Properties

Label 1050.2.i.c.151.1
Level $1050$
Weight $2$
Character 1050.151
Analytic conductor $8.384$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
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 151.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1050.151
Dual form 1050.2.i.c.751.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(-2.00000 + 1.73205i) q^{21} +6.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -3.00000 q^{34} +1.00000 q^{36} +(-4.00000 - 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} -3.00000 q^{41} +(2.50000 + 0.866025i) q^{42} +8.00000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(1.50000 + 2.59808i) q^{51} +(2.00000 - 3.46410i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} -4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{61} +5.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(1.50000 + 2.59808i) q^{68} +3.00000 q^{69} -9.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} -4.00000 q^{78} +(3.50000 + 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.50000 + 2.59808i) q^{82} -6.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} +(-4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(-10.0000 - 3.46410i) q^{91} +3.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{96} +17.0000 q^{97} +(1.00000 - 6.92820i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} + 2q^{6} + 5q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} + 2q^{6} + 5q^{7} + 2q^{8} - q^{9} - 6q^{11} - q^{12} - 8q^{13} - q^{14} - q^{16} + 3q^{17} - q^{18} + 4q^{19} - 4q^{21} + 12q^{22} - 3q^{23} - q^{24} + 4q^{26} + 2q^{27} - 4q^{28} - 12q^{29} - 5q^{31} - q^{32} - 6q^{33} - 6q^{34} + 2q^{36} - 8q^{37} + 4q^{38} + 4q^{39} - 6q^{41} + 5q^{42} + 16q^{43} - 6q^{44} - 3q^{46} - 9q^{47} + 2q^{48} + 11q^{49} + 3q^{51} + 4q^{52} - 12q^{53} - q^{54} + 5q^{56} - 8q^{57} + 6q^{58} - 6q^{59} - 2q^{61} + 10q^{62} - q^{63} + 2q^{64} - 6q^{66} - 8q^{67} + 3q^{68} + 6q^{69} - 18q^{71} - q^{72} - 14q^{73} - 8q^{74} - 8q^{76} - 24q^{77} - 8q^{78} + 7q^{79} - q^{81} + 3q^{82} - 12q^{83} - q^{84} - 8q^{86} + 6q^{87} - 6q^{88} - 3q^{89} - 20q^{91} + 6q^{92} - 5q^{93} - 9q^{94} - q^{96} + 34q^{97} + 2q^{98} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −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 \(0.806886\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 6.00000 1.27920
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 2.00000 + 3.46410i 0.392232 + 0.679366i
\(27\) 1.00000 0.192450
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −3.00000 5.19615i −0.522233 0.904534i
\(34\) −3.00000 −0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) 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 \(0.575267\pi\)
\(42\) 2.50000 + 0.866025i 0.385758 + 0.133631i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −3.00000 5.19615i −0.452267 0.783349i
\(45\) 0 0
\(46\) −1.50000 + 2.59808i −0.221163 + 0.383065i
\(47\) −4.50000 7.79423i −0.656392 1.13691i −0.981543 0.191243i \(-0.938748\pi\)
0.325150 0.945662i \(-0.394585\pi\)
\(48\) 1.00000 0.144338
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) −4.00000 −0.529813
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 5.00000 0.635001
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 + 5.19615i −0.369274 + 0.639602i
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −7.00000 + 12.1244i −0.819288 + 1.41905i 0.0869195 + 0.996215i \(0.472298\pi\)
−0.906208 + 0.422833i \(0.861036\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) −12.0000 + 10.3923i −1.36753 + 1.18431i
\(78\) −4.00000 −0.452911
\(79\) 3.50000 + 6.06218i 0.393781 + 0.682048i 0.992945 0.118578i \(-0.0378336\pi\)
−0.599164 + 0.800626i \(0.704500\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −0.500000 2.59808i −0.0545545 0.283473i
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 3.00000 5.19615i 0.321634 0.557086i
\(88\) −3.00000 + 5.19615i −0.319801 + 0.553912i
\(89\) −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i \(-0.217494\pi\)
−0.934508 + 0.355942i \(0.884160\pi\)
\(90\) 0 0
\(91\) −10.0000 3.46410i −1.04828 0.363137i
\(92\) 3.00000 0.312772
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) −4.50000 + 7.79423i −0.464140 + 0.803913i
\(95\) 0 0
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 17.0000 1.72609 0.863044 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) 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 \(0.963017\pi\)
\(102\) 1.50000 2.59808i 0.148522 0.257248i
\(103\) 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) −0.500000 2.59808i −0.0472456 0.245495i
\(113\) 3.00000 0.282216 0.141108 0.989994i \(-0.454933\pi\)
0.141108 + 0.989994i \(0.454933\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 2.00000 + 3.46410i 0.184900 + 0.320256i
\(118\) 6.00000 0.552345
\(119\) 6.00000 5.19615i 0.550019 0.476331i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) −1.00000 + 1.73205i −0.0905357 + 0.156813i
\(123\) 1.50000 2.59808i 0.135250 0.234261i
\(124\) −2.50000 4.33013i −0.224507 0.388857i
\(125\) 0 0
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −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 \(0.545310\pi\)
\(132\) 6.00000 0.522233
\(133\) 2.00000 + 10.3923i 0.173422 + 0.901127i
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 7.50000 12.9904i 0.640768 1.10984i −0.344493 0.938789i \(-0.611949\pi\)
0.985262 0.171054i \(-0.0547174\pi\)
\(138\) −1.50000 2.59808i −0.127688 0.221163i
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 0 0
\(141\) 9.00000 0.757937
\(142\) 4.50000 + 7.79423i 0.377632 + 0.654077i
\(143\) 12.0000 20.7846i 1.00349 1.73810i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 14.0000 1.15865
\(147\) −6.50000 + 2.59808i −0.536111 + 0.214286i
\(148\) 8.00000 0.657596
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 2.00000 + 3.46410i 0.162221 + 0.280976i
\(153\) −3.00000 −0.242536
\(154\) 15.0000 + 5.19615i 1.20873 + 0.418718i
\(155\) 0 0
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 3.50000 6.06218i 0.278445 0.482281i
\(159\) −6.00000 10.3923i −0.475831 0.824163i
\(160\) 0 0
\(161\) −1.50000 7.79423i −0.118217 0.614271i
\(162\) 1.00000 0.0785674
\(163\) −4.00000 6.92820i −0.313304 0.542659i 0.665771 0.746156i \(-0.268103\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −2.00000 + 1.73205i −0.154303 + 0.133631i
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) −3.00000 5.19615i −0.225494 0.390567i
\(178\) −1.50000 + 2.59808i −0.112430 + 0.194734i
\(179\) 9.00000 15.5885i 0.672692 1.16514i −0.304446 0.952529i \(-0.598471\pi\)
0.977138 0.212607i \(-0.0681952\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 2.00000 + 10.3923i 0.148250 + 0.770329i
\(183\) 2.00000 0.147844
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) 0 0
\(186\) −2.50000 + 4.33013i −0.183309 + 0.317500i
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) 9.00000 0.656392
\(189\) 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 \(-0.349257\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) −8.50000 14.7224i −0.610264 1.05701i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) −3.00000 5.19615i −0.213201 0.369274i
\(199\) −2.50000 + 4.33013i −0.177220 + 0.306955i −0.940927 0.338608i \(-0.890044\pi\)
0.763707 + 0.645563i \(0.223377\pi\)
\(200\) 0 0
\(201\) −4.00000 6.92820i −0.282138 0.488678i
\(202\) 12.0000 0.844317
\(203\) −15.0000 5.19615i −1.05279 0.364698i
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 6.50000 11.2583i 0.452876 0.784405i
\(207\) −1.50000 + 2.59808i −0.104257 + 0.180579i
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) −24.0000 −1.66011
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) 4.50000 7.79423i 0.308335 0.534052i
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −10.0000 + 8.66025i −0.678844 + 0.587896i
\(218\) −4.00000 −0.270914
\(219\) −7.00000 12.1244i −0.473016 0.819288i
\(220\) 0 0
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) −4.00000 6.92820i −0.268462 0.464991i
\(223\) 11.0000 0.736614 0.368307 0.929704i \(-0.379937\pi\)
0.368307 + 0.929704i \(0.379937\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 0 0
\(226\) −1.50000 2.59808i −0.0997785 0.172821i
\(227\) 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i \(-0.629553\pi\)
0.993210 0.116331i \(-0.0371134\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) 11.0000 + 19.0526i 0.726900 + 1.25903i 0.958187 + 0.286143i \(0.0923732\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) −3.00000 15.5885i −0.197386 1.02565i
\(232\) −6.00000 −0.393919
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 2.00000 3.46410i 0.130744 0.226455i
\(235\) 0 0
\(236\) −3.00000 5.19615i −0.195283 0.338241i
\(237\) −7.00000 −0.454699
\(238\) −7.50000 2.59808i −0.486153 0.168408i
\(239\) 3.00000 0.194054 0.0970269 0.995282i \(-0.469067\pi\)
0.0970269 + 0.995282i \(0.469067\pi\)
\(240\) 0 0
\(241\) 11.0000 19.0526i 0.708572 1.22728i −0.256814 0.966461i \(-0.582673\pi\)
0.965387 0.260822i \(-0.0839937\pi\)
\(242\) −12.5000 + 21.6506i −0.803530 + 1.39176i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) −3.00000 −0.191273
\(247\) −8.00000 13.8564i −0.509028 0.881662i
\(248\) −2.50000 + 4.33013i −0.158750 + 0.274963i
\(249\) 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 \(0.226453\pi\)
\(252\) 2.50000 + 0.866025i 0.157485 + 0.0545545i
\(253\) 18.0000 1.13165
\(254\) 8.00000 + 13.8564i 0.501965 + 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 8.00000 0.498058
\(259\) −4.00000 20.7846i −0.248548 1.29149i
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 9.00000 15.5885i 0.556022 0.963058i
\(263\) 1.50000 2.59808i 0.0924940 0.160204i −0.816066 0.577959i \(-0.803849\pi\)
0.908560 + 0.417755i \(0.137183\pi\)
\(264\) −3.00000 5.19615i −0.184637 0.319801i
\(265\) 0 0
\(266\) 8.00000 6.92820i 0.490511 0.424795i
\(267\) 3.00000 0.183597
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) 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 \(0.558865\pi\)
\(272\) −3.00000 −0.181902
\(273\) 8.00000 6.92820i 0.484182 0.419314i
\(274\) −15.0000 −0.906183
\(275\) 0 0
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) −13.0000 + 22.5167i −0.781094 + 1.35290i 0.150210 + 0.988654i \(0.452005\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) −1.00000 1.73205i −0.0599760 0.103882i
\(279\) 5.00000 0.299342
\(280\) 0 0
\(281\) 27.0000 1.61068 0.805342 0.592810i \(-0.201981\pi\)
0.805342 + 0.592810i \(0.201981\pi\)
\(282\) −4.50000 7.79423i −0.267971 0.464140i
\(283\) 11.0000 19.0526i 0.653882 1.13256i −0.328291 0.944577i \(-0.606473\pi\)
0.982173 0.187980i \(-0.0601941\pi\)
\(284\) 4.50000 7.79423i 0.267026 0.462502i
\(285\) 0 0
\(286\) −24.0000 −1.41915
\(287\) −7.50000 2.59808i −0.442711 0.153360i
\(288\) 1.00000 0.0589256
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) −8.50000 + 14.7224i −0.498279 + 0.863044i
\(292\) −7.00000 12.1244i −0.409644 0.709524i
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 5.50000 + 4.33013i 0.320767 + 0.252538i
\(295\) 0 0
\(296\) −4.00000 6.92820i −0.232495 0.402694i
\(297\) −3.00000 + 5.19615i −0.174078 + 0.301511i
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 6.00000 + 10.3923i 0.346989 + 0.601003i
\(300\) 0 0
\(301\) 20.0000 + 6.92820i 1.15278 + 0.399335i
\(302\) −16.0000 −0.920697
\(303\) −6.00000 10.3923i −0.344691 0.597022i
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 0 0
\(306\) 1.50000 + 2.59808i 0.0857493 + 0.148522i
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) −3.00000 15.5885i −0.170941 0.888235i
\(309\) −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 \(0.963660\pi\)
\(312\) 2.00000 3.46410i 0.113228 0.196116i
\(313\) −8.50000 14.7224i −0.480448 0.832161i 0.519300 0.854592i \(-0.326193\pi\)
−0.999748 + 0.0224310i \(0.992859\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) −7.00000 −0.393781
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) −6.00000 + 10.3923i −0.336463 + 0.582772i
\(319\) 18.0000 31.1769i 1.00781 1.74557i
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) −6.00000 + 5.19615i −0.334367 + 0.289570i
\(323\) 12.0000 0.667698
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) 2.00000 + 3.46410i 0.110600 + 0.191565i
\(328\) −3.00000 −0.165647
\(329\) −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 \(-0.420033\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) −4.00000 + 6.92820i −0.219199 + 0.379663i
\(334\) 0 0
\(335\) 0 0
\(336\) 2.50000 + 0.866025i 0.136386 + 0.0472456i
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) −1.50000 2.59808i −0.0815892 0.141317i
\(339\) −1.50000 + 2.59808i −0.0814688 + 0.141108i
\(340\) 0 0
\(341\) −15.0000 25.9808i −0.812296 1.40694i
\(342\) −4.00000 −0.216295
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −9.00000 + 15.5885i −0.483145 + 0.836832i −0.999813 0.0193540i \(-0.993839\pi\)
0.516667 + 0.856186i \(0.327172\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) −3.00000 5.19615i −0.159901 0.276956i
\(353\) −7.50000 + 12.9904i −0.399185 + 0.691408i −0.993626 0.112731i \(-0.964040\pi\)
0.594441 + 0.804139i \(0.297373\pi\)
\(354\) −3.00000 + 5.19615i −0.159448 + 0.276172i
\(355\) 0 0
\(356\) 3.00000 0.159000
\(357\) 1.50000 + 7.79423i 0.0793884 + 0.412514i
\(358\) −18.0000 −0.951330
\(359\) 18.0000 + 31.1769i 0.950004 + 1.64545i 0.745409 + 0.666608i \(0.232254\pi\)
0.204595 + 0.978847i \(0.434412\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −1.00000 1.73205i −0.0525588 0.0910346i
\(363\) 25.0000 1.31216
\(364\) 8.00000 6.92820i 0.419314 0.363137i
\(365\) 0 0
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) 14.0000 24.2487i 0.730794 1.26577i −0.225750 0.974185i \(-0.572483\pi\)
0.956544 0.291587i \(-0.0941834\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) 1.50000 + 2.59808i 0.0780869 + 0.135250i
\(370\) 0 0
\(371\) −24.0000 + 20.7846i −1.24602 + 1.07908i
\(372\) 5.00000 0.259238
\(373\) −4.00000 6.92820i −0.207112 0.358729i 0.743691 0.668523i \(-0.233073\pi\)
−0.950804 + 0.309794i \(0.899740\pi\)
\(374\) 9.00000 15.5885i 0.465379 0.806060i
\(375\) 0 0
\(376\) −4.50000 7.79423i −0.232070 0.401957i
\(377\) 24.0000 1.23606
\(378\) −0.500000 2.59808i −0.0257172 0.133631i
\(379\) −10.0000 −0.513665 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) 0 0
\(381\) 8.00000 13.8564i 0.409852 0.709885i
\(382\) −7.50000 + 12.9904i −0.383733 + 0.664646i
\(383\) −10.5000 18.1865i −0.536525 0.929288i −0.999088 0.0427020i \(-0.986403\pi\)
0.462563 0.886586i \(-0.346930\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 5.00000 0.254493
\(387\) −4.00000 6.92820i −0.203331 0.352180i
\(388\) −8.50000 + 14.7224i −0.431522 + 0.747418i
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 5.50000 + 4.33013i 0.277792 + 0.218704i
\(393\) −18.0000 −0.907980
\(394\) 0 0
\(395\) 0 0
\(396\) −3.00000 + 5.19615i −0.150756 + 0.261116i
\(397\) −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i \(-0.182649\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) 5.00000 0.250627
\(399\) −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 \(0.785466\pi\)
\(402\) −4.00000 + 6.92820i −0.199502 + 0.345547i
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) −6.00000 10.3923i −0.298511 0.517036i
\(405\) 0 0
\(406\) 3.00000 + 15.5885i 0.148888 + 0.773642i
\(407\) 48.0000 2.37927
\(408\) 1.50000 + 2.59808i 0.0742611 + 0.128624i
\(409\) −14.5000 + 25.1147i −0.716979 + 1.24184i 0.245212 + 0.969469i \(0.421142\pi\)
−0.962191 + 0.272374i \(0.912191\pi\)
\(410\) 0 0
\(411\) 7.50000 + 12.9904i 0.369948 + 0.640768i
\(412\) −13.0000 −0.640464
\(413\) −12.0000 + 10.3923i −0.590481 + 0.511372i
\(414\) 3.00000 0.147442
\(415\) 0 0
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) −1.00000 + 1.73205i −0.0489702 + 0.0848189i
\(418\) 12.0000 + 20.7846i 0.586939 + 1.01661i
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −4.00000 −0.194948 −0.0974740 0.995238i \(-0.531076\pi\)
−0.0974740 + 0.995238i \(0.531076\pi\)
\(422\) −4.00000 6.92820i −0.194717 0.337260i
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) 0 0
\(426\) −9.00000 −0.436051
\(427\) −1.00000 5.19615i −0.0483934 0.251459i
\(428\) 6.00000 0.290021
\(429\) 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 \(0.997876\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 12.5000 + 4.33013i 0.600019 + 0.207853i
\(435\) 0 0
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) 6.00000 10.3923i 0.287019 0.497131i
\(438\) −7.00000 + 12.1244i −0.334473 + 0.579324i
\(439\) 6.50000 + 11.2583i 0.310228 + 0.537331i 0.978412 0.206666i \(-0.0662612\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 12.0000 0.570782
\(443\) 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i \(0.0264433\pi\)
−0.426414 + 0.904528i \(0.640223\pi\)
\(444\) −4.00000 + 6.92820i −0.189832 + 0.328798i
\(445\) 0 0
\(446\) −5.50000 9.52628i −0.260433 0.451082i
\(447\) −6.00000 −0.283790
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) −3.00000 −0.141579 −0.0707894 0.997491i \(-0.522552\pi\)
−0.0707894 + 0.997491i \(0.522552\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) −1.50000 + 2.59808i −0.0705541 + 0.122203i
\(453\) 8.00000 + 13.8564i 0.375873 + 0.651031i
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) −1.00000 1.73205i −0.0467780 0.0810219i 0.841688 0.539964i \(-0.181562\pi\)
−0.888466 + 0.458942i \(0.848229\pi\)
\(458\) 11.0000 19.0526i 0.513996 0.890268i
\(459\) 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 \(0.183524\pi\)
\(462\) −12.0000 + 10.3923i −0.558291 + 0.483494i
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 15.0000 + 25.9808i 0.694117 + 1.20225i 0.970477 + 0.241192i \(0.0775384\pi\)
−0.276360 + 0.961054i \(0.589128\pi\)
\(468\) −4.00000 −0.184900
\(469\) −16.0000 + 13.8564i −0.738811 + 0.639829i
\(470\) 0 0
\(471\) −7.00000 12.1244i −0.322543 0.558661i
\(472\) −3.00000 + 5.19615i −0.138086 + 0.239172i
\(473\) −24.0000 + 41.5692i −1.10352 + 1.91135i
\(474\) 3.50000 + 6.06218i 0.160760 + 0.278445i
\(475\) 0 0
\(476\) 1.50000 + 7.79423i 0.0687524 + 0.357248i
\(477\) 12.0000 0.549442
\(478\) −1.50000 2.59808i −0.0686084 0.118833i
\(479\) −10.5000 + 18.1865i −0.479757 + 0.830964i −0.999730 0.0232187i \(-0.992609\pi\)
0.519973 + 0.854183i \(0.325942\pi\)
\(480\) 0 0
\(481\) 16.0000 + 27.7128i 0.729537 + 1.26360i
\(482\) −22.0000 −1.00207
\(483\) 7.50000 + 2.59808i 0.341262 + 0.118217i
\(484\) 25.0000 1.13636
\(485\) 0 0
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 12.5000 21.6506i 0.566429 0.981084i −0.430486 0.902597i \(-0.641658\pi\)
0.996915 0.0784867i \(-0.0250088\pi\)
\(488\) −1.00000 1.73205i −0.0452679 0.0784063i
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 1.50000 + 2.59808i 0.0676252 + 0.117130i
\(493\) −9.00000 + 15.5885i −0.405340 + 0.702069i
\(494\) −8.00000 + 13.8564i −0.359937 + 0.623429i
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) −22.5000 7.79423i −1.00926 0.349619i
\(498\) −6.00000 −0.268866
\(499\) −19.0000 32.9090i −0.850557 1.47321i −0.880707 0.473662i \(-0.842932\pi\)
0.0301498 0.999545i \(-0.490402\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −12.0000 20.7846i −0.535586 0.927663i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) −0.500000 2.59808i −0.0222718 0.115728i
\(505\) 0 0
\(506\) −9.00000 15.5885i −0.400099 0.692991i
\(507\) −1.50000 + 2.59808i −0.0666173 + 0.115385i
\(508\) 8.00000 13.8564i 0.354943 0.614779i
\(509\) 3.00000 + 5.19615i 0.132973 + 0.230315i 0.924821 0.380402i \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 0 0
\(511\) −28.0000 + 24.2487i −1.23865 + 1.07270i
\(512\) 1.00000 0.0441942
\(513\) 2.00000 + 3.46410i 0.0883022 + 0.152944i
\(514\) 9.00000 15.5885i 0.396973 0.687577i
\(515\) 0 0
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) 54.0000 2.37492
\(518\) −16.0000 + 13.8564i −0.703000 + 0.608816i
\(519\) −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 \(0.318822\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) 17.0000 + 29.4449i 0.743358 + 1.28753i 0.950958 + 0.309320i \(0.100101\pi\)
−0.207600 + 0.978214i \(0.566565\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) −3.00000 −0.130806
\(527\) 7.50000 + 12.9904i 0.326705 + 0.565870i
\(528\) −3.00000 + 5.19615i −0.130558 + 0.226134i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) −10.0000 3.46410i −0.433555 0.150188i
\(533\) 12.0000 0.519778
\(534\) −1.50000 2.59808i −0.0649113 0.112430i
\(535\) 0 0
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) 9.00000 + 15.5885i 0.388379 + 0.672692i
\(538\) 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 \(0.627741\pi\)
\(542\) 12.5000 21.6506i 0.536921 0.929974i
\(543\) −1.00000 + 1.73205i −0.0429141 + 0.0743294i
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) 0 0
\(546\) −10.0000 3.46410i −0.427960 0.148250i
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 7.50000 + 12.9904i 0.320384 + 0.554922i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 3.00000 0.127688
\(553\) 3.50000 + 18.1865i 0.148835 + 0.773370i
\(554\) 26.0000 1.10463
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) 15.0000 25.9808i 0.635570 1.10084i −0.350824 0.936442i \(-0.614098\pi\)
0.986394 0.164399i \(-0.0525683\pi\)
\(558\) −2.50000 4.33013i −0.105833 0.183309i
\(559\) −32.0000 −1.35346
\(560\) 0 0
\(561\) −18.0000 −0.759961
\(562\) −13.5000 23.3827i −0.569463 0.986339i
\(563\) −6.00000 + 10.3923i −0.252870 + 0.437983i −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) −4.50000 + 7.79423i −0.189484 + 0.328196i
\(565\) 0 0
\(566\) −22.0000 −0.924729
\(567\) −2.00000 + 1.73205i −0.0839921 + 0.0727393i
\(568\) −9.00000 −0.377632
\(569\) 7.50000 + 12.9904i 0.314416 + 0.544585i 0.979313 0.202350i \(-0.0648579\pi\)
−0.664897 + 0.746935i \(0.731525\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 12.0000 + 20.7846i 0.501745 + 0.869048i
\(573\) 15.0000 0.626634
\(574\) 1.50000 + 7.79423i 0.0626088 + 0.325325i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −1.00000 + 1.73205i −0.0416305 + 0.0721062i −0.886090 0.463513i \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) −2.50000 4.33013i −0.103896 0.179954i
\(580\) 0 0
\(581\) −15.0000 5.19615i −0.622305 0.215573i
\(582\) 17.0000 0.704673
\(583\) −36.0000 62.3538i −1.49097 2.58243i
\(584\) −7.00000 + 12.1244i −0.289662 + 0.501709i
\(585\) 0 0
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 1.00000 6.92820i 0.0412393 0.285714i
\(589\) −20.0000 −0.824086
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 + 6.92820i −0.164399 + 0.284747i
\(593\) 16.5000 + 28.5788i 0.677574 + 1.17359i 0.975709 + 0.219069i \(0.0703019\pi\)
−0.298136 + 0.954524i \(0.596365\pi\)
\(594\) 6.00000 0.246183
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −2.50000 4.33013i −0.102318 0.177220i
\(598\) 6.00000 10.3923i 0.245358 0.424973i
\(599\) −4.50000 + 7.79423i −0.183865 + 0.318464i −0.943193 0.332244i \(-0.892194\pi\)
0.759328 + 0.650708i \(0.225528\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) −4.00000 20.7846i −0.163028 0.847117i
\(603\) 8.00000 0.325785
\(604\) 8.00000 + 13.8564i 0.325515 + 0.563809i
\(605\) 0 0
\(606\) −6.00000 + 10.3923i −0.243733 + 0.422159i
\(607\) −5.50000 9.52628i −0.223238 0.386660i 0.732551 0.680712i \(-0.238329\pi\)
−0.955789 + 0.294052i \(0.904996\pi\)
\(608\) −4.00000 −0.162221
\(609\) 12.0000 10.3923i 0.486265 0.421117i
\(610\) 0 0
\(611\) 18.0000 + 31.1769i 0.728202 + 1.26128i
\(612\) 1.50000 2.59808i 0.0606339 0.105021i
\(613\) 17.0000 29.4449i 0.686624 1.18927i −0.286300 0.958140i \(-0.592425\pi\)
0.972924 0.231127i \(-0.0742412\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 0 0
\(616\) −12.0000 + 10.3923i −0.483494 + 0.418718i
\(617\) −21.0000 −0.845428 −0.422714 0.906263i \(-0.638923\pi\)
−0.422714 + 0.906263i \(0.638923\pi\)
\(618\) 6.50000 + 11.2583i 0.261468 + 0.452876i
\(619\) 23.0000 39.8372i 0.924448 1.60119i 0.132002 0.991250i \(-0.457860\pi\)
0.792446 0.609941i \(-0.208807\pi\)
\(620\) 0 0
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) 21.0000 0.842023
\(623\) −1.50000 7.79423i −0.0600962 0.312269i
\(624\) −4.00000 −0.160128
\(625\) 0 0
\(626\) −8.50000 + 14.7224i −0.339728 + 0.588427i
\(627\) 12.0000 20.7846i 0.479234 0.830057i
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) −24.0000 −0.956943
\(630\) 0 0
\(631\) 17.0000 0.676759 0.338380 0.941010i \(-0.390121\pi\)
0.338380 + 0.941010i \(0.390121\pi\)
\(632\) 3.50000 + 6.06218i 0.139223 + 0.241140i
\(633\) −4.00000 + 6.92820i −0.158986 + 0.275371i
\(634\) −6.00000 + 10.3923i −0.238290 + 0.412731i
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) −22.0000 17.3205i −0.871672 0.686264i
\(638\) −36.0000 −1.42525
\(639\) 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 \(-0.113179\pi\)
\(642\) −3.00000 5.19615i −0.118401 0.205076i
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 7.50000 + 2.59808i 0.295541 + 0.102379i
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) −6.00000 + 10.3923i −0.235884 + 0.408564i −0.959529 0.281609i \(-0.909132\pi\)
0.723645 + 0.690172i \(0.242465\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −18.0000 31.1769i −0.706562 1.22380i
\(650\) 0 0
\(651\) −2.50000 12.9904i −0.0979827 0.509133i
\(652\) 8.00000 0.313304
\(653\) 18.0000 + 31.1769i 0.704394 + 1.22005i 0.966910 + 0.255119i \(0.0821147\pi\)
−0.262515 + 0.964928i \(0.584552\pi\)
\(654\) 2.00000 3.46410i 0.0782062 0.135457i
\(655\) 0 0
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 14.0000 0.546192
\(658\) −18.0000 + 15.5885i −0.701713 + 0.607701i
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) −13.0000 + 22.5167i −0.505259 + 0.875135i
\(663\) −6.00000 10.3923i −0.233021 0.403604i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 8.00000 0.309994
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 0 0
\(669\) −5.50000 + 9.52628i −0.212642 + 0.368307i
\(670\) 0 0
\(671\) 12.0000 0.463255
\(672\) −0.500000 2.59808i −0.0192879 0.100223i
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 6.50000 + 11.2583i 0.250371 + 0.433655i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) −9.00000 15.5885i −0.345898 0.599113i 0.639618 0.768693i \(-0.279092\pi\)
−0.985517 + 0.169580i \(0.945759\pi\)
\(678\) 3.00000 0.115214
\(679\) 42.5000 + 14.7224i 1.63100 + 0.564995i
\(680\) 0 0
\(681\) 9.00000 + 15.5885i 0.344881 + 0.597351i
\(682\) −15.0000 + 25.9808i −0.574380 + 0.994855i
\(683\) −9.00000 + 15.5885i −0.344375 + 0.596476i −0.985240 0.171178i \(-0.945243\pi\)
0.640865 + 0.767654i \(0.278576\pi\)
\(684\) 2.00000 + 3.46410i 0.0764719 + 0.132453i
\(685\) 0 0
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) −22.0000 −0.839352
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) 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 \(0.609478\pi\)
\(692\) −6.00000 −0.228086
\(693\) 15.0000 + 5.19615i 0.569803 + 0.197386i
\(694\) 18.0000 0.683271
\(695\) 0 0
\(696\) 3.00000 5.19615i 0.113715 0.196960i
\(697\) −4.50000 + 7.79423i −0.170450 + 0.295227i
\(698\) 14.0000 + 24.2487i 0.529908 + 0.917827i
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) −48.0000 −1.81293 −0.906467 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 2.00000 + 3.46410i 0.0754851 + 0.130744i
\(703\) 16.0000 27.7128i 0.603451 1.04521i
\(704\) −3.00000 + 5.19615i −0.113067 + 0.195837i
\(705\) 0 0
\(706\) 15.0000 0.564532
\(707\) −24.0000 + 20.7846i −0.902613 + 0.781686i
\(708\) 6.00000 0.225494
\(709\) 23.0000 + 39.8372i 0.863783 + 1.49612i 0.868250 + 0.496126i \(0.165245\pi\)
−0.00446726 + 0.999990i \(0.501422\pi\)
\(710\) 0 0
\(711\) 3.50000 6.06218i 0.131260 0.227349i
\(712\) −1.50000 2.59808i −0.0562149 0.0973670i
\(713\) 15.0000 0.561754
\(714\) 6.00000 5.19615i 0.224544 0.194461i
\(715\) 0 0
\(716\) 9.00000 + 15.5885i 0.336346 + 0.582568i
\(717\) −1.50000 + 2.59808i −0.0560185 + 0.0970269i
\(718\) 18.0000 31.1769i 0.671754 1.16351i
\(719\) 13.5000 + 23.3827i 0.503465 + 0.872027i 0.999992 + 0.00400572i \(0.00127506\pi\)
−0.496527 + 0.868021i \(0.665392\pi\)
\(720\) 0 0
\(721\) 6.50000 + 33.7750i 0.242073 + 1.25785i
\(722\) −3.00000 −0.111648
\(723\) 11.0000 + 19.0526i 0.409094 + 0.708572i
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) −12.5000 21.6506i −0.463919 0.803530i
\(727\) −31.0000 −1.14973 −0.574863 0.818250i \(-0.694945\pi\)
−0.574863 + 0.818250i \(0.694945\pi\)
\(728\) −10.0000 3.46410i −0.370625 0.128388i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) −1.00000 + 1.73205i −0.0369611 + 0.0640184i
\(733\) −25.0000 43.3013i −0.923396 1.59937i −0.794121 0.607760i \(-0.792068\pi\)
−0.129275 0.991609i \(-0.541265\pi\)
\(734\) −28.0000 −1.03350
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −24.0000 41.5692i −0.884051 1.53122i
\(738\) 1.50000 2.59808i 0.0552158 0.0956365i
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 30.0000 + 10.3923i 1.10133 + 0.381514i
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) −2.50000 4.33013i −0.0916544 0.158750i
\(745\) 0 0
\(746\) −4.00000 + 6.92820i −0.146450 + 0.253660i
\(747\) 3.00000 + 5.19615i 0.109764 + 0.190117i
\(748\) −18.0000 −0.658145
\(749\) −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 \(0.739038\pi\)
\(752\) −4.50000 + 7.79423i −0.164098 + 0.284226i
\(753\) −12.0000 + 20.7846i −0.437304 + 0.757433i
\(754\) −12.0000 20.7846i −0.437014 0.756931i
\(755\) 0 0
\(756\) −2.00000 + 1.73205i −0.0727393 + 0.0629941i
\(757\) −4.00000 −0.145382 −0.0726912 0.997354i \(-0.523159\pi\)
−0.0726912 + 0.997354i \(0.523159\pi\)
\(758\) 5.00000 + 8.66025i 0.181608 + 0.314555i
\(759\) −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 \(0.885491\pi\)
\(762\) −16.0000 −0.579619
\(763\) 8.00000 6.92820i 0.289619 0.250818i
\(764\) 15.0000 0.542681
\(765\) 0 0
\(766\) −10.5000 + 18.1865i −0.379380 + 0.657106i
\(767\) 12.0000 20.7846i 0.433295 0.750489i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) −2.50000 4.33013i −0.0899770 0.155845i
\(773\) 6.00000 10.3923i 0.215805 0.373785i −0.737716 0.675111i \(-0.764096\pi\)
0.953521 + 0.301326i \(0.0974291\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) 0 0
\(776\) 17.0000 0.610264
\(777\) 20.0000 + 6.92820i 0.717496 + 0.248548i
\(778\) 0 0
\(779\) −6.00000 10.3923i −0.214972 0.372343i
\(780\) 0 0
\(781\) 27.0000 46.7654i 0.966136 1.67340i
\(782\) 4.50000 + 7.79423i 0.160920 + 0.278721i
\(783\) −6.00000 −0.214423
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 0 0