315470i 0.987481 + 0.157735i \(0.0504192\pi\)
−0.987481 + 0.157735i \(0.949581\pi\)
\(572\) 374.123 + 648.000i 0.654061 + 1.13287i
\(573\) 324.000i 0.565445i
\(574\) −324.000 187.061i −0.564460 0.325891i
\(575\) −173.205 −0.301226
\(576\) −192.000 −0.333333
\(577\) 504.000i 0.873484i −0.899587 0.436742i \(-0.856132\pi\)
0.899587 0.436742i \(-0.143868\pi\)
\(578\) 327.358 + 189.000i 0.566363 + 0.326990i
\(579\) 311.769i 0.538461i
\(580\) 623.538 360.000i 1.07507 0.620690i
\(581\) 936.000 1.61102
\(582\) 124.708 216.000i 0.214274 0.371134i
\(583\) −270.200 −0.463465
\(584\) 288.000 0.493151
\(585\) −270.000 −0.461538
\(586\) −58.0000 + 100.459i −0.0989761 + 0.171432i
\(587\) 408.764 0.696361 0.348181 0.937427i \(-0.386800\pi\)
0.348181 + 0.937427i \(0.386800\pi\)
\(588\) 204.382 + 354.000i 0.347588 + 0.602041i
\(589\) −96.0000 −0.162988
\(590\) 270.000 + 155.885i 0.457627 + 0.264211i
\(591\) 266.736i 0.451330i
\(592\) −748.246 432.000i −1.26393 0.729730i
\(593\) 998.000i 1.68297i −0.540282 0.841484i \(-0.681682\pi\)
0.540282 0.841484i \(-0.318318\pi\)
\(594\) −54.0000 + 93.5307i −0.0909091 + 0.157459i
\(595\) −519.615 −0.873303
\(596\) −576.000 997.661i −0.966443 1.67393i
\(597\) 324.000i 0.542714i
\(598\) 124.708 216.000i 0.208541 0.361204i
\(599\) 540.400i 0.902170i 0.892481 + 0.451085i \(0.148963\pi\)
−0.892481 + 0.451085i \(0.851037\pi\)
\(600\) 346.410i 0.577350i
\(601\) −614.000 −1.02163 −0.510815 0.859690i \(-0.670656\pi\)
−0.510815 + 0.859690i \(0.670656\pi\)
\(602\) −374.123 216.000i −0.621467 0.358804i
\(603\) −124.708 −0.206812
\(604\) 648.000 374.123i 1.07285 0.619409i
\(605\) 65.0000i 0.107438i
\(606\) 108.000 + 62.3538i 0.178218 + 0.102894i
\(607\) −654.715 −1.07861 −0.539304 0.842111i \(-0.681313\pi\)
−0.539304 + 0.842111i \(0.681313\pi\)
\(608\) 221.703 + 384.000i 0.364642 + 0.631579i
\(609\) −648.000 −1.06404
\(610\) −370.000 + 640.859i −0.606557 + 1.05059i
\(611\) 0 0
\(612\) −103.923 + 60.0000i −0.169809 + 0.0980392i
\(613\) 414.000i 0.675367i −0.941260 0.337684i \(-0.890357\pi\)
0.941260 0.337684i \(-0.109643\pi\)
\(614\) 468.000 + 270.200i 0.762215 + 0.440065i
\(615\) 155.885i 0.253471i
\(616\) 864.000 1.40260
\(617\) 58.0000i 0.0940032i 0.998895 + 0.0470016i \(0.0149666\pi\)
−0.998895 + 0.0470016i \(0.985033\pi\)
\(618\) 31.1769 + 18.0000i 0.0504481 + 0.0291262i
\(619\) 187.061i 0.302199i −0.988519 0.151100i \(-0.951719\pi\)
0.988519 0.151100i \(-0.0482815\pi\)
\(620\) −69.2820 120.000i −0.111745 0.193548i
\(621\) 36.0000 0.0579710
\(622\) −270.200 + 468.000i −0.434405 + 0.752412i
\(623\) −187.061 −0.300259
\(624\) 432.000 + 249.415i 0.692308 + 0.399704i
\(625\) 625.000 1.00000
\(626\) 468.000 810.600i 0.747604 1.29489i
\(627\) 249.415 0.397792
\(628\) −810.600 + 468.000i −1.29076 + 0.745223i
\(629\) −540.000 −0.858506
\(630\) −155.885 + 270.000i −0.247436 + 0.428571i
\(631\) 824.456i 1.30659i −0.757105 0.653293i \(-0.773387\pi\)
0.757105 0.653293i \(-0.226613\pi\)
\(632\) 720.533 1.14008
\(633\) 420.000i 0.663507i
\(634\) −250.000 + 433.013i −0.394322 + 0.682985i
\(635\) 1091.19i 1.71841i
\(636\) −156.000 + 90.0666i −0.245283 + 0.141614i
\(637\) 1062.00i 1.66719i
\(638\) −374.123 + 648.000i −0.586400 + 1.01567i
\(639\) 311.769i 0.487902i
\(640\) −320.000 + 554.256i −0.500000 + 0.866025i
\(641\) 810.000 1.26365 0.631825 0.775111i \(-0.282306\pi\)
0.631825 + 0.775111i \(0.282306\pi\)
\(642\) 561.184 + 324.000i 0.874119 + 0.504673i
\(643\) −415.692 −0.646489 −0.323244 0.946316i \(-0.604774\pi\)
−0.323244 + 0.946316i \(0.604774\pi\)
\(644\) −144.000 249.415i −0.223602 0.387291i
\(645\) 180.000i 0.279070i
\(646\) 240.000 + 138.564i 0.371517 + 0.214495i
\(647\) −983.805 −1.52056 −0.760282 0.649593i \(-0.774939\pi\)
−0.760282 + 0.649593i \(0.774939\pi\)
\(648\) 72.0000i 0.111111i
\(649\) −324.000 −0.499230
\(650\) −450.000 + 779.423i −0.692308 + 1.19911i
\(651\) 124.708i 0.191563i
\(652\) 249.415 + 432.000i 0.382539 + 0.662577i
\(653\) 950.000i 1.45482i 0.686201 + 0.727412i \(0.259277\pi\)
−0.686201 + 0.727412i \(0.740723\pi\)
\(654\) 78.0000 + 45.0333i 0.119266 + 0.0688583i
\(655\) −675.500 −1.03130
\(656\) −144.000 + 249.415i −0.219512 + 0.380206i
\(657\) 108.000i 0.164384i
\(658\) 0 0
\(659\) 1132.76i 1.71891i 0.511212 + 0.859455i \(0.329197\pi\)
−0.511212 + 0.859455i \(0.670803\pi\)
\(660\) 180.000 + 311.769i 0.272727 + 0.472377i
\(661\) −242.000 −0.366112 −0.183056 0.983102i \(-0.558599\pi\)
−0.183056 + 0.983102i \(0.558599\pi\)
\(662\) 374.123 648.000i 0.565140 0.978852i
\(663\) 311.769 0.470240
\(664\) 720.533i 1.08514i
\(665\) 720.000 1.08271
\(666\) −162.000 + 280.592i −0.243243 + 0.421310i
\(667\) 249.415 0.373936
\(668\) −263.272 456.000i −0.394119 0.682635i
\(669\) 162.000 0.242152
\(670\) −207.846 + 360.000i −0.310218 + 0.537313i
\(671\) 769.031i 1.14610i
\(672\) 498.831 288.000i 0.742307 0.428571i
\(673\) 324.000i 0.481426i −0.970596 0.240713i \(-0.922619\pi\)
0.970596 0.240713i \(-0.0773813\pi\)
\(674\) 468.000 810.600i 0.694362 1.20267i
\(675\) −129.904 −0.192450
\(676\) −310.000 536.936i −0.458580 0.794284i
\(677\) 806.000i 1.19055i −0.803523 0.595273i \(-0.797044\pi\)
0.803523 0.595273i \(-0.202956\pi\)
\(678\) −17.3205 + 30.0000i −0.0255465 + 0.0442478i
\(679\) 748.246i 1.10198i
\(680\) 400.000i 0.588235i
\(681\) 372.000 0.546256
\(682\) 124.708 + 72.0000i 0.182856 + 0.105572i
\(683\) 575.041 0.841934 0.420967 0.907076i \(-0.361691\pi\)
0.420967 + 0.907076i \(0.361691\pi\)
\(684\) 144.000 83.1384i 0.210526 0.121547i
\(685\) 550.000 0.802920
\(686\) −180.000 103.923i −0.262391 0.151491i
\(687\) −585.433 −0.852159
\(688\) −166.277 + 288.000i −0.241682 + 0.418605i
\(689\) 468.000 0.679245
\(690\) 60.0000 103.923i 0.0869565 0.150613i
\(691\) 775.959i 1.12295i 0.827494 + 0.561475i \(0.189766\pi\)
−0.827494 + 0.561475i \(0.810234\pi\)
\(692\) 505.759 292.000i 0.730865 0.421965i
\(693\) 324.000i 0.467532i
\(694\) 972.000 + 561.184i 1.40058 + 0.808623i
\(695\) 935.307 1.34577
\(696\) 498.831i 0.716711i
\(697\) 180.000i 0.258250i
\(698\) 751.710 + 434.000i 1.07695 + 0.621777i
\(699\) 315.233i 0.450977i
\(700\) 519.615 + 900.000i 0.742307 + 1.28571i
\(701\) 756.000 1.07846 0.539230 0.842159i \(-0.318715\pi\)
0.539230 + 0.842159i \(0.318715\pi\)
\(702\) 93.5307 162.000i 0.133235 0.230769i
\(703\) 748.246 1.06436
\(704\) 665.108i 0.944755i
\(705\) 0 0
\(706\) −158.000 + 273.664i −0.223796 + 0.387626i
\(707\) −374.123 −0.529170
\(708\) −187.061 + 108.000i −0.264211 + 0.152542i
\(709\) 310.000 0.437236 0.218618 0.975811i \(-0.429845\pi\)
0.218618 + 0.975811i \(0.429845\pi\)
\(710\) −900.000 519.615i −1.26761 0.731852i
\(711\) 270.200i 0.380028i
\(712\) 144.000i 0.202247i
\(713\) 48.0000i 0.0673212i
\(714\) 180.000 311.769i 0.252101 0.436651i
\(715\) 935.307i 1.30812i
\(716\) −252.000 + 145.492i −0.351955 + 0.203201i
\(717\) 612.000i 0.853556i
\(718\) 457.261 792.000i 0.636854 1.10306i
\(719\) 83.1384i 0.115631i −0.998327 0.0578153i \(-0.981587\pi\)
0.998327 0.0578153i \(-0.0184135\pi\)
\(720\) 207.846 + 120.000i 0.288675 + 0.166667i
\(721\) −108.000 −0.149792
\(722\) 292.717 + 169.000i 0.405425 + 0.234072i
\(723\) −183.597 −0.253938
\(724\) 524.000 + 907.595i 0.723757 + 1.25358i
\(725\) −900.000 −1.24138
\(726\) 39.0000 + 22.5167i 0.0537190 + 0.0310147i
\(727\) 1091.19 1.50095 0.750476 0.660898i \(-0.229824\pi\)
0.750476 + 0.660898i \(0.229824\pi\)
\(728\) −1496.49 −2.05562
\(729\) 27.0000 0.0370370
\(730\) −311.769 180.000i −0.427081 0.246575i
\(731\) 207.846i 0.284331i
\(732\) −256.344 444.000i −0.350196 0.606557i
\(733\) 1206.00i 1.64529i −0.568553 0.822647i \(-0.692497\pi\)
0.568553 0.822647i \(-0.307503\pi\)
\(734\) −378.000 218.238i −0.514986 0.297328i
\(735\) 510.955i 0.695177i
\(736\) −192.000 + 110.851i −0.260870 + 0.150613i
\(737\) 432.000i 0.586160i
\(738\) 93.5307 + 54.0000i 0.126735 + 0.0731707i
\(739\) 484.974i 0.656257i −0.944633 0.328129i \(-0.893582\pi\)
0.944633 0.328129i \(-0.106418\pi\)
\(740\) 540.000 + 935.307i 0.729730 + 1.26393i
\(741\) −432.000 −0.582996
\(742\) 270.200 468.000i 0.364151 0.630728i
\(743\) −1122.37 −1.51059 −0.755295 0.655385i \(-0.772507\pi\)
−0.755295 + 0.655385i \(0.772507\pi\)
\(744\) 96.0000 0.129032
\(745\) 1440.00i 1.93289i
\(746\) −270.000 + 467.654i −0.361930 + 0.626882i
\(747\) −270.200 −0.361713
\(748\) −207.846 360.000i −0.277869 0.481283i
\(749\) −1944.00 −2.59546
\(750\) −216.506 + 375.000i −0.288675 + 0.500000i
\(751\) 242.487i 0.322886i −0.986882 0.161443i \(-0.948385\pi\)
0.986882 0.161443i \(-0.0516147\pi\)
\(752\) 0 0
\(753\) 558.000i 0.741036i
\(754\) 648.000 1122.37i 0.859416 1.48855i
\(755\) −935.307 −1.23882
\(756\) −108.000 187.061i −0.142857 0.247436i
\(757\) 846.000i 1.11757i 0.829313 + 0.558785i \(0.188732\pi\)
−0.829313 + 0.558785i \(0.811268\pi\)
\(758\) −325.626 + 564.000i −0.429585 + 0.744063i
\(759\) 124.708i 0.164305i
\(760\) 554.256i 0.729285i
\(761\) −1458.00 −1.91590 −0.957950 0.286935i \(-0.907364\pi\)
−0.957950 + 0.286935i \(0.907364\pi\)
\(762\) −654.715 378.000i −0.859206 0.496063i
\(763\) −270.200 −0.354128
\(764\) −648.000 + 374.123i −0.848168 + 0.489690i
\(765\) 150.000 0.196078
\(766\) −96.0000 55.4256i −0.125326 0.0723572i
\(767\) 561.184 0.731662
\(768\) −221.703 384.000i −0.288675 0.500000i
\(769\) −1282.00 −1.66710 −0.833550 0.552444i \(-0.813695\pi\)
−0.833550 + 0.552444i \(0.813695\pi\)
\(770\) −935.307 540.000i −1.21468 0.701299i
\(771\) 24.2487i 0.0314510i
\(772\) 623.538 360.000i 0.807692 0.466321i
\(773\) 422.000i 0.545925i 0.962025 + 0.272962i \(0.0880035\pi\)
−0.962025 + 0.272962i \(0.911997\pi\)
\(774\) 108.000 + 62.3538i 0.139535 + 0.0805605i
\(775\) 173.205i 0.223490i
\(776\) 576.000 0.742268
\(777\) 972.000i 1.25097i
\(778\) 498.831 + 288.000i 0.641170 + 0.370180i
\(779\) 249.415i 0.320174i
\(780\) −311.769 540.000i −0.399704 0.692308i
\(781\) 1080.00 1.38284