Properties

Label 1050.2.o.h.949.1
Level $1050$
Weight $2$
Character 1050.949
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.h.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(-0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 - 1.50000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-2.00000 + 1.73205i) q^{21} -6.00000i q^{22} +(2.59808 - 1.50000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(-1.73205 - 2.00000i) q^{28} +6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.19615 - 3.00000i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(3.46410 + 2.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} -3.00000 q^{41} +(0.866025 - 2.50000i) q^{42} +8.00000i q^{43} +(3.00000 + 5.19615i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-7.79423 + 4.50000i) q^{47} +1.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(1.50000 + 2.59808i) q^{51} +(-3.46410 - 2.00000i) q^{52} +(-10.3923 - 6.00000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} +4.00000i q^{57} +(-5.19615 + 3.00000i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{61} -5.00000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(6.92820 + 4.00000i) q^{67} +(-2.59808 + 1.50000i) q^{68} -3.00000 q^{69} -9.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-12.1244 - 7.00000i) q^{73} +(4.00000 - 6.92820i) q^{74} -4.00000 q^{76} +(10.3923 + 12.0000i) q^{77} -4.00000i q^{78} +(-3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.59808 - 1.50000i) q^{82} -6.00000i q^{83} +(0.500000 + 2.59808i) q^{84} +(-4.00000 - 6.92820i) q^{86} +(-5.19615 - 3.00000i) q^{87} +(-5.19615 - 3.00000i) q^{88} +(1.50000 + 2.59808i) q^{89} +(-10.0000 - 3.46410i) q^{91} -3.00000i q^{92} +(4.33013 - 2.50000i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{96} -17.0000i q^{97} +(6.92820 + 1.00000i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} - 12q^{11} + 2q^{14} - 2q^{16} - 8q^{19} - 8q^{21} + 2q^{24} + 8q^{26} + 24q^{29} - 10q^{31} + 12q^{34} + 4q^{36} - 8q^{39} - 12q^{41} + 12q^{44} - 6q^{46} - 22q^{49} + 6q^{51} + 2q^{54} + 10q^{56} + 12q^{59} - 4q^{61} - 4q^{64} - 12q^{66} - 12q^{69} - 36q^{71} + 16q^{74} - 16q^{76} - 14q^{79} - 2q^{81} + 2q^{84} - 16q^{86} + 6q^{89} - 40q^{91} + 18q^{94} - 2q^{96} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 0.866025 2.50000i 0.327327 0.944911i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.59808 1.50000i −0.630126 0.363803i 0.150675 0.988583i \(-0.451855\pi\)
−0.780801 + 0.624780i \(0.785189\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 6.00000i 1.27920i
\(23\) 2.59808 1.50000i 0.541736 0.312772i −0.204046 0.978961i \(-0.565409\pi\)
0.745782 + 0.666190i \(0.232076\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) 2.00000 + 3.46410i 0.392232 + 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) −1.73205 2.00000i −0.327327 0.377964i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 5.19615 3.00000i 0.904534 0.522233i
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −6.92820 + 4.00000i −1.13899 + 0.657596i −0.946180 0.323640i \(-0.895093\pi\)
−0.192809 + 0.981236i \(0.561760\pi\)
\(38\) 3.46410 + 2.00000i 0.561951 + 0.324443i
\(39\) −2.00000 + 3.46410i −0.320256 + 0.554700i
\(40\) 0 0
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0.866025 2.50000i 0.133631 0.385758i
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) 3.00000 + 5.19615i 0.452267 + 0.783349i
\(45\) 0 0
\(46\) −1.50000 + 2.59808i −0.221163 + 0.383065i
\(47\) −7.79423 + 4.50000i −1.13691 + 0.656392i −0.945662 0.325150i \(-0.894585\pi\)
−0.191243 + 0.981543i \(0.561252\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) 0 0
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) −3.46410 2.00000i −0.480384 0.277350i
\(53\) −10.3923 6.00000i −1.42749 0.824163i −0.430570 0.902557i \(-0.641688\pi\)
−0.996922 + 0.0783936i \(0.975021\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 4.00000i 0.529813i
\(58\) −5.19615 + 3.00000i −0.682288 + 0.393919i
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 5.00000i 0.635001i
\(63\) 2.59808 0.500000i 0.327327 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −3.00000 + 5.19615i −0.369274 + 0.639602i
\(67\) 6.92820 + 4.00000i 0.846415 + 0.488678i 0.859440 0.511237i \(-0.170813\pi\)
−0.0130248 + 0.999915i \(0.504146\pi\)
\(68\) −2.59808 + 1.50000i −0.315063 + 0.181902i
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) −12.1244 7.00000i −1.41905 0.819288i −0.422833 0.906208i \(-0.638964\pi\)
−0.996215 + 0.0869195i \(0.972298\pi\)
\(74\) 4.00000 6.92820i 0.464991 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 10.3923 + 12.0000i 1.18431 + 1.36753i
\(78\) 4.00000i 0.452911i
\(79\) −3.50000 6.06218i −0.393781 0.682048i 0.599164 0.800626i \(-0.295500\pi\)
−0.992945 + 0.118578i \(0.962166\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.59808 1.50000i 0.286910 0.165647i
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 0.500000 + 2.59808i 0.0545545 + 0.283473i
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) −5.19615 3.00000i −0.557086 0.321634i
\(88\) −5.19615 3.00000i −0.553912 0.319801i
\(89\) 1.50000 + 2.59808i 0.159000 + 0.275396i 0.934508 0.355942i \(-0.115840\pi\)
−0.775509 + 0.631337i \(0.782506\pi\)
\(90\) 0 0
\(91\) −10.0000 3.46410i −1.04828 0.363137i
\(92\) 3.00000i 0.312772i
\(93\) 4.33013 2.50000i 0.449013 0.259238i
\(94\) 4.50000 7.79423i 0.464140 0.803913i
\(95\) 0 0
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 17.0000i 1.72609i −0.505128 0.863044i \(-0.668555\pi\)
0.505128 0.863044i \(-0.331445\pi\)
\(98\) 6.92820 + 1.00000i 0.699854 + 0.101015i
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) −2.59808 1.50000i −0.257248 0.148522i
\(103\) −11.2583 + 6.50000i −1.10932 + 0.640464i −0.938652 0.344865i \(-0.887925\pi\)
−0.170664 + 0.985329i \(0.554591\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) −5.19615 + 3.00000i −0.502331 + 0.290021i −0.729676 0.683793i \(-0.760329\pi\)
0.227345 + 0.973814i \(0.426996\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) −2.00000 + 3.46410i −0.191565 + 0.331801i −0.945769 0.324840i \(-0.894690\pi\)
0.754204 + 0.656640i \(0.228023\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) −2.59808 + 0.500000i −0.245495 + 0.0472456i
\(113\) 3.00000i 0.282216i 0.989994 + 0.141108i \(0.0450665\pi\)
−0.989994 + 0.141108i \(0.954933\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 3.46410 2.00000i 0.320256 0.184900i
\(118\) 6.00000i 0.552345i
\(119\) −6.00000 + 5.19615i −0.550019 + 0.476331i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 1.73205 + 1.00000i 0.156813 + 0.0905357i
\(123\) 2.59808 + 1.50000i 0.234261 + 0.135250i
\(124\) 2.50000 + 4.33013i 0.224507 + 0.388857i
\(125\) 0 0
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) 16.0000i 1.41977i 0.704317 + 0.709885i \(0.251253\pi\)
−0.704317 + 0.709885i \(0.748747\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 4.00000 6.92820i 0.352180 0.609994i
\(130\) 0 0
\(131\) 9.00000 + 15.5885i 0.786334 + 1.36197i 0.928199 + 0.372084i \(0.121357\pi\)
−0.141865 + 0.989886i \(0.545310\pi\)
\(132\) 6.00000i 0.522233i
\(133\) −10.3923 + 2.00000i −0.901127 + 0.173422i
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) −12.9904 7.50000i −1.10984 0.640768i −0.171054 0.985262i \(-0.554717\pi\)
−0.938789 + 0.344493i \(0.888051\pi\)
\(138\) 2.59808 1.50000i 0.221163 0.127688i
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 9.00000 0.757937
\(142\) 7.79423 4.50000i 0.654077 0.377632i
\(143\) 20.7846 + 12.0000i 1.73810 + 1.00349i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 14.0000 1.15865
\(147\) 2.59808 + 6.50000i 0.214286 + 0.536111i
\(148\) 8.00000i 0.657596i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 3.46410 2.00000i 0.280976 0.162221i
\(153\) 3.00000i 0.242536i
\(154\) −15.0000 5.19615i −1.20873 0.418718i
\(155\) 0 0
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) 12.1244 + 7.00000i 0.967629 + 0.558661i 0.898513 0.438948i \(-0.144649\pi\)
0.0691164 + 0.997609i \(0.477982\pi\)
\(158\) 6.06218 + 3.50000i 0.482281 + 0.278445i
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) −1.50000 7.79423i −0.118217 0.614271i
\(162\) 1.00000i 0.0785674i
\(163\) 6.92820 4.00000i 0.542659 0.313304i −0.203497 0.979076i \(-0.565231\pi\)
0.746156 + 0.665771i \(0.231897\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) −1.73205 2.00000i −0.133631 0.154303i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) 6.92820 + 4.00000i 0.528271 + 0.304997i
\(173\) −5.19615 + 3.00000i −0.395056 + 0.228086i −0.684349 0.729155i \(-0.739913\pi\)
0.289292 + 0.957241i \(0.406580\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) −5.19615 + 3.00000i −0.390567 + 0.225494i
\(178\) −2.59808 1.50000i −0.194734 0.112430i
\(179\) −9.00000 + 15.5885i −0.672692 + 1.16514i 0.304446 + 0.952529i \(0.401529\pi\)
−0.977138 + 0.212607i \(0.931805\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 10.3923 2.00000i 0.770329 0.148250i
\(183\) 2.00000i 0.147844i
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) 0 0
\(186\) −2.50000 + 4.33013i −0.183309 + 0.317500i
\(187\) 15.5885 9.00000i 1.13994 0.658145i
\(188\) 9.00000i 0.656392i
\(189\) −2.50000 0.866025i −0.181848 0.0629941i
\(190\) 0 0
\(191\) −7.50000 12.9904i −0.542681 0.939951i −0.998749 0.0500060i \(-0.984076\pi\)
0.456068 0.889945i \(-0.349257\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) −4.33013 2.50000i −0.311689 0.179954i 0.335993 0.941865i \(-0.390928\pi\)
−0.647682 + 0.761911i \(0.724262\pi\)
\(194\) 8.50000 + 14.7224i 0.610264 + 1.05701i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 5.19615 3.00000i 0.369274 0.213201i
\(199\) 2.50000 4.33013i 0.177220 0.306955i −0.763707 0.645563i \(-0.776623\pi\)
0.940927 + 0.338608i \(0.109956\pi\)
\(200\) 0 0
\(201\) −4.00000 6.92820i −0.282138 0.488678i
\(202\) 12.0000i 0.844317i
\(203\) 5.19615 15.0000i 0.364698 1.05279i
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) 6.50000 11.2583i 0.452876 0.784405i
\(207\) 2.59808 + 1.50000i 0.180579 + 0.104257i
\(208\) −3.46410 + 2.00000i −0.240192 + 0.138675i
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −10.3923 + 6.00000i −0.713746 + 0.412082i
\(213\) 7.79423 + 4.50000i 0.534052 + 0.308335i
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 8.66025 + 10.0000i 0.587896 + 0.678844i
\(218\) 4.00000i 0.270914i
\(219\) 7.00000 + 12.1244i 0.473016 + 0.819288i
\(220\) 0 0
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) −6.92820 + 4.00000i −0.464991 + 0.268462i
\(223\) 11.0000i 0.736614i 0.929704 + 0.368307i \(0.120063\pi\)
−0.929704 + 0.368307i \(0.879937\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 0 0
\(226\) −1.50000 2.59808i −0.0997785 0.172821i
\(227\) −15.5885 9.00000i −1.03464 0.597351i −0.116331 0.993210i \(-0.537113\pi\)
−0.918311 + 0.395860i \(0.870447\pi\)
\(228\) 3.46410 + 2.00000i 0.229416 + 0.132453i
\(229\) −11.0000 19.0526i −0.726900 1.25903i −0.958187 0.286143i \(-0.907627\pi\)
0.231287 0.972886i \(-0.425707\pi\)
\(230\) 0 0
\(231\) −3.00000 15.5885i −0.197386 1.02565i
\(232\) 6.00000i 0.393919i
\(233\) 5.19615 3.00000i 0.340411 0.196537i −0.320043 0.947403i \(-0.603697\pi\)
0.660454 + 0.750867i \(0.270364\pi\)
\(234\) −2.00000 + 3.46410i −0.130744 + 0.226455i
\(235\) 0 0
\(236\) −3.00000 5.19615i −0.195283 0.338241i
\(237\) 7.00000i 0.454699i
\(238\) 2.59808 7.50000i 0.168408 0.486153i
\(239\) −3.00000 −0.194054 −0.0970269 0.995282i \(-0.530933\pi\)
−0.0970269 + 0.995282i \(0.530933\pi\)
\(240\) 0 0
\(241\) 11.0000 19.0526i 0.708572 1.22728i −0.256814 0.966461i \(-0.582673\pi\)
0.965387 0.260822i \(-0.0839937\pi\)
\(242\) 21.6506 + 12.5000i 1.39176 + 0.803530i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) −3.00000 −0.191273
\(247\) −13.8564 + 8.00000i −0.881662 + 0.509028i
\(248\) −4.33013 2.50000i −0.274963 0.158750i
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0.866025 2.50000i 0.0545545 0.157485i
\(253\) 18.0000i 1.13165i
\(254\) −8.00000 13.8564i −0.501965 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 15.5885 9.00000i 0.972381 0.561405i 0.0724199 0.997374i \(-0.476928\pi\)
0.899961 + 0.435970i \(0.143595\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 4.00000 + 20.7846i 0.248548 + 1.29149i
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) −15.5885 9.00000i −0.963058 0.556022i
\(263\) 2.59808 + 1.50000i 0.160204 + 0.0924940i 0.577959 0.816066i \(-0.303849\pi\)
−0.417755 + 0.908560i \(0.637183\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) 0 0
\(266\) 8.00000 6.92820i 0.490511 0.424795i
\(267\) 3.00000i 0.183597i
\(268\) 6.92820 4.00000i 0.423207 0.244339i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) 12.5000 + 21.6506i 0.759321 + 1.31518i 0.943197 + 0.332233i \(0.107802\pi\)
−0.183876 + 0.982949i \(0.558865\pi\)
\(272\) 3.00000i 0.181902i
\(273\) 6.92820 + 8.00000i 0.419314 + 0.484182i
\(274\) 15.0000 0.906183
\(275\) 0 0
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) 22.5167 + 13.0000i 1.35290 + 0.781094i 0.988654 0.150210i \(-0.0479951\pi\)
0.364241 + 0.931305i \(0.381328\pi\)
\(278\) 1.73205 1.00000i 0.103882 0.0599760i
\(279\) −5.00000 −0.299342
\(280\) 0 0
\(281\) 27.0000 1.61068 0.805342 0.592810i \(-0.201981\pi\)
0.805342 + 0.592810i \(0.201981\pi\)
\(282\) −7.79423 + 4.50000i −0.464140 + 0.267971i
\(283\) 19.0526 + 11.0000i 1.13256 + 0.653882i 0.944577 0.328291i \(-0.106473\pi\)
0.187980 + 0.982173i \(0.439806\pi\)
\(284\) −4.50000 + 7.79423i −0.267026 + 0.462502i
\(285\) 0 0
\(286\) −24.0000 −1.41915
\(287\) −2.59808 + 7.50000i −0.153360 + 0.442711i
\(288\) 1.00000i 0.0589256i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) 0 0
\(291\) −8.50000 + 14.7224i −0.498279 + 0.863044i
\(292\) −12.1244 + 7.00000i −0.709524 + 0.409644i
\(293\) 18.0000i 1.05157i −0.850617 0.525786i \(-0.823771\pi\)
0.850617 0.525786i \(-0.176229\pi\)
\(294\) −5.50000 4.33013i −0.320767 0.252538i
\(295\) 0 0
\(296\) −4.00000 6.92820i −0.232495 0.402694i
\(297\) 5.19615 + 3.00000i 0.301511 + 0.174078i
\(298\) 5.19615 + 3.00000i 0.301005 + 0.173785i
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 0 0
\(301\) 20.0000 + 6.92820i 1.15278 + 0.399335i
\(302\) 16.0000i 0.920697i
\(303\) 10.3923 6.00000i 0.597022 0.344691i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 0 0
\(306\) 1.50000 + 2.59808i 0.0857493 + 0.148522i
\(307\) 20.0000i 1.14146i −0.821138 0.570730i \(-0.806660\pi\)
0.821138 0.570730i \(-0.193340\pi\)
\(308\) 15.5885 3.00000i 0.888235 0.170941i
\(309\) 13.0000 0.739544
\(310\) 0 0
\(311\) −10.5000 + 18.1865i −0.595400 + 1.03126i 0.398090 + 0.917346i \(0.369673\pi\)
−0.993490 + 0.113917i \(0.963660\pi\)
\(312\) −3.46410 2.00000i −0.196116 0.113228i
\(313\) 14.7224 8.50000i 0.832161 0.480448i −0.0224310 0.999748i \(-0.507141\pi\)
0.854592 + 0.519300i \(0.173807\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −7.00000 −0.393781
\(317\) −10.3923 + 6.00000i −0.583690 + 0.336994i −0.762598 0.646872i \(-0.776077\pi\)
0.178908 + 0.983866i \(0.442743\pi\)
\(318\) −10.3923 6.00000i −0.582772 0.336463i
\(319\) −18.0000 + 31.1769i −1.00781 + 1.74557i
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 5.19615 + 6.00000i 0.289570 + 0.334367i
\(323\) 12.0000i 0.667698i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) 3.46410 2.00000i 0.191565 0.110600i
\(328\) 3.00000i 0.165647i
\(329\) 4.50000 + 23.3827i 0.248093 + 1.28913i
\(330\) 0 0
\(331\) −13.0000 22.5167i −0.714545 1.23763i −0.963135 0.269019i \(-0.913301\pi\)
0.248590 0.968609i \(-0.420033\pi\)
\(332\) −5.19615 3.00000i −0.285176 0.164646i
\(333\) −6.92820 4.00000i −0.379663 0.219199i
\(334\) 0 0
\(335\) 0 0
\(336\) 2.50000 + 0.866025i 0.136386 + 0.0472456i
\(337\) 13.0000i 0.708155i 0.935216 + 0.354078i \(0.115205\pi\)
−0.935216 + 0.354078i \(0.884795\pi\)
\(338\) 2.59808 1.50000i 0.141317 0.0815892i
\(339\) 1.50000 2.59808i 0.0814688 0.141108i
\(340\) 0 0
\(341\) −15.0000 25.9808i −0.812296 1.40694i
\(342\) 4.00000i 0.216295i
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) 15.5885 + 9.00000i 0.836832 + 0.483145i 0.856186 0.516667i \(-0.172828\pi\)
−0.0193540 + 0.999813i \(0.506161\pi\)
\(348\) −5.19615 + 3.00000i −0.278543 + 0.160817i
\(349\) 28.0000 1.49881 0.749403 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) −5.19615 + 3.00000i −0.276956 + 0.159901i
\(353\) −12.9904 7.50000i −0.691408 0.399185i 0.112731 0.993626i \(-0.464040\pi\)
−0.804139 + 0.594441i \(0.797373\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) 0 0
\(356\) 3.00000 0.159000
\(357\) 7.79423 1.50000i 0.412514 0.0793884i
\(358\) 18.0000i 0.951330i
\(359\) −18.0000 31.1769i −0.950004 1.64545i −0.745409 0.666608i \(-0.767746\pi\)
−0.204595 0.978847i \(-0.565588\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −1.73205 + 1.00000i −0.0910346 + 0.0525588i
\(363\) 25.0000i 1.31216i
\(364\) −8.00000 + 6.92820i −0.419314 + 0.363137i
\(365\) 0 0
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) −24.2487 14.0000i −1.26577 0.730794i −0.291587 0.956544i \(-0.594183\pi\)
−0.974185 + 0.225750i \(0.927517\pi\)
\(368\) −2.59808 1.50000i −0.135434 0.0781929i
\(369\) −1.50000 2.59808i −0.0780869 0.135250i
\(370\) 0 0
\(371\) −24.0000 + 20.7846i −1.24602 + 1.07908i
\(372\) 5.00000i 0.259238i
\(373\) 6.92820 4.00000i 0.358729 0.207112i −0.309794 0.950804i \(-0.600260\pi\)
0.668523 + 0.743691i \(0.266927\pi\)
\(374\) −9.00000 + 15.5885i −0.465379 + 0.806060i
\(375\) 0 0
\(376\) −4.50000 7.79423i −0.232070 0.401957i
\(377\) 24.0000i 1.23606i
\(378\) 2.59808 0.500000i 0.133631 0.0257172i
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 0 0
\(381\) 8.00000 13.8564i 0.409852 0.709885i
\(382\) 12.9904 + 7.50000i 0.664646 + 0.383733i
\(383\) 18.1865 10.5000i 0.929288 0.536525i 0.0427020 0.999088i \(-0.486403\pi\)
0.886586 + 0.462563i \(0.153070\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 5.00000 0.254493
\(387\) −6.92820 + 4.00000i −0.352180 + 0.203331i
\(388\) −14.7224 8.50000i −0.747418 0.431522i
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 4.33013 5.50000i 0.218704 0.277792i
\(393\) 18.0000i 0.907980i
\(394\) 0 0
\(395\) 0 0
\(396\) −3.00000 + 5.19615i −0.150756 + 0.261116i
\(397\) −1.73205 + 1.00000i −0.0869291 + 0.0501886i −0.542834 0.839840i \(-0.682649\pi\)
0.455905 + 0.890028i \(0.349316\pi\)
\(398\) 5.00000i 0.250627i
\(399\) 10.0000 + 3.46410i 0.500626 + 0.173422i
\(400\) 0 0
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) 6.92820 + 4.00000i 0.345547 + 0.199502i
\(403\) 17.3205 + 10.0000i 0.862796 + 0.498135i
\(404\) 6.00000 + 10.3923i 0.298511 + 0.517036i
\(405\) 0 0
\(406\) 3.00000 + 15.5885i 0.148888 + 0.773642i
\(407\) 48.0000i 2.37927i
\(408\) −2.59808 + 1.50000i −0.128624 + 0.0742611i
\(409\) 14.5000 25.1147i 0.716979 1.24184i −0.245212 0.969469i \(-0.578858\pi\)
0.962191 0.272374i \(-0.0878089\pi\)
\(410\) 0 0
\(411\) 7.50000 + 12.9904i 0.369948 + 0.640768i
\(412\) 13.0000i 0.640464i
\(413\) −10.3923 12.0000i −0.511372 0.590481i
\(414\) −3.00000 −0.147442
\(415\) 0 0
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 1.73205 + 1.00000i 0.0848189 + 0.0489702i
\(418\) −20.7846 + 12.0000i −1.01661 + 0.586939i
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) −4.00000 −0.194948 −0.0974740 0.995238i \(-0.531076\pi\)
−0.0974740 + 0.995238i \(0.531076\pi\)
\(422\) −6.92820 + 4.00000i −0.337260 + 0.194717i
\(423\) −7.79423 4.50000i −0.378968 0.218797i
\(424\) 6.00000 10.3923i 0.291386 0.504695i
\(425\) 0 0
\(426\) −9.00000 −0.436051
\(427\) −5.19615 + 1.00000i −0.251459 + 0.0483934i
\(428\) 6.00000i 0.290021i
\(429\) −12.0000 20.7846i −0.579365 1.00349i
\(430\) 0 0
\(431\) −10.5000 + 18.1865i −0.505767 + 0.876014i 0.494211 + 0.869342i \(0.335457\pi\)
−0.999978 + 0.00667224i \(0.997876\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 7.00000i 0.336399i −0.985753 0.168199i \(-0.946205\pi\)
0.985753 0.168199i \(-0.0537952\pi\)
\(434\) −12.5000 4.33013i −0.600019 0.207853i
\(435\) 0 0
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) −10.3923 6.00000i −0.497131 0.287019i
\(438\) −12.1244 7.00000i −0.579324 0.334473i
\(439\) −6.50000 11.2583i −0.310228 0.537331i 0.668184 0.743996i \(-0.267072\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 12.0000i 0.570782i
\(443\) −20.7846 + 12.0000i −0.987507 + 0.570137i −0.904528 0.426414i \(-0.859777\pi\)
−0.0829786 + 0.996551i \(0.526443\pi\)
\(444\) 4.00000 6.92820i 0.189832 0.328798i
\(445\) 0 0
\(446\) −5.50000 9.52628i −0.260433 0.451082i
\(447\) 6.00000i 0.283790i
\(448\) −0.866025 + 2.50000i −0.0409159 + 0.118114i
\(449\) 3.00000 0.141579 0.0707894 0.997491i \(-0.477448\pi\)
0.0707894 + 0.997491i \(0.477448\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) 2.59808 + 1.50000i 0.122203 + 0.0705541i
\(453\) −13.8564 + 8.00000i −0.651031 + 0.375873i
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) −1.73205 + 1.00000i −0.0810219 + 0.0467780i −0.539964 0.841688i \(-0.681562\pi\)
0.458942 + 0.888466i \(0.348229\pi\)
\(458\) 19.0526 + 11.0000i 0.890268 + 0.513996i
\(459\) −1.50000 + 2.59808i −0.0700140 + 0.121268i
\(460\) 0 0
\(461\) 36.0000 1.67669 0.838344 0.545142i \(-0.183524\pi\)
0.838344 + 0.545142i \(0.183524\pi\)
\(462\) 10.3923 + 12.0000i 0.483494 + 0.558291i
\(463\) 13.0000i 0.604161i −0.953282 0.302081i \(-0.902319\pi\)
0.953282 0.302081i \(-0.0976812\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 25.9808 15.0000i 1.20225 0.694117i 0.241192 0.970477i \(-0.422462\pi\)
0.961054 + 0.276360i \(0.0891283\pi\)
\(468\) 4.00000i 0.184900i
\(469\) 16.0000 13.8564i 0.738811 0.639829i
\(470\) 0 0
\(471\) −7.00000 12.1244i −0.322543 0.558661i
\(472\) 5.19615 + 3.00000i 0.239172 + 0.138086i
\(473\) −41.5692 24.0000i −1.91135 1.10352i
\(474\) −3.50000 6.06218i −0.160760 0.278445i
\(475\) 0 0
\(476\) 1.50000 + 7.79423i 0.0687524 + 0.357248i
\(477\) 12.0000i 0.549442i
\(478\) 2.59808 1.50000i 0.118833 0.0686084i
\(479\) 10.5000 18.1865i 0.479757 0.830964i −0.519973 0.854183i \(-0.674058\pi\)
0.999730 + 0.0232187i \(0.00739140\pi\)
\(480\) 0 0
\(481\) 16.0000 + 27.7128i 0.729537 + 1.26360i
\(482\) 22.0000i 1.00207i
\(483\) −2.59808 + 7.50000i −0.118217 + 0.341262i
\(484\) −25.0000 −1.13636
\(485\) 0 0
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −21.6506 12.5000i −0.981084 0.566429i −0.0784867 0.996915i \(-0.525009\pi\)
−0.902597 + 0.430486i \(0.858342\pi\)
\(488\) 1.73205 1.00000i 0.0784063 0.0452679i
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 2.59808 1.50000i 0.117130 0.0676252i
\(493\) −15.5885 9.00000i −0.702069 0.405340i
\(494\) 8.00000 13.8564i 0.359937 0.623429i
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) −7.79423 + 22.5000i −0.349619 + 1.00926i
\(498\) 6.00000i 0.268866i
\(499\) 19.0000 + 32.9090i 0.850557 + 1.47321i 0.880707 + 0.473662i \(0.157068\pi\)
−0.0301498 + 0.999545i \(0.509598\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −20.7846 + 12.0000i −0.927663 + 0.535586i
\(503\) 24.0000i 1.07011i 0.844818 + 0.535054i \(0.179709\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(504\) 0.500000 + 2.59808i 0.0222718 + 0.115728i
\(505\) 0 0
\(506\) −9.00000 15.5885i −0.400099 0.692991i
\(507\) 2.59808 + 1.50000i 0.115385 + 0.0666173i
\(508\) 13.8564 + 8.00000i 0.614779 + 0.354943i
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) −28.0000 + 24.2487i −1.23865 + 1.07270i
\(512\) 1.00000i 0.0441942i
\(513\) −3.46410 + 2.00000i −0.152944 + 0.0883022i
\(514\) −9.00000 + 15.5885i −0.396973 + 0.687577i
\(515\) 0 0
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) 54.0000i 2.37492i
\(518\) −13.8564 16.0000i −0.608816 0.703000i
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −10.5000 + 18.1865i −0.460013 + 0.796766i −0.998961 0.0455727i \(-0.985489\pi\)
0.538948 + 0.842339i \(0.318822\pi\)
\(522\) −5.19615 3.00000i −0.227429 0.131306i
\(523\) −29.4449 + 17.0000i −1.28753 + 0.743358i −0.978214 0.207600i \(-0.933435\pi\)
−0.309320 + 0.950958i \(0.600101\pi\)
\(524\) 18.0000 0.786334
\(525\) 0 0
\(526\) −3.00000 −0.130806
\(527\) 12.9904 7.50000i 0.565870 0.326705i
\(528\) −5.19615 3.00000i −0.226134 0.130558i
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) −3.46410 + 10.0000i −0.150188 + 0.433555i
\(533\) 12.0000i 0.519778i
\(534\) 1.50000 + 2.59808i 0.0649113 + 0.112430i
\(535\) 0 0
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) 15.5885 9.00000i 0.672692 0.388379i
\(538\) 0 0
\(539\) 39.0000 15.5885i 1.67985 0.671442i
\(540\) 0 0
\(541\) 14.0000 + 24.2487i 0.601907 + 1.04253i 0.992532 + 0.121984i \(0.0389256\pi\)
−0.390625 + 0.920550i \(0.627741\pi\)
\(542\) −21.6506 12.5000i −0.929974 0.536921i
\(543\) −1.73205 1.00000i −0.0743294 0.0429141i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 0 0
\(546\) −10.0000 3.46410i −0.427960 0.148250i
\(547\) 8.00000i 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) −12.9904 + 7.50000i −0.554922 + 0.320384i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 0 0
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 3.00000i 0.127688i
\(553\) −18.1865 + 3.50000i −0.773370 + 0.148835i
\(554\) −26.0000 −1.10463
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) −25.9808 15.0000i −1.10084 0.635570i −0.164399 0.986394i \(-0.552568\pi\)
−0.936442 + 0.350824i \(0.885902\pi\)
\(558\) 4.33013 2.50000i 0.183309 0.105833i
\(559\) 32.0000 1.35346
\(560\) 0 0
\(561\) −18.0000 −0.759961
\(562\) −23.3827 + 13.5000i −0.986339 + 0.569463i
\(563\) −10.3923 6.00000i −0.437983 0.252870i 0.264758 0.964315i \(-0.414708\pi\)
−0.702742 + 0.711445i \(0.748041\pi\)
\(564\) 4.50000 7.79423i 0.189484 0.328196i
\(565\) 0 0
\(566\) −22.0000 −0.924729
\(567\) 1.73205 + 2.00000i 0.0727393 + 0.0839921i
\(568\) 9.00000i 0.377632i
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 20.7846 12.0000i 0.869048 0.501745i
\(573\) 15.0000i 0.626634i
\(574\) −1.50000 7.79423i −0.0626088 0.325325i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 1.73205 + 1.00000i 0.0721062 + 0.0416305i 0.535620 0.844459i \(-0.320078\pi\)
−0.463513 + 0.886090i \(0.653411\pi\)
\(578\) 6.92820 + 4.00000i 0.288175 + 0.166378i
\(579\) 2.50000 + 4.33013i 0.103896 + 0.179954i
\(580\) 0 0
\(581\) −15.0000 5.19615i −0.622305 0.215573i
\(582\) 17.0000i 0.704673i
\(583\) 62.3538 36.0000i 2.58243 1.49097i
\(584\) 7.00000 12.1244i 0.289662 0.501709i
\(585\) 0 0
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) 18.0000i 0.742940i −0.928445 0.371470i \(-0.878854\pi\)
0.928445 0.371470i \(-0.121146\pi\)
\(588\) 6.92820 + 1.00000i 0.285714 + 0.0412393i
\(589\) 20.0000 0.824086
\(590\) 0 0
\(591\) 0 0
\(592\) 6.92820 + 4.00000i 0.284747 + 0.164399i
\(593\) −28.5788 + 16.5000i −1.17359 + 0.677574i −0.954524 0.298136i \(-0.903635\pi\)
−0.219069 + 0.975709i \(0.570302\pi\)
\(594\) −6.00000 −0.246183
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −4.33013 + 2.50000i −0.177220 + 0.102318i
\(598\) 10.3923 + 6.00000i 0.424973 + 0.245358i
\(599\) 4.50000 7.79423i 0.183865 0.318464i −0.759328 0.650708i \(-0.774472\pi\)
0.943193 + 0.332244i \(0.107806\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) −20.7846 + 4.00000i −0.847117 + 0.163028i
\(603\) 8.00000i 0.325785i
\(604\) −8.00000 13.8564i −0.325515 0.563809i
\(605\) 0 0
\(606\) −6.00000 + 10.3923i −0.243733 + 0.422159i
\(607\) −9.52628 + 5.50000i −0.386660 + 0.223238i −0.680712 0.732551i \(-0.738329\pi\)
0.294052 + 0.955789i \(0.404996\pi\)
\(608\) 4.00000i 0.162221i
\(609\) −12.0000 + 10.3923i −0.486265 + 0.421117i
\(610\) 0 0
\(611\) 18.0000 + 31.1769i 0.728202 + 1.26128i
\(612\) −2.59808 1.50000i −0.105021 0.0606339i
\(613\) 29.4449 + 17.0000i 1.18927 + 0.686624i 0.958140 0.286300i \(-0.0924254\pi\)
0.231127 + 0.972924i \(0.425759\pi\)
\(614\) 10.0000 + 17.3205i 0.403567 + 0.698999i
\(615\) 0 0
\(616\) −12.0000 + 10.3923i −0.483494 + 0.418718i
\(617\) 21.0000i 0.845428i 0.906263 + 0.422714i \(0.138923\pi\)
−0.906263 + 0.422714i \(0.861077\pi\)
\(618\) −11.2583 + 6.50000i −0.452876 + 0.261468i
\(619\) −23.0000 + 39.8372i −0.924448 + 1.60119i −0.132002 + 0.991250i \(0.542140\pi\)
−0.792446 + 0.609941i \(0.791193\pi\)
\(620\) 0 0
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) 21.0000i 0.842023i
\(623\) 7.79423 1.50000i 0.312269 0.0600962i
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) −8.50000 + 14.7224i −0.339728 + 0.588427i
\(627\) −20.7846 12.0000i −0.830057 0.479234i
\(628\) 12.1244 7.00000i 0.483814 0.279330i
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) 17.0000 0.676759 0.338380 0.941010i \(-0.390121\pi\)
0.338380 + 0.941010i \(0.390121\pi\)
\(632\) 6.06218 3.50000i 0.241140 0.139223i
\(633\) −6.92820 4.00000i −0.275371 0.158986i
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) −17.3205 + 22.0000i −0.686264 + 0.871672i
\(638\) 36.0000i 1.42525i
\(639\) −4.50000 7.79423i −0.178017 0.308335i
\(640\) 0 0
\(641\) 19.5000 33.7750i 0.770204 1.33403i −0.167247 0.985915i \(-0.553488\pi\)
0.937451 0.348117i \(-0.113179\pi\)
\(642\) −5.19615 + 3.00000i −0.205076 + 0.118401i
\(643\) 34.0000i 1.34083i −0.741987 0.670415i \(-0.766116\pi\)
0.741987 0.670415i \(-0.233884\pi\)
\(644\) −7.50000 2.59808i −0.295541 0.102379i
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 10.3923 + 6.00000i 0.408564 + 0.235884i 0.690172 0.723645i \(-0.257535\pi\)
−0.281609 + 0.959529i \(0.590868\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 18.0000 + 31.1769i 0.706562 + 1.22380i
\(650\) 0 0
\(651\) −2.50000 12.9904i −0.0979827 0.509133i
\(652\) 8.00000i 0.313304i
\(653\) −31.1769 + 18.0000i −1.22005 + 0.704394i −0.964928 0.262515i \(-0.915448\pi\)
−0.255119 + 0.966910i \(0.582115\pi\)
\(654\) −2.00000 + 3.46410i −0.0782062 + 0.135457i
\(655\) 0 0
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 14.0000i 0.546192i
\(658\) −15.5885 18.0000i −0.607701 0.701713i
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) 22.5167 + 13.0000i 0.875135 + 0.505259i
\(663\) 10.3923 6.00000i 0.403604 0.233021i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 8.00000 0.309994
\(667\) 15.5885 9.00000i 0.603587 0.348481i
\(668\) 0 0
\(669\) 5.50000 9.52628i 0.212642 0.368307i
\(670\) 0 0
\(671\) 12.0000 0.463255
\(672\) −2.59808 + 0.500000i −0.100223 + 0.0192879i
\(673\) 19.0000i 0.732396i −0.930537 0.366198i \(-0.880659\pi\)
0.930537 0.366198i \(-0.119341\pi\)
\(674\) −6.50000 11.2583i −0.250371 0.433655i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) −15.5885 + 9.00000i −0.599113 + 0.345898i −0.768693 0.639618i \(-0.779092\pi\)
0.169580 + 0.985517i \(0.445759\pi\)
\(678\) 3.00000i 0.115214i
\(679\) −42.5000 14.7224i −1.63100 0.564995i
\(680\) 0 0
\(681\) 9.00000 + 15.5885i 0.344881 + 0.597351i
\(682\) 25.9808 + 15.0000i 0.994855 + 0.574380i
\(683\) −15.5885 9.00000i −0.596476 0.344375i 0.171178 0.985240i \(-0.445243\pi\)
−0.767654 + 0.640865i \(0.778576\pi\)
\(684\) −2.00000 3.46410i −0.0764719 0.132453i
\(685\) 0 0
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 22.0000i 0.839352i
\(688\) 6.92820 4.00000i 0.264135 0.152499i
\(689\) −24.0000 + 41.5692i −0.914327 + 1.58366i
\(690\) 0 0
\(691\) 17.0000 + 29.4449i 0.646710 + 1.12014i 0.983904 + 0.178700i \(0.0571891\pi\)
−0.337193 + 0.941435i \(0.609478\pi\)
\(692\) 6.00000i 0.228086i
\(693\) −5.19615 + 15.0000i −0.197386 + 0.569803i
\(694\) −18.0000 −0.683271
\(695\) 0 0
\(696\) 3.00000 5.19615i 0.113715 0.196960i
\(697\) 7.79423 + 4.50000i 0.295227 + 0.170450i
\(698\) −24.2487 + 14.0000i −0.917827 + 0.529908i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) −48.0000 −1.81293 −0.906467 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 3.46410 2.00000i 0.130744 0.0754851i
\(703\) 27.7128 + 16.0000i 1.04521 + 0.603451i
\(704\) 3.00000 5.19615i 0.113067 0.195837i
\(705\) 0 0
\(706\) 15.0000 0.564532
\(707\) 20.7846 + 24.0000i 0.781686 + 0.902613i
\(708\) 6.00000i 0.225494i
\(709\) −23.0000 39.8372i −0.863783 1.49612i −0.868250 0.496126i \(-0.834755\pi\)
0.00446726 0.999990i \(-0.498578\pi\)
\(710\) 0 0
\(711\) 3.50000 6.06218i 0.131260 0.227349i
\(712\) −2.59808 + 1.50000i −0.0973670 + 0.0562149i
\(713\) 15.0000i 0.561754i
\(714\) −6.00000 + 5.19615i −0.224544 + 0.194461i
\(715\) 0 0
\(716\) 9.00000 + 15.5885i 0.336346 + 0.582568i
\(717\) 2.59808 + 1.50000i 0.0970269 + 0.0560185i
\(718\) 31.1769 + 18.0000i 1.16351 + 0.671754i
\(719\) −13.5000 23.3827i −0.503465 0.872027i −0.999992 0.00400572i \(-0.998725\pi\)
0.496527 0.868021i \(-0.334608\pi\)
\(720\) 0 0
\(721\) 6.50000 + 33.7750i 0.242073 + 1.25785i
\(722\) 3.00000i 0.111648i
\(723\) −19.0526 + 11.0000i −0.708572 + 0.409094i
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) 0 0
\(726\) −12.5000 21.6506i −0.463919 0.803530i
\(727\) 31.0000i 1.14973i 0.818250 + 0.574863i \(0.194945\pi\)
−0.818250 + 0.574863i \(0.805055\pi\)
\(728\) 3.46410 10.0000i 0.128388 0.370625i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 1.73205 + 1.00000i 0.0640184 + 0.0369611i
\(733\) 43.3013 25.0000i 1.59937 0.923396i 0.607760 0.794121i \(-0.292068\pi\)
0.991609 0.129275i \(-0.0412651\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −41.5692 + 24.0000i −1.53122 + 0.884051i
\(738\) 2.59808 + 1.50000i 0.0956365 + 0.0552158i
\(739\) −8.00000 + 13.8564i −0.294285 + 0.509716i −0.974818 0.223001i \(-0.928415\pi\)
0.680534 + 0.732717i \(0.261748\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 10.3923 30.0000i 0.381514 1.10133i
\(743\) 9.00000i 0.330178i 0.986279 + 0.165089i \(0.0527911\pi\)
−0.986279 + 0.165089i \(0.947209\pi\)
\(744\) 2.50000 + 4.33013i 0.0916544 + 0.158750i
\(745\) 0 0
\(746\) −4.00000 + 6.92820i −0.146450 + 0.253660i
\(747\) 5.19615 3.00000i 0.190117 0.109764i
\(748\) 18.0000i 0.658145i
\(749\) 3.00000 + 15.5885i 0.109618 + 0.569590i
\(750\) 0 0
\(751\) 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) 7.79423 + 4.50000i 0.284226 + 0.164098i
\(753\) −20.7846 12.0000i −0.757433 0.437304i
\(754\) 12.0000 + 20.7846i 0.437014 + 0.756931i
\(755\) 0 0
\(756\) −2.00000 + 1.73205i −0.0727393 + 0.0629941i
\(757\) 4.00000i 0.145382i 0.997354 + 0.0726912i \(0.0231588\pi\)
−0.997354 + 0.0726912i \(0.976841\pi\)
\(758\) −8.66025 + 5.00000i −0.314555 + 0.181608i
\(759\) 9.00000 15.5885i 0.326679 0.565825i
\(760\) 0 0
\(761\) −4.50000 7.79423i −0.163125 0.282541i 0.772863 0.634573i \(-0.218824\pi\)
−0.935988 + 0.352032i \(0.885491\pi\)
\(762\) 16.0000i 0.579619i
\(763\) 6.92820 + 8.00000i 0.250818 + 0.289619i
\(764\) −15.0000 −0.542681
\(765\) 0 0
\(766\) −10.5000 + 18.1865i −0.379380 + 0.657106i
\(767\) −20.7846 12.0000i −0.750489 0.433295i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) −4.33013 + 2.50000i −0.155845 + 0.0899770i
\(773\) 10.3923 + 6.00000i 0.373785 + 0.215805i 0.675111 0.737716i \(-0.264096\pi\)
−0.301326 + 0.953521i \(0.597429\pi\)
\(774\) 4.00000 6.92820i 0.143777 0.249029i
\(775\) 0 0
\(776\) 17.0000 0.610264
\(777\) 6.92820 20.0000i 0.248548 0.717496i
\(778\) 0 0
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) 27.0000 46.7654i 0.966136 1.67340i
\(782\) 7.79423 4.50000i 0.278721 0.160920i
\(783\) 6.00000i 0.214423i
\(784\) −1.00000 + 6.92820i −0.0357143 + 0.247436i