Properties

Label 770.2.i.d.331.1
Level $770$
Weight $2$
Character 770.331
Analytic conductor $6.148$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.14848095564\)
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 331.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 770.331
Dual form 770.2.i.d.221.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.50000 + 2.59808i) q^{12} -1.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +3.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(3.00000 + 5.19615i) q^{18} +(-2.00000 + 3.46410i) q^{19} +1.00000 q^{20} +(6.00000 - 5.19615i) q^{21} +1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(1.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} +9.00000 q^{27} +(2.00000 - 1.73205i) q^{28} +1.00000 q^{29} +(1.50000 - 2.59808i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +6.00000 q^{34} +(-2.50000 - 0.866025i) q^{35} +6.00000 q^{36} +(-4.00000 + 6.92820i) q^{37} +(2.00000 + 3.46410i) q^{38} +(1.50000 + 2.59808i) q^{39} +(0.500000 - 0.866025i) q^{40} -12.0000 q^{41} +(-1.50000 - 7.79423i) q^{42} +12.0000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(2.00000 + 3.46410i) q^{46} +(3.00000 - 5.19615i) q^{47} +3.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -1.00000 q^{50} +(9.00000 - 15.5885i) q^{51} +(0.500000 + 0.866025i) q^{52} +(3.00000 + 5.19615i) q^{53} +(4.50000 - 7.79423i) q^{54} -1.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +12.0000 q^{57} +(0.500000 - 0.866025i) q^{58} +(-7.50000 - 12.9904i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(-1.50000 + 2.59808i) q^{61} -8.00000 q^{62} +(-15.0000 - 5.19615i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(3.50000 + 6.06218i) q^{67} +(3.00000 - 5.19615i) q^{68} +12.0000 q^{69} +(-2.00000 + 1.73205i) q^{70} +10.0000 q^{71} +(3.00000 - 5.19615i) q^{72} +(2.00000 + 3.46410i) q^{73} +(4.00000 + 6.92820i) q^{74} +(-1.50000 + 2.59808i) q^{75} +4.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +3.00000 q^{78} +(-7.50000 + 12.9904i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{82} +10.0000 q^{83} +(-7.50000 - 2.59808i) q^{84} -6.00000 q^{85} +(6.00000 - 10.3923i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} -6.00000 q^{90} +(-0.500000 - 2.59808i) q^{91} +4.00000 q^{92} +(-12.0000 + 20.7846i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(1.50000 - 2.59808i) q^{96} -5.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - 3 q^{3} - q^{4} - q^{5} - 6 q^{6} + q^{7} - 2 q^{8} - 6 q^{9} + O(q^{10}) \) \( 2 q + q^{2} - 3 q^{3} - q^{4} - q^{5} - 6 q^{6} + q^{7} - 2 q^{8} - 6 q^{9} + q^{10} + q^{11} - 3 q^{12} - 2 q^{13} + 5 q^{14} + 6 q^{15} - q^{16} + 6 q^{17} + 6 q^{18} - 4 q^{19} + 2 q^{20} + 12 q^{21} + 2 q^{22} - 4 q^{23} + 3 q^{24} - q^{25} - q^{26} + 18 q^{27} + 4 q^{28} + 2 q^{29} + 3 q^{30} - 8 q^{31} + q^{32} + 3 q^{33} + 12 q^{34} - 5 q^{35} + 12 q^{36} - 8 q^{37} + 4 q^{38} + 3 q^{39} + q^{40} - 24 q^{41} - 3 q^{42} + 24 q^{43} + q^{44} - 6 q^{45} + 4 q^{46} + 6 q^{47} + 6 q^{48} - 13 q^{49} - 2 q^{50} + 18 q^{51} + q^{52} + 6 q^{53} + 9 q^{54} - 2 q^{55} - q^{56} + 24 q^{57} + q^{58} - 15 q^{59} - 3 q^{60} - 3 q^{61} - 16 q^{62} - 30 q^{63} + 2 q^{64} + q^{65} - 3 q^{66} + 7 q^{67} + 6 q^{68} + 24 q^{69} - 4 q^{70} + 20 q^{71} + 6 q^{72} + 4 q^{73} + 8 q^{74} - 3 q^{75} + 8 q^{76} - 4 q^{77} + 6 q^{78} - 15 q^{79} - q^{80} - 9 q^{81} - 12 q^{82} + 20 q^{83} - 15 q^{84} - 12 q^{85} + 12 q^{86} - 3 q^{87} - q^{88} - 6 q^{89} - 12 q^{90} - q^{91} + 8 q^{92} - 24 q^{93} - 6 q^{94} - 4 q^{95} + 3 q^{96} - 10 q^{97} - 2 q^{98} - 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −1.50000 2.59808i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −3.00000 −1.22474
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) −1.00000 −0.353553
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) −1.50000 + 2.59808i −0.433013 + 0.750000i
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 2.50000 + 0.866025i 0.668153 + 0.231455i
\(15\) 3.00000 0.774597
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 3.00000 + 5.19615i 0.707107 + 1.22474i
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 1.00000 0.223607
\(21\) 6.00000 5.19615i 1.30931 1.13389i
\(22\) 1.00000 0.213201
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 1.50000 + 2.59808i 0.306186 + 0.530330i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) 9.00000 1.73205
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 6.00000 1.02899
\(35\) −2.50000 0.866025i −0.422577 0.146385i
\(36\) 6.00000 1.00000
\(37\) −4.00000 + 6.92820i −0.657596 + 1.13899i 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) 1.50000 + 2.59808i 0.240192 + 0.416025i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) −1.50000 7.79423i −0.231455 1.20268i
\(43\) 12.0000 1.82998 0.914991 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) −3.00000 5.19615i −0.447214 0.774597i
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 3.00000 0.433013
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) −1.00000 −0.141421
\(51\) 9.00000 15.5885i 1.26025 2.18282i
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 4.50000 7.79423i 0.612372 1.06066i
\(55\) −1.00000 −0.134840
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 12.0000 1.58944
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) −7.50000 12.9904i −0.976417 1.69120i −0.675178 0.737655i \(-0.735933\pi\)
−0.301239 0.953549i \(-0.597400\pi\)
\(60\) −1.50000 2.59808i −0.193649 0.335410i
\(61\) −1.50000 + 2.59808i −0.192055 + 0.332650i −0.945931 0.324367i \(-0.894849\pi\)
0.753876 + 0.657017i \(0.228182\pi\)
\(62\) −8.00000 −1.01600
\(63\) −15.0000 5.19615i −1.88982 0.654654i
\(64\) 1.00000 0.125000
\(65\) 0.500000 0.866025i 0.0620174 0.107417i
\(66\) −1.50000 2.59808i −0.184637 0.319801i
\(67\) 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i \(-0.0260283\pi\)
−0.569066 + 0.822292i \(0.692695\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) 12.0000 1.44463
\(70\) −2.00000 + 1.73205i −0.239046 + 0.207020i
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 3.00000 5.19615i 0.353553 0.612372i
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) −1.50000 + 2.59808i −0.173205 + 0.300000i
\(76\) 4.00000 0.458831
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) 3.00000 0.339683
\(79\) −7.50000 + 12.9904i −0.843816 + 1.46153i 0.0428296 + 0.999082i \(0.486363\pi\)
−0.886646 + 0.462450i \(0.846971\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −6.00000 + 10.3923i −0.662589 + 1.14764i
\(83\) 10.0000 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) −7.50000 2.59808i −0.818317 0.283473i
\(85\) −6.00000 −0.650791
\(86\) 6.00000 10.3923i 0.646997 1.12063i
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) −6.00000 −0.632456
\(91\) −0.500000 2.59808i −0.0524142 0.272352i
\(92\) 4.00000 0.417029
\(93\) −12.0000 + 20.7846i −1.24434 + 2.15526i
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) −2.00000 3.46410i −0.205196 0.355409i
\(96\) 1.50000 2.59808i 0.153093 0.265165i
\(97\) −5.00000 −0.507673 −0.253837 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) −6.00000 −0.603023
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i \(-0.118979\pi\)
−0.781697 + 0.623658i \(0.785646\pi\)
\(102\) −9.00000 15.5885i −0.891133 1.54349i
\(103\) −3.00000 + 5.19615i −0.295599 + 0.511992i −0.975124 0.221660i \(-0.928852\pi\)
0.679525 + 0.733652i \(0.262186\pi\)
\(104\) 1.00000 0.0980581
\(105\) 1.50000 + 7.79423i 0.146385 + 0.760639i
\(106\) 6.00000 0.582772
\(107\) 1.00000 1.73205i 0.0966736 0.167444i −0.813632 0.581380i \(-0.802513\pi\)
0.910306 + 0.413936i \(0.135846\pi\)
\(108\) −4.50000 7.79423i −0.433013 0.750000i
\(109\) 3.00000 + 5.19615i 0.287348 + 0.497701i 0.973176 0.230063i \(-0.0738931\pi\)
−0.685828 + 0.727764i \(0.740560\pi\)
\(110\) −0.500000 + 0.866025i −0.0476731 + 0.0825723i
\(111\) 24.0000 2.27798
\(112\) −2.50000 0.866025i −0.236228 0.0818317i
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 6.00000 10.3923i 0.561951 0.973329i
\(115\) −2.00000 3.46410i −0.186501 0.323029i
\(116\) −0.500000 0.866025i −0.0464238 0.0804084i
\(117\) 3.00000 5.19615i 0.277350 0.480384i
\(118\) −15.0000 −1.38086
\(119\) −12.0000 + 10.3923i −1.10004 + 0.952661i
\(120\) −3.00000 −0.273861
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 1.50000 + 2.59808i 0.135804 + 0.235219i
\(123\) 18.0000 + 31.1769i 1.62301 + 2.81113i
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) 1.00000 0.0894427
\(126\) −12.0000 + 10.3923i −1.06904 + 0.925820i
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −18.0000 31.1769i −1.58481 2.74497i
\(130\) −0.500000 0.866025i −0.0438529 0.0759555i
\(131\) −4.00000 + 6.92820i −0.349482 + 0.605320i −0.986157 0.165812i \(-0.946976\pi\)
0.636676 + 0.771132i \(0.280309\pi\)
\(132\) −3.00000 −0.261116
\(133\) −10.0000 3.46410i −0.867110 0.300376i
\(134\) 7.00000 0.604708
\(135\) −4.50000 + 7.79423i −0.387298 + 0.670820i
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −3.50000 6.06218i −0.299025 0.517927i 0.676888 0.736086i \(-0.263328\pi\)
−0.975913 + 0.218159i \(0.929995\pi\)
\(138\) 6.00000 10.3923i 0.510754 0.884652i
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0.500000 + 2.59808i 0.0422577 + 0.219578i
\(141\) −18.0000 −1.51587
\(142\) 5.00000 8.66025i 0.419591 0.726752i
\(143\) −0.500000 0.866025i −0.0418121 0.0724207i
\(144\) −3.00000 5.19615i −0.250000 0.433013i
\(145\) −0.500000 + 0.866025i −0.0415227 + 0.0719195i
\(146\) 4.00000 0.331042
\(147\) 16.5000 + 12.9904i 1.36090 + 1.07143i
\(148\) 8.00000 0.657596
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 1.50000 + 2.59808i 0.122474 + 0.212132i
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) 2.00000 3.46410i 0.162221 0.280976i
\(153\) −36.0000 −2.91043
\(154\) 0.500000 + 2.59808i 0.0402911 + 0.209359i
\(155\) 8.00000 0.642575
\(156\) 1.50000 2.59808i 0.120096 0.208013i
\(157\) 6.00000 + 10.3923i 0.478852 + 0.829396i 0.999706 0.0242497i \(-0.00771967\pi\)
−0.520854 + 0.853646i \(0.674386\pi\)
\(158\) 7.50000 + 12.9904i 0.596668 + 1.03346i
\(159\) 9.00000 15.5885i 0.713746 1.23625i
\(160\) −1.00000 −0.0790569
\(161\) −10.0000 3.46410i −0.788110 0.273009i
\(162\) −9.00000 −0.707107
\(163\) −7.50000 + 12.9904i −0.587445 + 1.01749i 0.407120 + 0.913375i \(0.366533\pi\)
−0.994566 + 0.104111i \(0.966800\pi\)
\(164\) 6.00000 + 10.3923i 0.468521 + 0.811503i
\(165\) 1.50000 + 2.59808i 0.116775 + 0.202260i
\(166\) 5.00000 8.66025i 0.388075 0.672166i
\(167\) −7.00000 −0.541676 −0.270838 0.962625i \(-0.587301\pi\)
−0.270838 + 0.962625i \(0.587301\pi\)
\(168\) −6.00000 + 5.19615i −0.462910 + 0.400892i
\(169\) −12.0000 −0.923077
\(170\) −3.00000 + 5.19615i −0.230089 + 0.398527i
\(171\) −12.0000 20.7846i −0.917663 1.58944i
\(172\) −6.00000 10.3923i −0.457496 0.792406i
\(173\) 0.500000 0.866025i 0.0380143 0.0658427i −0.846392 0.532560i \(-0.821230\pi\)
0.884407 + 0.466717i \(0.154563\pi\)
\(174\) −3.00000 −0.227429
\(175\) 2.00000 1.73205i 0.151186 0.130931i
\(176\) −1.00000 −0.0753778
\(177\) −22.5000 + 38.9711i −1.69120 + 2.92925i
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −3.50000 6.06218i −0.261602 0.453108i 0.705066 0.709142i \(-0.250918\pi\)
−0.966668 + 0.256034i \(0.917584\pi\)
\(180\) −3.00000 + 5.19615i −0.223607 + 0.387298i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −2.50000 0.866025i −0.185312 0.0641941i
\(183\) 9.00000 0.665299
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) −4.00000 6.92820i −0.294086 0.509372i
\(186\) 12.0000 + 20.7846i 0.879883 + 1.52400i
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) −6.00000 −0.437595
\(189\) 4.50000 + 23.3827i 0.327327 + 1.70084i
\(190\) −4.00000 −0.290191
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) −1.50000 2.59808i −0.108253 0.187500i
\(193\) −2.00000 3.46410i −0.143963 0.249351i 0.785022 0.619467i \(-0.212651\pi\)
−0.928986 + 0.370116i \(0.879318\pi\)
\(194\) −2.50000 + 4.33013i −0.179490 + 0.310885i
\(195\) −3.00000 −0.214834
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 25.0000 1.78118 0.890588 0.454811i \(-0.150293\pi\)
0.890588 + 0.454811i \(0.150293\pi\)
\(198\) −3.00000 + 5.19615i −0.213201 + 0.369274i
\(199\) −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i \(-0.211948\pi\)
−0.928166 + 0.372168i \(0.878615\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 10.5000 18.1865i 0.740613 1.28278i
\(202\) 3.00000 0.211079
\(203\) 0.500000 + 2.59808i 0.0350931 + 0.182349i
\(204\) −18.0000 −1.26025
\(205\) 6.00000 10.3923i 0.419058 0.725830i
\(206\) 3.00000 + 5.19615i 0.209020 + 0.362033i
\(207\) −12.0000 20.7846i −0.834058 1.44463i
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) −4.00000 −0.276686
\(210\) 7.50000 + 2.59808i 0.517549 + 0.179284i
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) −15.0000 25.9808i −1.02778 1.78017i
\(214\) −1.00000 1.73205i −0.0683586 0.118401i
\(215\) −6.00000 + 10.3923i −0.409197 + 0.708749i
\(216\) −9.00000 −0.612372
\(217\) 16.0000 13.8564i 1.08615 0.940634i
\(218\) 6.00000 0.406371
\(219\) 6.00000 10.3923i 0.405442 0.702247i
\(220\) 0.500000 + 0.866025i 0.0337100 + 0.0583874i
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 12.0000 20.7846i 0.805387 1.39497i
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 6.00000 0.400000
\(226\) −7.50000 + 12.9904i −0.498893 + 0.864107i
\(227\) −9.00000 15.5885i −0.597351 1.03464i −0.993210 0.116331i \(-0.962887\pi\)
0.395860 0.918311i \(-0.370447\pi\)
\(228\) −6.00000 10.3923i −0.397360 0.688247i
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) −4.00000 −0.263752
\(231\) 7.50000 + 2.59808i 0.493464 + 0.170941i
\(232\) −1.00000 −0.0656532
\(233\) 8.00000 13.8564i 0.524097 0.907763i −0.475509 0.879711i \(-0.657736\pi\)
0.999606 0.0280525i \(-0.00893057\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) −7.50000 + 12.9904i −0.488208 + 0.845602i
\(237\) 45.0000 2.92306
\(238\) 3.00000 + 15.5885i 0.194461 + 1.01045i
\(239\) −11.0000 −0.711531 −0.355765 0.934575i \(-0.615780\pi\)
−0.355765 + 0.934575i \(0.615780\pi\)
\(240\) −1.50000 + 2.59808i −0.0968246 + 0.167705i
\(241\) 8.00000 + 13.8564i 0.515325 + 0.892570i 0.999842 + 0.0177875i \(0.00566223\pi\)
−0.484516 + 0.874782i \(0.661004\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 3.00000 0.192055
\(245\) 1.00000 6.92820i 0.0638877 0.442627i
\(246\) 36.0000 2.29528
\(247\) 2.00000 3.46410i 0.127257 0.220416i
\(248\) 4.00000 + 6.92820i 0.254000 + 0.439941i
\(249\) −15.0000 25.9808i −0.950586 1.64646i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 3.00000 + 15.5885i 0.188982 + 0.981981i
\(253\) −4.00000 −0.251478
\(254\) −0.500000 + 0.866025i −0.0313728 + 0.0543393i
\(255\) 9.00000 + 15.5885i 0.563602 + 0.976187i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.50000 + 12.9904i −0.467837 + 0.810318i −0.999325 0.0367485i \(-0.988300\pi\)
0.531487 + 0.847066i \(0.321633\pi\)
\(258\) −36.0000 −2.24126
\(259\) −20.0000 6.92820i −1.24274 0.430498i
\(260\) −1.00000 −0.0620174
\(261\) −3.00000 + 5.19615i −0.185695 + 0.321634i
\(262\) 4.00000 + 6.92820i 0.247121 + 0.428026i
\(263\) 7.50000 + 12.9904i 0.462470 + 0.801021i 0.999083 0.0428069i \(-0.0136300\pi\)
−0.536614 + 0.843828i \(0.680297\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) −6.00000 −0.368577
\(266\) −8.00000 + 6.92820i −0.490511 + 0.424795i
\(267\) 18.0000 1.10158
\(268\) 3.50000 6.06218i 0.213797 0.370306i
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 4.50000 + 7.79423i 0.273861 + 0.474342i
\(271\) 10.5000 18.1865i 0.637830 1.10475i −0.348079 0.937465i \(-0.613166\pi\)
0.985908 0.167288i \(-0.0535009\pi\)
\(272\) −6.00000 −0.363803
\(273\) −6.00000 + 5.19615i −0.363137 + 0.314485i
\(274\) −7.00000 −0.422885
\(275\) 0.500000 0.866025i 0.0301511 0.0522233i
\(276\) −6.00000 10.3923i −0.361158 0.625543i
\(277\) −12.5000 21.6506i −0.751052 1.30086i −0.947313 0.320309i \(-0.896213\pi\)
0.196261 0.980552i \(-0.437120\pi\)
\(278\) 8.00000 13.8564i 0.479808 0.831052i
\(279\) 48.0000 2.87368
\(280\) 2.50000 + 0.866025i 0.149404 + 0.0517549i
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) −9.00000 + 15.5885i −0.535942 + 0.928279i
\(283\) 8.00000 + 13.8564i 0.475551 + 0.823678i 0.999608 0.0280052i \(-0.00891551\pi\)
−0.524057 + 0.851683i \(0.675582\pi\)
\(284\) −5.00000 8.66025i −0.296695 0.513892i
\(285\) −6.00000 + 10.3923i −0.355409 + 0.615587i
\(286\) −1.00000 −0.0591312
\(287\) −6.00000 31.1769i −0.354169 1.84032i
\(288\) −6.00000 −0.353553
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0.500000 + 0.866025i 0.0293610 + 0.0508548i
\(291\) 7.50000 + 12.9904i 0.439658 + 0.761510i
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 19.5000 7.79423i 1.13726 0.454569i
\(295\) 15.0000 0.873334
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 4.50000 + 7.79423i 0.261116 + 0.452267i
\(298\) −3.00000 5.19615i −0.173785 0.301005i
\(299\) 2.00000 3.46410i 0.115663 0.200334i
\(300\) 3.00000 0.173205
\(301\) 6.00000 + 31.1769i 0.345834 + 1.79701i
\(302\) 5.00000 0.287718
\(303\) 4.50000 7.79423i 0.258518 0.447767i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) −1.50000 2.59808i −0.0858898 0.148765i
\(306\) −18.0000 + 31.1769i −1.02899 + 1.78227i
\(307\) −26.0000 −1.48390 −0.741949 0.670456i \(-0.766098\pi\)
−0.741949 + 0.670456i \(0.766098\pi\)
\(308\) 2.50000 + 0.866025i 0.142451 + 0.0493464i
\(309\) 18.0000 1.02398
\(310\) 4.00000 6.92820i 0.227185 0.393496i
\(311\) −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) −1.50000 2.59808i −0.0849208 0.147087i
\(313\) 1.50000 2.59808i 0.0847850 0.146852i −0.820515 0.571626i \(-0.806313\pi\)
0.905300 + 0.424774i \(0.139646\pi\)
\(314\) 12.0000 0.677199
\(315\) 12.0000 10.3923i 0.676123 0.585540i
\(316\) 15.0000 0.843816
\(317\) 12.0000 20.7846i 0.673987 1.16738i −0.302777 0.953062i \(-0.597914\pi\)
0.976764 0.214318i \(-0.0687530\pi\)
\(318\) −9.00000 15.5885i −0.504695 0.874157i
\(319\) 0.500000 + 0.866025i 0.0279946 + 0.0484881i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −6.00000 −0.334887
\(322\) −8.00000 + 6.92820i −0.445823 + 0.386094i
\(323\) −24.0000 −1.33540
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 0.500000 + 0.866025i 0.0277350 + 0.0480384i
\(326\) 7.50000 + 12.9904i 0.415387 + 0.719471i
\(327\) 9.00000 15.5885i 0.497701 0.862044i
\(328\) 12.0000 0.662589
\(329\) 15.0000 + 5.19615i 0.826977 + 0.286473i
\(330\) 3.00000 0.165145
\(331\) 3.50000 6.06218i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) −5.00000 8.66025i −0.274411 0.475293i
\(333\) −24.0000 41.5692i −1.31519 2.27798i
\(334\) −3.50000 + 6.06218i −0.191511 + 0.331708i
\(335\) −7.00000 −0.382451
\(336\) 1.50000 + 7.79423i 0.0818317 + 0.425210i
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 22.5000 + 38.9711i 1.22203 + 2.11662i
\(340\) 3.00000 + 5.19615i 0.162698 + 0.281801i
\(341\) 4.00000 6.92820i 0.216612 0.375183i
\(342\) −24.0000 −1.29777
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −12.0000 −0.646997
\(345\) −6.00000 + 10.3923i −0.323029 + 0.559503i
\(346\) −0.500000 0.866025i −0.0268802 0.0465578i
\(347\) −15.0000 25.9808i −0.805242 1.39472i −0.916127 0.400887i \(-0.868702\pi\)
0.110885 0.993833i \(-0.464631\pi\)
\(348\) −1.50000 + 2.59808i −0.0804084 + 0.139272i
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) −0.500000 2.59808i −0.0267261 0.138873i
\(351\) −9.00000 −0.480384
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 22.5000 + 38.9711i 1.19586 + 2.07129i
\(355\) −5.00000 + 8.66025i −0.265372 + 0.459639i
\(356\) 6.00000 0.317999
\(357\) 45.0000 + 15.5885i 2.38165 + 0.825029i
\(358\) −7.00000 −0.369961
\(359\) −1.50000 + 2.59808i −0.0791670 + 0.137121i −0.902891 0.429870i \(-0.858559\pi\)
0.823724 + 0.566991i \(0.191893\pi\)
\(360\) 3.00000 + 5.19615i 0.158114 + 0.273861i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) 3.00000 0.157459
\(364\) −2.00000 + 1.73205i −0.104828 + 0.0907841i
\(365\) −4.00000 −0.209370
\(366\) 4.50000 7.79423i 0.235219 0.407411i
\(367\) 12.0000 + 20.7846i 0.626395 + 1.08495i 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 36.0000 62.3538i 1.87409 3.24601i
\(370\) −8.00000 −0.415900
\(371\) −12.0000 + 10.3923i −0.623009 + 0.539542i
\(372\) 24.0000 1.24434
\(373\) 1.50000 2.59808i 0.0776671 0.134523i −0.824576 0.565751i \(-0.808586\pi\)
0.902243 + 0.431228i \(0.141920\pi\)
\(374\) 3.00000 + 5.19615i 0.155126 + 0.268687i
\(375\) −1.50000 2.59808i −0.0774597 0.134164i
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −1.00000 −0.0515026
\(378\) 22.5000 + 7.79423i 1.15728 + 0.400892i
\(379\) 13.0000 0.667765 0.333883 0.942615i \(-0.391641\pi\)
0.333883 + 0.942615i \(0.391641\pi\)
\(380\) −2.00000 + 3.46410i −0.102598 + 0.177705i
\(381\) 1.50000 + 2.59808i 0.0768473 + 0.133103i
\(382\) −9.00000 15.5885i −0.460480 0.797575i
\(383\) 7.00000 12.1244i 0.357683 0.619526i −0.629890 0.776684i \(-0.716900\pi\)
0.987573 + 0.157159i \(0.0502334\pi\)
\(384\) −3.00000 −0.153093
\(385\) −0.500000 2.59808i −0.0254824 0.132410i
\(386\) −4.00000 −0.203595
\(387\) −36.0000 + 62.3538i −1.82998 + 3.16962i
\(388\) 2.50000 + 4.33013i 0.126918 + 0.219829i
\(389\) 11.0000 + 19.0526i 0.557722 + 0.966003i 0.997686 + 0.0679877i \(0.0216579\pi\)
−0.439964 + 0.898015i \(0.645009\pi\)
\(390\) −1.50000 + 2.59808i −0.0759555 + 0.131559i
\(391\) −24.0000 −1.21373
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 24.0000 1.21064
\(394\) 12.5000 21.6506i 0.629741 1.09074i
\(395\) −7.50000 12.9904i −0.377366 0.653617i
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) −4.00000 −0.200502
\(399\) 6.00000 + 31.1769i 0.300376 + 1.56080i
\(400\) 1.00000 0.0500000
\(401\) −11.5000 + 19.9186i −0.574283 + 0.994687i 0.421837 + 0.906672i \(0.361386\pi\)
−0.996119 + 0.0880147i \(0.971948\pi\)
\(402\) −10.5000 18.1865i −0.523692 0.907062i
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) 1.50000 2.59808i 0.0746278 0.129259i
\(405\) 9.00000 0.447214
\(406\) 2.50000 + 0.866025i 0.124073 + 0.0429801i
\(407\) −8.00000 −0.396545
\(408\) −9.00000 + 15.5885i −0.445566 + 0.771744i
\(409\) 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i \(-0.0541630\pi\)
−0.639430 + 0.768849i \(0.720830\pi\)
\(410\) −6.00000 10.3923i −0.296319 0.513239i
\(411\) −10.5000 + 18.1865i −0.517927 + 0.897076i
\(412\) 6.00000 0.295599
\(413\) 30.0000 25.9808i 1.47620 1.27843i
\(414\) −24.0000 −1.17954
\(415\) −5.00000 + 8.66025i −0.245440 + 0.425115i
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) −24.0000 41.5692i −1.17529 2.03565i
\(418\) −2.00000 + 3.46410i −0.0978232 + 0.169435i
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 6.00000 5.19615i 0.292770 0.253546i
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) 4.00000 6.92820i 0.194717 0.337260i
\(423\) 18.0000 + 31.1769i 0.875190 + 1.51587i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 3.00000 5.19615i 0.145521 0.252050i
\(426\) −30.0000 −1.45350
\(427\) −7.50000 2.59808i −0.362950 0.125730i
\(428\) −2.00000 −0.0966736
\(429\) −1.50000 + 2.59808i −0.0724207 + 0.125436i
\(430\) 6.00000 + 10.3923i 0.289346 + 0.501161i
\(431\) −3.50000 6.06218i −0.168589 0.292005i 0.769335 0.638846i \(-0.220588\pi\)
−0.937924 + 0.346841i \(0.887254\pi\)
\(432\) −4.50000 + 7.79423i −0.216506 + 0.375000i
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) −4.00000 20.7846i −0.192006 0.997693i
\(435\) 3.00000 0.143839
\(436\) 3.00000 5.19615i 0.143674 0.248851i
\(437\) −8.00000 13.8564i −0.382692 0.662842i
\(438\) −6.00000 10.3923i −0.286691 0.496564i
\(439\) 9.50000 16.4545i 0.453410 0.785330i −0.545185 0.838316i \(-0.683541\pi\)
0.998595 + 0.0529862i \(0.0168739\pi\)
\(440\) 1.00000 0.0476731
\(441\) 6.00000 41.5692i 0.285714 1.97949i
\(442\) −6.00000 −0.285391
\(443\) 14.0000 24.2487i 0.665160 1.15209i −0.314082 0.949396i \(-0.601697\pi\)
0.979242 0.202695i \(-0.0649700\pi\)
\(444\) −12.0000 20.7846i −0.569495 0.986394i
\(445\) −3.00000 5.19615i −0.142214 0.246321i
\(446\) −6.00000 + 10.3923i −0.284108 + 0.492090i
\(447\) −18.0000 −0.851371
\(448\) 0.500000 + 2.59808i 0.0236228 + 0.122748i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 3.00000 5.19615i 0.141421 0.244949i
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 7.50000 + 12.9904i 0.352770 + 0.611016i
\(453\) 7.50000 12.9904i 0.352381 0.610341i
\(454\) −18.0000 −0.844782
\(455\) 2.50000 + 0.866025i 0.117202 + 0.0405999i
\(456\) −12.0000 −0.561951
\(457\) −17.0000 + 29.4449i −0.795226 + 1.37737i 0.127469 + 0.991843i \(0.459315\pi\)
−0.922695 + 0.385530i \(0.874019\pi\)
\(458\) −2.00000 3.46410i −0.0934539 0.161867i
\(459\) 27.0000 + 46.7654i 1.26025 + 2.18282i
\(460\) −2.00000 + 3.46410i −0.0932505 + 0.161515i
\(461\) −15.0000 −0.698620 −0.349310 0.937007i \(-0.613584\pi\)
−0.349310 + 0.937007i \(0.613584\pi\)
\(462\) 6.00000 5.19615i 0.279145 0.241747i
\(463\) 34.0000 1.58011 0.790057 0.613033i \(-0.210051\pi\)
0.790057 + 0.613033i \(0.210051\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) −12.0000 20.7846i −0.556487 0.963863i
\(466\) −8.00000 13.8564i −0.370593 0.641886i
\(467\) 18.0000 31.1769i 0.832941 1.44270i −0.0627555 0.998029i \(-0.519989\pi\)
0.895696 0.444667i \(-0.146678\pi\)
\(468\) −6.00000 −0.277350
\(469\) −14.0000 + 12.1244i −0.646460 + 0.559851i
\(470\) 6.00000 0.276759
\(471\) 18.0000 31.1769i 0.829396 1.43656i
\(472\) 7.50000 + 12.9904i 0.345215 + 0.597931i
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) 22.5000 38.9711i 1.03346 1.79000i
\(475\) 4.00000 0.183533
\(476\) 15.0000 + 5.19615i 0.687524 + 0.238165i
\(477\) −36.0000 −1.64833
\(478\) −5.50000 + 9.52628i −0.251564 + 0.435722i
\(479\) 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i \(-0.0553307\pi\)
−0.642246 + 0.766498i \(0.721997\pi\)
\(480\) 1.50000 + 2.59808i 0.0684653 + 0.118585i
\(481\) 4.00000 6.92820i 0.182384 0.315899i
\(482\) 16.0000 0.728780
\(483\) 6.00000 + 31.1769i 0.273009 + 1.41860i
\(484\) 1.00000 0.0454545
\(485\) 2.50000 4.33013i 0.113519 0.196621i
\(486\) 0 0
\(487\) 18.0000 + 31.1769i 0.815658 + 1.41276i 0.908855 + 0.417113i \(0.136958\pi\)
−0.0931967 + 0.995648i \(0.529709\pi\)
\(488\) 1.50000 2.59808i 0.0679018 0.117609i
\(489\) 45.0000 2.03497
\(490\) −5.50000 4.33013i −0.248465 0.195615i
\(491\) −14.0000 −0.631811 −0.315906 0.948791i \(-0.602308\pi\)
−0.315906 + 0.948791i \(0.602308\pi\)
\(492\) 18.0000 31.1769i 0.811503 1.40556i
\(493\) 3.00000 + 5.19615i 0.135113 + 0.234023i
\(494\) −2.00000 3.46410i −0.0899843 0.155857i
\(495\) 3.00000 5.19615i 0.134840 0.233550i
\(496\) 8.00000 0.359211
\(497\) 5.00000 + 25.9808i 0.224281 + 1.16540i
\(498\) −30.0000 −1.34433
\(499\) −18.0000 + 31.1769i −0.805791 + 1.39567i 0.109965 + 0.993935i \(0.464926\pi\)
−0.915756 + 0.401735i \(0.868407\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 10.5000 + 18.1865i 0.469105 + 0.812514i
\(502\) 0 0
\(503\) 9.00000 0.401290 0.200645 0.979664i \(-0.435696\pi\)
0.200645 + 0.979664i \(0.435696\pi\)
\(504\) 15.0000 + 5.19615i 0.668153 + 0.231455i
\(505\) −3.00000 −0.133498
\(506\) −2.00000 + 3.46410i −0.0889108 + 0.153998i
\(507\) 18.0000 + 31.1769i 0.799408 + 1.38462i
\(508\) 0.500000 + 0.866025i 0.0221839 + 0.0384237i
\(509\) 21.0000 36.3731i 0.930809 1.61221i 0.148866 0.988857i \(-0.452438\pi\)
0.781943 0.623350i \(-0.214229\pi\)
\(510\) 18.0000 0.797053
\(511\) −8.00000 + 6.92820i −0.353899 + 0.306486i
\(512\) −1.00000 −0.0441942
\(513\) −18.0000 + 31.1769i −0.794719 + 1.37649i
\(514\) 7.50000 + 12.9904i 0.330811 + 0.572981i
\(515\) −3.00000 5.19615i −0.132196 0.228970i
\(516\) −18.0000 + 31.1769i −0.792406 + 1.37249i
\(517\) 6.00000 0.263880
\(518\) −16.0000 + 13.8564i −0.703000 + 0.608816i
\(519\) −3.00000 −0.131685
\(520\) −0.500000 + 0.866025i −0.0219265 + 0.0379777i
\(521\) −5.00000 8.66025i −0.219054 0.379413i 0.735465 0.677563i \(-0.236964\pi\)
−0.954519 + 0.298150i \(0.903630\pi\)
\(522\) 3.00000 + 5.19615i 0.131306 + 0.227429i
\(523\) −11.0000 + 19.0526i −0.480996 + 0.833110i −0.999762 0.0218062i \(-0.993058\pi\)
0.518766 + 0.854916i \(0.326392\pi\)
\(524\) 8.00000 0.349482
\(525\) −7.50000 2.59808i −0.327327 0.113389i
\(526\) 15.0000 0.654031
\(527\) 24.0000 41.5692i 1.04546 1.81078i
\(528\) 1.50000 + 2.59808i 0.0652791 + 0.113067i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −3.00000 + 5.19615i −0.130312 + 0.225706i
\(531\) 90.0000 3.90567
\(532\) 2.00000 + 10.3923i 0.0867110 + 0.450564i
\(533\) 12.0000 0.519778
\(534\) 9.00000 15.5885i 0.389468 0.674579i
\(535\) 1.00000 + 1.73205i 0.0432338 + 0.0748831i
\(536\) −3.50000 6.06218i −0.151177 0.261846i
\(537\) −10.5000 + 18.1865i −0.453108 + 0.784807i
\(538\) 0 0
\(539\) −5.50000 4.33013i −0.236902 0.186512i
\(540\) 9.00000 0.387298
\(541\) 8.50000 14.7224i 0.365444 0.632967i −0.623404 0.781900i \(-0.714251\pi\)
0.988847 + 0.148933i \(0.0475840\pi\)
\(542\) −10.5000 18.1865i −0.451014 0.781179i
\(543\) −3.00000 5.19615i −0.128742 0.222988i
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) −6.00000 −0.257012
\(546\) 1.50000 + 7.79423i 0.0641941 + 0.333562i
\(547\) 18.0000 0.769624 0.384812 0.922995i \(-0.374266\pi\)
0.384812 + 0.922995i \(0.374266\pi\)
\(548\) −3.50000 + 6.06218i −0.149513 + 0.258963i
\(549\) −9.00000 15.5885i −0.384111 0.665299i
\(550\) −0.500000 0.866025i −0.0213201 0.0369274i
\(551\) −2.00000 + 3.46410i −0.0852029 + 0.147576i
\(552\) −12.0000 −0.510754
\(553\) −37.5000 12.9904i −1.59466 0.552407i
\(554\) −25.0000 −1.06215
\(555\) −12.0000 + 20.7846i −0.509372 + 0.882258i
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) −3.00000 5.19615i −0.127114 0.220168i 0.795443 0.606028i \(-0.207238\pi\)
−0.922557 + 0.385860i \(0.873905\pi\)
\(558\) 24.0000 41.5692i 1.01600 1.75977i
\(559\) −12.0000 −0.507546
\(560\) 2.00000 1.73205i 0.0845154 0.0731925i
\(561\) 18.0000 0.759961
\(562\) −6.00000 + 10.3923i −0.253095 + 0.438373i
\(563\) 14.0000 + 24.2487i 0.590030 + 1.02196i 0.994228 + 0.107290i \(0.0342173\pi\)
−0.404198 + 0.914671i \(0.632449\pi\)
\(564\) 9.00000 + 15.5885i 0.378968 + 0.656392i
\(565\) 7.50000 12.9904i 0.315527 0.546509i
\(566\) 16.0000 0.672530
\(567\) 18.0000 15.5885i 0.755929 0.654654i
\(568\) −10.0000 −0.419591
\(569\) 2.00000 3.46410i 0.0838444 0.145223i −0.821054 0.570851i \(-0.806613\pi\)
0.904898 + 0.425628i \(0.139947\pi\)
\(570\) 6.00000 + 10.3923i 0.251312 + 0.435286i
\(571\) −15.0000 25.9808i −0.627730 1.08726i −0.988006 0.154415i \(-0.950651\pi\)
0.360276 0.932846i \(-0.382683\pi\)
\(572\) −0.500000 + 0.866025i −0.0209061 + 0.0362103i
\(573\) −54.0000 −2.25588
\(574\) −30.0000 10.3923i −1.25218 0.433766i
\(575\) 4.00000 0.166812
\(576\) −3.00000 + 5.19615i −0.125000 + 0.216506i
\(577\) 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i \(0.0565899\pi\)
−0.338965 + 0.940799i \(0.610077\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) −6.00000 + 10.3923i −0.249351 + 0.431889i
\(580\) 1.00000 0.0415227
\(581\) 5.00000 + 25.9808i 0.207435 + 1.07786i
\(582\) 15.0000 0.621770
\(583\) −3.00000 + 5.19615i −0.124247 + 0.215203i
\(584\) −2.00000 3.46410i −0.0827606 0.143346i
\(585\) 3.00000 + 5.19615i 0.124035 + 0.214834i
\(586\) 13.0000 22.5167i 0.537025 0.930155i
\(587\) 11.0000 0.454019 0.227009 0.973893i \(-0.427105\pi\)
0.227009 + 0.973893i \(0.427105\pi\)
\(588\) 3.00000 20.7846i 0.123718 0.857143i
\(589\) 32.0000 1.31854
\(590\) 7.50000 12.9904i 0.308770 0.534806i
\(591\) −37.5000 64.9519i −1.54254 2.67176i
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 9.00000 0.369274
\(595\) −3.00000 15.5885i −0.122988 0.639064i
\(596\) −6.00000 −0.245770
\(597\) −6.00000 + 10.3923i −0.245564 + 0.425329i
\(598\) −2.00000 3.46410i −0.0817861 0.141658i
\(599\) 6.00000 + 10.3923i 0.245153 + 0.424618i 0.962175 0.272433i \(-0.0878284\pi\)
−0.717021 + 0.697051i \(0.754495\pi\)
\(600\) 1.50000 2.59808i 0.0612372 0.106066i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 30.0000 + 10.3923i 1.22271 + 0.423559i
\(603\) −42.0000 −1.71037
\(604\) 2.50000 4.33013i 0.101724 0.176190i
\(605\) −0.500000 0.866025i −0.0203279 0.0352089i
\(606\) −4.50000 7.79423i −0.182800 0.316619i
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) −4.00000 −0.162221
\(609\) 6.00000 5.19615i 0.243132 0.210559i
\(610\) −3.00000 −0.121466
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) 18.0000 + 31.1769i 0.727607 + 1.26025i
\(613\) 13.0000 + 22.5167i 0.525065 + 0.909439i 0.999574 + 0.0291886i \(0.00929235\pi\)
−0.474509 + 0.880251i \(0.657374\pi\)
\(614\) −13.0000 + 22.5167i −0.524637 + 0.908698i
\(615\) −36.0000 −1.45166
\(616\) 2.00000 1.73205i 0.0805823 0.0697863i
\(617\) −3.00000 −0.120775 −0.0603877 0.998175i \(-0.519234\pi\)
−0.0603877 + 0.998175i \(0.519234\pi\)
\(618\) 9.00000 15.5885i 0.362033 0.627060i
\(619\) −14.0000 24.2487i −0.562708 0.974638i −0.997259 0.0739910i \(-0.976426\pi\)
0.434551 0.900647i \(-0.356907\pi\)
\(620\) −4.00000 6.92820i −0.160644 0.278243i
\(621\) −18.0000 + 31.1769i −0.722315 + 1.25109i
\(622\) −6.00000 −0.240578
\(623\) −15.0000 5.19615i −0.600962 0.208179i
\(624\) −3.00000 −0.120096
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −1.50000 2.59808i −0.0599521 0.103840i
\(627\) 6.00000 + 10.3923i 0.239617 + 0.415029i
\(628\) 6.00000 10.3923i 0.239426 0.414698i
\(629\) −48.0000 −1.91389
\(630\) −3.00000 15.5885i −0.119523 0.621059i
\(631\) −10.0000 −0.398094 −0.199047 0.979990i \(-0.563785\pi\)
−0.199047 + 0.979990i \(0.563785\pi\)
\(632\) 7.50000 12.9904i 0.298334 0.516730i
\(633\) −12.0000 20.7846i −0.476957 0.826114i
\(634\) −12.0000 20.7846i −0.476581 0.825462i
\(635\) 0.500000 0.866025i 0.0198419 0.0343672i
\(636\) −18.0000 −0.713746
\(637\) 6.50000 2.59808i 0.257539 0.102940i
\(638\) 1.00000 0.0395904
\(639\) −30.0000 + 51.9615i −1.18678 + 2.05557i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −18.5000 32.0429i −0.730706 1.26562i −0.956582 0.291464i \(-0.905858\pi\)
0.225876 0.974156i \(-0.427476\pi\)
\(642\) −3.00000 + 5.19615i −0.118401 + 0.205076i
\(643\) 47.0000 1.85350 0.926750 0.375680i \(-0.122591\pi\)
0.926750 + 0.375680i \(0.122591\pi\)
\(644\) 2.00000 + 10.3923i 0.0788110 + 0.409514i
\(645\) 36.0000 1.41750
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) 11.0000 + 19.0526i 0.432455 + 0.749033i 0.997084 0.0763112i \(-0.0243142\pi\)
−0.564629 + 0.825345i \(0.690981\pi\)
\(648\) 4.50000 + 7.79423i 0.176777 + 0.306186i
\(649\) 7.50000 12.9904i 0.294401 0.509917i
\(650\) 1.00000 0.0392232
\(651\) −60.0000 20.7846i −2.35159 0.814613i
\(652\) 15.0000 0.587445
\(653\) 12.0000 20.7846i 0.469596 0.813365i −0.529799 0.848123i \(-0.677733\pi\)
0.999396 + 0.0347583i \(0.0110661\pi\)
\(654\) −9.00000 15.5885i −0.351928 0.609557i
\(655\) −4.00000 6.92820i −0.156293 0.270707i
\(656\) 6.00000 10.3923i 0.234261 0.405751i
\(657\) −24.0000 −0.936329
\(658\) 12.0000 10.3923i 0.467809 0.405134i
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 1.50000 2.59808i 0.0583874 0.101130i
\(661\) −1.00000 1.73205i −0.0388955 0.0673690i 0.845922 0.533306i \(-0.179051\pi\)
−0.884818 + 0.465937i \(0.845717\pi\)
\(662\) −3.50000 6.06218i −0.136031 0.235613i
\(663\) −9.00000 + 15.5885i −0.349531 + 0.605406i
\(664\) −10.0000 −0.388075
\(665\) 8.00000 6.92820i 0.310227 0.268664i
\(666\) −48.0000 −1.85996
\(667\) −2.00000 + 3.46410i −0.0774403 + 0.134131i
\(668\) 3.50000 + 6.06218i 0.135419 + 0.234553i
\(669\) 18.0000 + 31.1769i 0.695920 + 1.20537i
\(670\) −3.50000 + 6.06218i −0.135217 + 0.234202i
\(671\) −3.00000 −0.115814
\(672\) 7.50000 + 2.59808i 0.289319 + 0.100223i
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −16.0000 + 27.7128i −0.616297 + 1.06746i
\(675\) −4.50000 7.79423i −0.173205 0.300000i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −13.0000 + 22.5167i −0.499631 + 0.865386i −1.00000 0.000426509i \(-0.999864\pi\)
0.500369 + 0.865812i \(0.333198\pi\)
\(678\) 45.0000 1.72821
\(679\) −2.50000 12.9904i −0.0959412 0.498525i
\(680\) 6.00000 0.230089
\(681\) −27.0000 + 46.7654i −1.03464 + 1.79205i
\(682\) −4.00000 6.92820i −0.153168 0.265295i
\(683\) 1.50000 + 2.59808i 0.0573959 + 0.0994126i 0.893296 0.449469i \(-0.148387\pi\)
−0.835900 + 0.548882i \(0.815054\pi\)
\(684\) −12.0000 + 20.7846i −0.458831 + 0.794719i
\(685\) 7.00000 0.267456
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) −12.0000 −0.457829
\(688\) −6.00000 + 10.3923i −0.228748 + 0.396203i
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 6.00000 + 10.3923i 0.228416 + 0.395628i
\(691\) −18.5000 + 32.0429i −0.703773 + 1.21897i 0.263359 + 0.964698i \(0.415170\pi\)
−0.967132 + 0.254273i \(0.918164\pi\)
\(692\) −1.00000 −0.0380143
\(693\) −3.00000 15.5885i −0.113961 0.592157i
\(694\) −30.0000 −1.13878
\(695\) −8.00000 + 13.8564i −0.303457 + 0.525603i
\(696\) 1.50000 + 2.59808i 0.0568574 + 0.0984798i
\(697\) −36.0000 62.3538i −1.36360 2.36182i
\(698\) −17.0000 + 29.4449i −0.643459 + 1.11450i
\(699\) −48.0000 −1.81553
\(700\) −2.50000 0.866025i −0.0944911 0.0327327i
\(701\) 15.0000 0.566542 0.283271 0.959040i \(-0.408580\pi\)
0.283271 + 0.959040i \(0.408580\pi\)
\(702\) −4.50000 + 7.79423i −0.169842 + 0.294174i
\(703\) −16.0000 27.7128i −0.603451 1.04521i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 9.00000 15.5885i 0.338960 0.587095i
\(706\) 18.0000 0.677439
\(707\) −6.00000 + 5.19615i −0.225653 + 0.195421i
\(708\) 45.0000 1.69120
\(709\) −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) 5.00000 + 8.66025i 0.187647 + 0.325014i
\(711\) −45.0000 77.9423i −1.68763 2.92306i
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 32.0000 1.19841
\(714\) 36.0000 31.1769i 1.34727 1.16677i
\(715\) 1.00000 0.0373979
\(716\) −3.50000 + 6.06218i −0.130801 + 0.226554i
\(717\) 16.5000 + 28.5788i 0.616204 + 1.06730i
\(718\) 1.50000 + 2.59808i 0.0559795 + 0.0969593i
\(719\) −25.0000 + 43.3013i −0.932343 + 1.61486i −0.153037 + 0.988220i \(0.548906\pi\)
−0.779305 + 0.626644i \(0.784428\pi\)
\(720\) 6.00000 0.223607
\(721\) −15.0000 5.19615i −0.558629 0.193515i
\(722\) 3.00000 0.111648
\(723\) 24.0000 41.5692i 0.892570 1.54598i
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) −0.500000 0.866025i −0.0185695 0.0321634i
\(726\) 1.50000 2.59808i 0.0556702 0.0964237i
\(727\) −26.0000 −0.964287 −0.482143 0.876092i \(-0.660142\pi\)
−0.482143 + 0.876092i \(0.660142\pi\)
\(728\) 0.500000 + 2.59808i 0.0185312 + 0.0962911i
\(729\) −27.0000 −1.00000
\(730\) −2.00000 + 3.46410i −0.0740233 + 0.128212i
\(731\) 36.0000 + 62.3538i 1.33151 + 2.30624i
\(732\) −4.50000 7.79423i −0.166325 0.288083i
\(733\) 6.50000 11.2583i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) 24.0000 0.885856
\(735\) −19.5000 + 7.79423i −0.719268 + 0.287494i
\(736\) −4.00000 −0.147442
\(737\) −3.50000 + 6.06218i −0.128924 + 0.223303i
\(738\) −36.0000 62.3538i −1.32518 2.29528i
\(739\) −15.0000 25.9808i −0.551784 0.955718i −0.998146 0.0608653i \(-0.980614\pi\)
0.446362 0.894852i \(-0.352719\pi\)
\(740\) −4.00000 + 6.92820i −0.147043 + 0.254686i
\(741\) −12.0000 −0.440831
\(742\) 3.00000 + 15.5885i 0.110133 + 0.572270i
\(743\) −20.0000 −0.733729 −0.366864 0.930274i \(-0.619569\pi\)
−0.366864 + 0.930274i \(0.619569\pi\)
\(744\) 12.0000 20.7846i 0.439941 0.762001i
\(745\) 3.00000 + 5.19615i 0.109911 + 0.190372i
\(746\) −1.50000 2.59808i −0.0549189 0.0951223i
\(747\) −30.0000 + 51.9615i −1.09764 + 1.90117i
\(748\) 6.00000 0.219382
\(749\) 5.00000 + 1.73205i 0.182696 + 0.0632878i
\(750\) −3.00000 −0.109545
\(751\) 10.0000 17.3205i 0.364905 0.632034i −0.623856 0.781540i \(-0.714435\pi\)
0.988761 + 0.149505i \(0.0477681\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −0.500000 + 0.866025i −0.0182089 + 0.0315388i
\(755\) −5.00000 −0.181969
\(756\) 18.0000 15.5885i 0.654654 0.566947i
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 6.50000 11.2583i 0.236091 0.408921i
\(759\) 6.00000 + 10.3923i 0.217786 + 0.377217i
\(760\) 2.00000 + 3.46410i 0.0725476 + 0.125656i
\(761\) 11.0000 19.0526i 0.398750 0.690655i −0.594822 0.803857i \(-0.702778\pi\)
0.993572 + 0.113203i \(0.0361109\pi\)
\(762\) 3.00000 0.108679
\(763\) −12.0000 + 10.3923i −0.434429 + 0.376227i
\(764\) −18.0000 −0.651217
\(765\) 18.0000 31.1769i 0.650791 1.12720i
\(766\) −7.00000 12.1244i −0.252920 0.438071i
\(767\) 7.50000 + 12.9904i 0.270809 + 0.469055i
\(768\) −1.50000 + 2.59808i −0.0541266 + 0.0937500i
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) −2.50000 0.866025i −0.0900937 0.0312094i
\(771\) 45.0000 1.62064
\(772\) −2.00000 + 3.46410i −0.0719816 + 0.124676i
\(773\) 18.0000 + 31.1769i 0.647415 + 1.12136i 0.983738 + 0.179609i \(0.0574833\pi\)
−0.336323 + 0.941747i \(0.609183\pi\)
\(774\) 36.0000 + 62.3538i 1.29399 + 2.24126i