Properties

Label 21.2.e.a.16.1
Level $21$
Weight $2$
Character 21.16
Analytic conductor $0.168$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 21.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.167685844245\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 21.16
Dual form 21.2.e.a.4.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.00000 - 1.73205i) q^{5} +2.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.00000 - 1.73205i) q^{5} +2.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-1.00000 + 1.73205i) q^{12} +1.00000 q^{13} +(1.00000 - 5.19615i) q^{14} -2.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} -4.00000 q^{20} +(2.00000 + 1.73205i) q^{21} -4.00000 q^{22} +(0.500000 + 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(4.00000 + 3.46410i) q^{28} +4.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(-4.50000 - 7.79423i) q^{31} +(4.00000 + 6.92820i) q^{32} +(1.00000 - 1.73205i) q^{33} +(-1.00000 + 5.19615i) q^{35} +2.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} -10.0000 q^{41} +(-5.00000 + 1.73205i) q^{42} +5.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{45} +(3.00000 - 5.19615i) q^{47} -4.00000 q^{48} +(5.50000 - 4.33013i) q^{49} -2.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(-6.00000 - 10.3923i) q^{53} +(-1.00000 + 1.73205i) q^{54} +4.00000 q^{55} +1.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(6.00000 + 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{60} +(-5.00000 + 8.66025i) q^{61} +18.0000 q^{62} +(0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{66} +(2.50000 + 4.33013i) q^{67} +(-8.00000 - 6.92820i) q^{70} -6.00000 q^{71} +(1.50000 + 2.59808i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(0.500000 - 0.866025i) q^{75} +2.00000 q^{76} +(-4.00000 - 3.46410i) q^{77} +2.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-4.00000 - 6.92820i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(10.0000 - 17.3205i) q^{82} +6.00000 q^{83} +(1.00000 - 5.19615i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(-2.00000 - 3.46410i) q^{87} +(-8.00000 + 13.8564i) q^{89} -4.00000 q^{90} +(-2.50000 + 0.866025i) q^{91} +(-4.50000 + 7.79423i) q^{93} +(6.00000 + 10.3923i) q^{94} +(1.00000 + 1.73205i) q^{95} +(4.00000 - 6.92820i) q^{96} -6.00000 q^{97} +(2.00000 + 13.8564i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - q^{3} - 2q^{4} + 2q^{5} + 4q^{6} - 5q^{7} - q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - q^{3} - 2q^{4} + 2q^{5} + 4q^{6} - 5q^{7} - q^{9} + 4q^{10} + 2q^{11} - 2q^{12} + 2q^{13} + 2q^{14} - 4q^{15} + 4q^{16} - 2q^{18} - q^{19} - 8q^{20} + 4q^{21} - 8q^{22} + q^{25} - 2q^{26} + 2q^{27} + 8q^{28} + 8q^{29} + 4q^{30} - 9q^{31} + 8q^{32} + 2q^{33} - 2q^{35} + 4q^{36} - 3q^{37} - 2q^{38} - q^{39} - 20q^{41} - 10q^{42} + 10q^{43} + 4q^{44} + 2q^{45} + 6q^{47} - 8q^{48} + 11q^{49} - 4q^{50} - 2q^{52} - 12q^{53} - 2q^{54} + 8q^{55} + 2q^{57} - 8q^{58} + 12q^{59} + 4q^{60} - 10q^{61} + 36q^{62} + q^{63} - 16q^{64} + 2q^{65} + 4q^{66} + 5q^{67} - 16q^{70} - 12q^{71} + 3q^{73} - 6q^{74} + q^{75} + 4q^{76} - 8q^{77} + 4q^{78} + q^{79} - 8q^{80} - q^{81} + 20q^{82} + 12q^{83} + 2q^{84} - 10q^{86} - 4q^{87} - 16q^{89} - 8q^{90} - 5q^{91} - 9q^{93} + 12q^{94} + 2q^{95} + 8q^{96} - 12q^{97} + 4q^{98} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 2.00000 0.816497
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 2.00000 + 3.46410i 0.632456 + 1.09545i
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) −1.00000 + 1.73205i −0.288675 + 0.500000i
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 1.00000 5.19615i 0.267261 1.38873i
\(15\) −2.00000 −0.516398
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) −4.00000 −0.894427
\(21\) 2.00000 + 1.73205i 0.436436 + 0.377964i
\(22\) −4.00000 −0.852803
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 1.00000 0.192450
\(28\) 4.00000 + 3.46410i 0.755929 + 0.654654i
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 2.00000 3.46410i 0.365148 0.632456i
\(31\) −4.50000 7.79423i −0.808224 1.39988i −0.914093 0.405505i \(-0.867096\pi\)
0.105869 0.994380i \(-0.466238\pi\)
\(32\) 4.00000 + 6.92820i 0.707107 + 1.22474i
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) 0 0
\(35\) −1.00000 + 5.19615i −0.169031 + 0.878310i
\(36\) 2.00000 0.333333
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) −5.00000 + 1.73205i −0.771517 + 0.267261i
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 2.00000 3.46410i 0.301511 0.522233i
\(45\) 1.00000 + 1.73205i 0.149071 + 0.258199i
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) −4.00000 −0.577350
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −2.00000 −0.282843
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i \(-0.858312\pi\)
0.0783936 0.996922i \(-0.475021\pi\)
\(54\) −1.00000 + 1.73205i −0.136083 + 0.235702i
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) −4.00000 + 6.92820i −0.525226 + 0.909718i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 2.00000 + 3.46410i 0.258199 + 0.447214i
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 18.0000 2.28600
\(63\) 0.500000 2.59808i 0.0629941 0.327327i
\(64\) −8.00000 −1.00000
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 2.00000 + 3.46410i 0.246183 + 0.426401i
\(67\) 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i \(-0.0678686\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −8.00000 6.92820i −0.956183 0.828079i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) −3.00000 5.19615i −0.348743 0.604040i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 2.00000 0.229416
\(77\) −4.00000 3.46410i −0.455842 0.394771i
\(78\) 2.00000 0.226455
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) −4.00000 6.92820i −0.447214 0.774597i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 10.0000 17.3205i 1.10432 1.91273i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 1.00000 5.19615i 0.109109 0.566947i
\(85\) 0 0
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) −2.00000 3.46410i −0.214423 0.371391i
\(88\) 0 0
\(89\) −8.00000 + 13.8564i −0.847998 + 1.46878i 0.0349934 + 0.999388i \(0.488859\pi\)
−0.882992 + 0.469389i \(0.844474\pi\)
\(90\) −4.00000 −0.421637
\(91\) −2.50000 + 0.866025i −0.262071 + 0.0907841i
\(92\) 0 0
\(93\) −4.50000 + 7.79423i −0.466628 + 0.808224i
\(94\) 6.00000 + 10.3923i 0.618853 + 1.07188i
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) 4.00000 6.92820i 0.408248 0.707107i
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 2.00000 + 13.8564i 0.202031 + 1.39971i
\(99\) −2.00000 −0.201008
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) 3.50000 6.06218i 0.344865 0.597324i −0.640464 0.767988i \(-0.721258\pi\)
0.985329 + 0.170664i \(0.0545913\pi\)
\(104\) 0 0
\(105\) 5.00000 1.73205i 0.487950 0.169031i
\(106\) 24.0000 2.33109
\(107\) 4.00000 6.92820i 0.386695 0.669775i −0.605308 0.795991i \(-0.706950\pi\)
0.992003 + 0.126217i \(0.0402834\pi\)
\(108\) −1.00000 1.73205i −0.0962250 0.166667i
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) −4.00000 + 6.92820i −0.381385 + 0.660578i
\(111\) 3.00000 0.284747
\(112\) −2.00000 + 10.3923i −0.188982 + 0.981981i
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) −1.00000 + 1.73205i −0.0936586 + 0.162221i
\(115\) 0 0
\(116\) −4.00000 6.92820i −0.371391 0.643268i
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) −24.0000 −2.20938
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −10.0000 17.3205i −0.905357 1.56813i
\(123\) 5.00000 + 8.66025i 0.450835 + 0.780869i
\(124\) −9.00000 + 15.5885i −0.808224 + 1.39988i
\(125\) 12.0000 1.07331
\(126\) 4.00000 + 3.46410i 0.356348 + 0.308607i
\(127\) −15.0000 −1.33103 −0.665517 0.746382i \(-0.731789\pi\)
−0.665517 + 0.746382i \(0.731789\pi\)
\(128\) 0 0
\(129\) −2.50000 4.33013i −0.220113 0.381246i
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) 7.00000 12.1244i 0.611593 1.05931i −0.379379 0.925241i \(-0.623862\pi\)
0.990972 0.134069i \(-0.0428042\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0.500000 2.59808i 0.0433555 0.225282i
\(134\) −10.0000 −0.863868
\(135\) 1.00000 1.73205i 0.0860663 0.149071i
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) −3.00000 −0.254457 −0.127228 0.991873i \(-0.540608\pi\)
−0.127228 + 0.991873i \(0.540608\pi\)
\(140\) 10.0000 3.46410i 0.845154 0.292770i
\(141\) −6.00000 −0.505291
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) 2.00000 + 3.46410i 0.166667 + 0.288675i
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) −6.00000 −0.496564
\(147\) −6.50000 2.59808i −0.536111 0.214286i
\(148\) 6.00000 0.493197
\(149\) 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i \(-0.669768\pi\)
0.999953 + 0.00974235i \(0.00310113\pi\)
\(150\) 1.00000 + 1.73205i 0.0816497 + 0.141421i
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 10.0000 3.46410i 0.805823 0.279145i
\(155\) −18.0000 −1.44579
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i \(0.0220180\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) 1.00000 + 1.73205i 0.0795557 + 0.137795i
\(159\) −6.00000 + 10.3923i −0.475831 + 0.824163i
\(160\) 16.0000 1.26491
\(161\) 0 0
\(162\) 2.00000 0.157135
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 10.0000 + 17.3205i 0.780869 + 1.35250i
\(165\) −2.00000 3.46410i −0.155700 0.269680i
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) −14.0000 −1.08335 −0.541676 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) −5.00000 8.66025i −0.381246 0.660338i
\(173\) −4.00000 + 6.92820i −0.304114 + 0.526742i −0.977064 0.212947i \(-0.931694\pi\)
0.672949 + 0.739689i \(0.265027\pi\)
\(174\) 8.00000 0.606478
\(175\) −2.00000 1.73205i −0.151186 0.130931i
\(176\) 8.00000 0.603023
\(177\) 6.00000 10.3923i 0.450988 0.781133i
\(178\) −16.0000 27.7128i −1.19925 2.07716i
\(179\) −1.00000 1.73205i −0.0747435 0.129460i 0.826231 0.563331i \(-0.190480\pi\)
−0.900975 + 0.433872i \(0.857147\pi\)
\(180\) 2.00000 3.46410i 0.149071 0.258199i
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) 1.00000 5.19615i 0.0741249 0.385164i
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) −9.00000 15.5885i −0.659912 1.14300i
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) −2.50000 + 0.866025i −0.181848 + 0.0629941i
\(190\) −4.00000 −0.290191
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) 4.00000 + 6.92820i 0.288675 + 0.500000i
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) 6.00000 10.3923i 0.430775 0.746124i
\(195\) −2.00000 −0.143223
\(196\) −13.0000 5.19615i −0.928571 0.371154i
\(197\) 16.0000 1.13995 0.569976 0.821661i \(-0.306952\pi\)
0.569976 + 0.821661i \(0.306952\pi\)
\(198\) 2.00000 3.46410i 0.142134 0.246183i
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) 2.50000 4.33013i 0.176336 0.305424i
\(202\) 4.00000 0.281439
\(203\) −10.0000 + 3.46410i −0.701862 + 0.243132i
\(204\) 0 0
\(205\) −10.0000 + 17.3205i −0.698430 + 1.20972i
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 0 0
\(208\) 2.00000 3.46410i 0.138675 0.240192i
\(209\) −2.00000 −0.138343
\(210\) −2.00000 + 10.3923i −0.138013 + 0.717137i
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −12.0000 + 20.7846i −0.824163 + 1.42749i
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) 8.00000 + 13.8564i 0.546869 + 0.947204i
\(215\) 5.00000 8.66025i 0.340997 0.590624i
\(216\) 0 0
\(217\) 18.0000 + 15.5885i 1.22192 + 1.05821i
\(218\) 18.0000 1.21911
\(219\) 1.50000 2.59808i 0.101361 0.175562i
\(220\) −4.00000 6.92820i −0.269680 0.467099i
\(221\) 0 0
\(222\) −3.00000 + 5.19615i −0.201347 + 0.348743i
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) −16.0000 13.8564i −1.06904 0.925820i
\(225\) −1.00000 −0.0666667
\(226\) −10.0000 + 17.3205i −0.665190 + 1.15214i
\(227\) −9.00000 15.5885i −0.597351 1.03464i −0.993210 0.116331i \(-0.962887\pi\)
0.395860 0.918311i \(-0.370447\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) 9.50000 16.4545i 0.627778 1.08734i −0.360219 0.932868i \(-0.617298\pi\)
0.987997 0.154475i \(-0.0493686\pi\)
\(230\) 0 0
\(231\) −1.00000 + 5.19615i −0.0657952 + 0.341882i
\(232\) 0 0
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) −1.00000 1.73205i −0.0653720 0.113228i
\(235\) −6.00000 10.3923i −0.391397 0.677919i
\(236\) 12.0000 20.7846i 0.781133 1.35296i
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −4.00000 + 6.92820i −0.258199 + 0.447214i
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 7.00000 + 12.1244i 0.449977 + 0.779383i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 20.0000 1.28037
\(245\) −2.00000 13.8564i −0.127775 0.885253i
\(246\) −20.0000 −1.27515
\(247\) −0.500000 + 0.866025i −0.0318142 + 0.0551039i
\(248\) 0 0
\(249\) −3.00000 5.19615i −0.190117 0.329293i
\(250\) −12.0000 + 20.7846i −0.758947 + 1.31453i
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) −5.00000 + 1.73205i −0.314970 + 0.109109i
\(253\) 0 0
\(254\) 15.0000 25.9808i 0.941184 1.63018i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −13.0000 + 22.5167i −0.810918 + 1.40455i 0.101305 + 0.994855i \(0.467698\pi\)
−0.912222 + 0.409695i \(0.865635\pi\)
\(258\) 10.0000 0.622573
\(259\) 1.50000 7.79423i 0.0932055 0.484310i
\(260\) −4.00000 −0.248069
\(261\) −2.00000 + 3.46410i −0.123797 + 0.214423i
\(262\) 14.0000 + 24.2487i 0.864923 + 1.49809i
\(263\) −2.00000 3.46410i −0.123325 0.213606i 0.797752 0.602986i \(-0.206023\pi\)
−0.921077 + 0.389380i \(0.872689\pi\)
\(264\) 0 0
\(265\) −24.0000 −1.47431
\(266\) 4.00000 + 3.46410i 0.245256 + 0.212398i
\(267\) 16.0000 0.979184
\(268\) 5.00000 8.66025i 0.305424 0.529009i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 2.00000 + 3.46410i 0.121716 + 0.210819i
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 0 0
\(273\) 2.00000 + 1.73205i 0.121046 + 0.104828i
\(274\) −24.0000 −1.44989
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 0 0
\(277\) −6.50000 11.2583i −0.390547 0.676448i 0.601975 0.798515i \(-0.294381\pi\)
−0.992522 + 0.122068i \(0.961047\pi\)
\(278\) 3.00000 5.19615i 0.179928 0.311645i
\(279\) 9.00000 0.538816
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 6.00000 10.3923i 0.357295 0.618853i
\(283\) 5.50000 + 9.52628i 0.326941 + 0.566279i 0.981903 0.189383i \(-0.0606488\pi\)
−0.654962 + 0.755662i \(0.727315\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 1.00000 1.73205i 0.0592349 0.102598i
\(286\) −4.00000 −0.236525
\(287\) 25.0000 8.66025i 1.47570 0.511199i
\(288\) −8.00000 −0.471405
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 8.00000 + 13.8564i 0.469776 + 0.813676i
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) 3.00000 5.19615i 0.175562 0.304082i
\(293\) 8.00000 0.467365 0.233682 0.972313i \(-0.424922\pi\)
0.233682 + 0.972313i \(0.424922\pi\)
\(294\) 11.0000 8.66025i 0.641533 0.505076i
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) 12.0000 + 20.7846i 0.695141 + 1.20402i
\(299\) 0 0
\(300\) −2.00000 −0.115470
\(301\) −12.5000 + 4.33013i −0.720488 + 0.249584i
\(302\) −32.0000 −1.84139
\(303\) −1.00000 + 1.73205i −0.0574485 + 0.0995037i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 10.0000 + 17.3205i 0.572598 + 0.991769i
\(306\) 0 0
\(307\) −17.0000 −0.970241 −0.485121 0.874447i \(-0.661224\pi\)
−0.485121 + 0.874447i \(0.661224\pi\)
\(308\) −2.00000 + 10.3923i −0.113961 + 0.592157i
\(309\) −7.00000 −0.398216
\(310\) 18.0000 31.1769i 1.02233 1.77073i
\(311\) 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) −28.0000 −1.58013
\(315\) −4.00000 3.46410i −0.225374 0.195180i
\(316\) −2.00000 −0.112509
\(317\) −12.0000 + 20.7846i −0.673987 + 1.16738i 0.302777 + 0.953062i \(0.402086\pi\)
−0.976764 + 0.214318i \(0.931247\pi\)
\(318\) −12.0000 20.7846i −0.672927 1.16554i
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) −8.00000 + 13.8564i −0.447214 + 0.774597i
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 + 1.73205i −0.0555556 + 0.0962250i
\(325\) 0.500000 + 0.866025i 0.0277350 + 0.0480384i
\(326\) −4.00000 6.92820i −0.221540 0.383718i
\(327\) −4.50000 + 7.79423i −0.248851 + 0.431022i
\(328\) 0 0
\(329\) −3.00000 + 15.5885i −0.165395 + 0.859419i
\(330\) 8.00000 0.440386
\(331\) 12.5000 21.6506i 0.687062 1.19003i −0.285722 0.958313i \(-0.592233\pi\)
0.972784 0.231714i \(-0.0744333\pi\)
\(332\) −6.00000 10.3923i −0.329293 0.570352i
\(333\) −1.50000 2.59808i −0.0821995 0.142374i
\(334\) 14.0000 24.2487i 0.766046 1.32683i
\(335\) 10.0000 0.546358
\(336\) 10.0000 3.46410i 0.545545 0.188982i
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) 12.0000 20.7846i 0.652714 1.13053i
\(339\) −5.00000 8.66025i −0.271563 0.470360i
\(340\) 0 0
\(341\) 9.00000 15.5885i 0.487377 0.844162i
\(342\) 2.00000 0.108148
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) −8.00000 13.8564i −0.430083 0.744925i
\(347\) −16.0000 27.7128i −0.858925 1.48770i −0.872955 0.487800i \(-0.837799\pi\)
0.0140303 0.999902i \(-0.495534\pi\)
\(348\) −4.00000 + 6.92820i −0.214423 + 0.371391i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 5.00000 1.73205i 0.267261 0.0925820i
\(351\) 1.00000 0.0533761
\(352\) −8.00000 + 13.8564i −0.426401 + 0.738549i
\(353\) −17.0000 29.4449i −0.904819 1.56719i −0.821160 0.570697i \(-0.806673\pi\)
−0.0836583 0.996495i \(-0.526660\pi\)
\(354\) 12.0000 + 20.7846i 0.637793 + 1.10469i
\(355\) −6.00000 + 10.3923i −0.318447 + 0.551566i
\(356\) 32.0000 1.69600
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −13.0000 + 22.5167i −0.683265 + 1.18345i
\(363\) −7.00000 −0.367405
\(364\) 4.00000 + 3.46410i 0.209657 + 0.181568i
\(365\) 6.00000 0.314054
\(366\) −10.0000 + 17.3205i −0.522708 + 0.905357i
\(367\) 4.50000 + 7.79423i 0.234898 + 0.406855i 0.959243 0.282582i \(-0.0911910\pi\)
−0.724345 + 0.689438i \(0.757858\pi\)
\(368\) 0 0
\(369\) 5.00000 8.66025i 0.260290 0.450835i
\(370\) −12.0000 −0.623850
\(371\) 24.0000 + 20.7846i 1.24602 + 1.07908i
\(372\) 18.0000 0.933257
\(373\) −11.5000 + 19.9186i −0.595447 + 1.03135i 0.398036 + 0.917370i \(0.369692\pi\)
−0.993484 + 0.113975i \(0.963641\pi\)
\(374\) 0 0
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 1.00000 5.19615i 0.0514344 0.267261i
\(379\) 3.00000 0.154100 0.0770498 0.997027i \(-0.475450\pi\)
0.0770498 + 0.997027i \(0.475450\pi\)
\(380\) 2.00000 3.46410i 0.102598 0.177705i
\(381\) 7.50000 + 12.9904i 0.384237 + 0.665517i
\(382\) −10.0000 17.3205i −0.511645 0.886194i
\(383\) 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210411i \(0.0674801\pi\)
\(384\) 0 0
\(385\) −10.0000 + 3.46410i −0.509647 + 0.176547i
\(386\) 22.0000 1.11977
\(387\) −2.50000 + 4.33013i −0.127082 + 0.220113i
\(388\) 6.00000 + 10.3923i 0.304604 + 0.527589i
\(389\) 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 2.00000 3.46410i 0.101274 0.175412i
\(391\) 0 0
\(392\) 0 0
\(393\) −14.0000 −0.706207
\(394\) −16.0000 + 27.7128i −0.806068 + 1.39615i
\(395\) −1.00000 1.73205i −0.0503155 0.0871489i
\(396\) 2.00000 + 3.46410i 0.100504 + 0.174078i
\(397\) 4.50000 7.79423i 0.225849 0.391181i −0.730725 0.682672i \(-0.760818\pi\)
0.956574 + 0.291491i \(0.0941512\pi\)
\(398\) 0 0
\(399\) −2.50000 + 0.866025i −0.125157 + 0.0433555i
\(400\) 4.00000 0.200000
\(401\) 18.0000 31.1769i 0.898877 1.55690i 0.0699455 0.997551i \(-0.477717\pi\)
0.828932 0.559350i \(-0.188949\pi\)
\(402\) 5.00000 + 8.66025i 0.249377 + 0.431934i
\(403\) −4.50000 7.79423i −0.224161 0.388258i
\(404\) −2.00000 + 3.46410i −0.0995037 + 0.172345i
\(405\) −2.00000 −0.0993808
\(406\) 4.00000 20.7846i 0.198517 1.03152i
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) −20.0000 34.6410i −0.987730 1.71080i
\(411\) 6.00000 10.3923i 0.295958 0.512615i
\(412\) −14.0000 −0.689730
\(413\) −24.0000 20.7846i −1.18096 1.02274i
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 4.00000 + 6.92820i 0.196116 + 0.339683i
\(417\) 1.50000 + 2.59808i 0.0734553 + 0.127228i
\(418\) 2.00000 3.46410i 0.0978232 0.169435i
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) −8.00000 6.92820i −0.390360 0.338062i
\(421\) −7.00000 −0.341159 −0.170580 0.985344i \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(422\) −4.00000 + 6.92820i −0.194717 + 0.337260i
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 5.00000 25.9808i 0.241967 1.25730i
\(428\) −16.0000 −0.773389
\(429\) 1.00000 1.73205i 0.0482805 0.0836242i
\(430\) 10.0000 + 17.3205i 0.482243 + 0.835269i
\(431\) 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) 2.00000 3.46410i 0.0962250 0.166667i
\(433\) 31.0000 1.48976 0.744882 0.667196i \(-0.232506\pi\)
0.744882 + 0.667196i \(0.232506\pi\)
\(434\) −45.0000 + 15.5885i −2.16007 + 0.748270i
\(435\) −8.00000 −0.383571
\(436\) −9.00000 + 15.5885i −0.431022 + 0.746552i
\(437\) 0 0
\(438\) 3.00000 + 5.19615i 0.143346 + 0.248282i
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) −3.00000 5.19615i −0.142374 0.246598i
\(445\) 16.0000 + 27.7128i 0.758473 + 1.31371i
\(446\) −16.0000 + 27.7128i −0.757622 + 1.31224i
\(447\) −12.0000 −0.567581
\(448\) 20.0000 6.92820i 0.944911 0.327327i
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 1.00000 1.73205i 0.0471405 0.0816497i
\(451\) −10.0000 17.3205i −0.470882 0.815591i
\(452\) −10.0000 17.3205i −0.470360 0.814688i
\(453\) 8.00000 13.8564i 0.375873 0.651031i
\(454\) 36.0000 1.68956
\(455\) −1.00000 + 5.19615i −0.0468807 + 0.243599i
\(456\) 0 0
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 19.0000 + 32.9090i 0.887812 + 1.53773i
\(459\) 0 0
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) −8.00000 6.92820i −0.372194 0.322329i
\(463\) −17.0000 −0.790057 −0.395029 0.918669i \(-0.629265\pi\)
−0.395029 + 0.918669i \(0.629265\pi\)
\(464\) 8.00000 13.8564i 0.371391 0.643268i
\(465\) 9.00000 + 15.5885i 0.417365 + 0.722897i
\(466\) −6.00000 10.3923i −0.277945 0.481414i
\(467\) −3.00000 + 5.19615i −0.138823 + 0.240449i −0.927052 0.374934i \(-0.877665\pi\)
0.788228 + 0.615383i \(0.210999\pi\)
\(468\) 2.00000 0.0924500
\(469\) −10.0000 8.66025i −0.461757 0.399893i
\(470\) 24.0000 1.10704
\(471\) 7.00000 12.1244i 0.322543 0.558661i
\(472\) 0 0
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) 1.00000 1.73205i 0.0459315 0.0795557i
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) 14.0000 + 24.2487i 0.639676 + 1.10795i 0.985504 + 0.169654i \(0.0542649\pi\)
−0.345827 + 0.938298i \(0.612402\pi\)
\(480\) −8.00000 13.8564i −0.365148 0.632456i
\(481\) −1.50000 + 2.59808i −0.0683941 + 0.118462i
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) −6.00000 + 10.3923i −0.272446 + 0.471890i
\(486\) −1.00000 1.73205i −0.0453609 0.0785674i
\(487\) −15.5000 26.8468i −0.702372 1.21654i −0.967632 0.252367i \(-0.918791\pi\)
0.265260 0.964177i \(-0.414542\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 26.0000 + 10.3923i 1.17456 + 0.469476i
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 10.0000 17.3205i 0.450835 0.780869i
\(493\) 0 0
\(494\) −1.00000 1.73205i −0.0449921 0.0779287i
\(495\) −2.00000 + 3.46410i −0.0898933 + 0.155700i
\(496\) −36.0000 −1.61645
\(497\) 15.0000 5.19615i 0.672842 0.233079i
\(498\) 12.0000 0.537733
\(499\) −18.5000 + 32.0429i −0.828174 + 1.43444i 0.0712957 + 0.997455i \(0.477287\pi\)
−0.899469 + 0.436984i \(0.856047\pi\)
\(500\) −12.0000 20.7846i −0.536656 0.929516i
\(501\) 7.00000 + 12.1244i 0.312737 + 0.541676i
\(502\) 8.00000 13.8564i 0.357057 0.618442i
\(503\) −42.0000 −1.87269 −0.936344 0.351085i \(-0.885813\pi\)
−0.936344 + 0.351085i \(0.885813\pi\)
\(504\) 0 0
\(505\) −4.00000 −0.177998
\(506\) 0 0
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 15.0000 + 25.9808i 0.665517 + 1.15271i
\(509\) −1.00000 + 1.73205i −0.0443242 + 0.0767718i −0.887336 0.461123i \(-0.847447\pi\)
0.843012 + 0.537895i \(0.180780\pi\)
\(510\) 0 0
\(511\) −6.00000 5.19615i −0.265424 0.229864i
\(512\) 32.0000 1.41421
\(513\) −0.500000 + 0.866025i −0.0220755 + 0.0382360i
\(514\) −26.0000 45.0333i −1.14681 1.98633i
\(515\) −7.00000 12.1244i −0.308457 0.534263i
\(516\) −5.00000 + 8.66025i −0.220113 + 0.381246i
\(517\) 12.0000 0.527759
\(518\) 12.0000 + 10.3923i 0.527250 + 0.456612i
\(519\) 8.00000 0.351161
\(520\) 0 0
\(521\) −6.00000 10.3923i −0.262865 0.455295i 0.704137 0.710064i \(-0.251334\pi\)
−0.967002 + 0.254769i \(0.918001\pi\)
\(522\) −4.00000 6.92820i −0.175075 0.303239i
\(523\) −15.5000 + 26.8468i −0.677768 + 1.17393i 0.297884 + 0.954602i \(0.403719\pi\)
−0.975652 + 0.219326i \(0.929614\pi\)
\(524\) −28.0000 −1.22319
\(525\) −0.500000 + 2.59808i −0.0218218 + 0.113389i
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) −4.00000 6.92820i −0.174078 0.301511i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 24.0000 41.5692i 1.04249 1.80565i
\(531\) −12.0000 −0.520756
\(532\) −5.00000 + 1.73205i −0.216777 + 0.0750939i
\(533\) −10.0000 −0.433148
\(534\) −16.0000 + 27.7128i −0.692388 + 1.19925i
\(535\) −8.00000 13.8564i −0.345870 0.599065i
\(536\) 0 0
\(537\) −1.00000 + 1.73205i −0.0431532 + 0.0747435i
\(538\) 12.0000 0.517357
\(539\) 13.0000 + 5.19615i 0.559950 + 0.223814i
\(540\) −4.00000 −0.172133
\(541\) 9.50000 16.4545i 0.408437 0.707433i −0.586278 0.810110i \(-0.699407\pi\)
0.994715 + 0.102677i \(0.0327407\pi\)
\(542\) −16.0000 27.7128i −0.687259 1.19037i
\(543\) −6.50000 11.2583i −0.278942 0.483141i
\(544\) 0 0
\(545\) −18.0000 −0.771035
\(546\) −5.00000 + 1.73205i −0.213980 + 0.0741249i
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 12.0000 20.7846i 0.512615 0.887875i
\(549\) −5.00000 8.66025i −0.213395 0.369611i
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) −2.00000 + 3.46410i −0.0852029 + 0.147576i
\(552\) 0 0
\(553\) −0.500000 + 2.59808i −0.0212622 + 0.110481i
\(554\) 26.0000 1.10463
\(555\) 3.00000 5.19615i 0.127343 0.220564i
\(556\) 3.00000 + 5.19615i 0.127228 + 0.220366i
\(557\) 1.00000 + 1.73205i 0.0423714 + 0.0733893i 0.886433 0.462856i \(-0.153175\pi\)
−0.844062 + 0.536246i \(0.819842\pi\)
\(558\) −9.00000 + 15.5885i −0.381000 + 0.659912i
\(559\) 5.00000 0.211477
\(560\) 16.0000 + 13.8564i 0.676123 + 0.585540i
\(561\) 0 0
\(562\) 4.00000 6.92820i 0.168730 0.292249i
\(563\) 13.0000 + 22.5167i 0.547885 + 0.948964i 0.998419 + 0.0562051i \(0.0179001\pi\)
−0.450535 + 0.892759i \(0.648767\pi\)
\(564\) 6.00000 + 10.3923i 0.252646 + 0.437595i
\(565\) 10.0000 17.3205i 0.420703 0.728679i
\(566\) −22.0000 −0.924729
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) 13.0000 22.5167i 0.544988 0.943948i −0.453619 0.891196i \(-0.649867\pi\)
0.998608 0.0527519i \(-0.0167993\pi\)
\(570\) 2.00000 + 3.46410i 0.0837708 + 0.145095i
\(571\) 9.50000 + 16.4545i 0.397563 + 0.688599i 0.993425 0.114488i \(-0.0365228\pi\)
−0.595862 + 0.803087i \(0.703189\pi\)
\(572\) 2.00000 3.46410i 0.0836242 0.144841i
\(573\) 10.0000 0.417756
\(574\) −10.0000 + 51.9615i −0.417392 + 2.16883i
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) 8.50000 + 14.7224i 0.353860 + 0.612903i 0.986922 0.161198i \(-0.0515357\pi\)
−0.633062 + 0.774101i \(0.718202\pi\)
\(578\) 17.0000 + 29.4449i 0.707107 + 1.22474i
\(579\) −5.50000 + 9.52628i −0.228572 + 0.395899i
\(580\) −16.0000 −0.664364
\(581\) −15.0000 + 5.19615i −0.622305 + 0.215573i
\(582\) −12.0000 −0.497416
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) 0 0
\(585\) 1.00000 + 1.73205i 0.0413449 + 0.0716115i
\(586\) −8.00000 + 13.8564i −0.330477 + 0.572403i
\(587\) 16.0000 0.660391 0.330195 0.943913i \(-0.392885\pi\)
0.330195 + 0.943913i \(0.392885\pi\)
\(588\) 2.00000 + 13.8564i 0.0824786 + 0.571429i
\(589\) 9.00000 0.370839
\(590\) −24.0000 + 41.5692i −0.988064 + 1.71138i
\(591\) −8.00000 13.8564i −0.329076 0.569976i
\(592\) 6.00000 + 10.3923i 0.246598 + 0.427121i
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −24.0000 −0.983078
\(597\) 0 0
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) −9.00000 −0.367118 −0.183559 0.983009i \(-0.558762\pi\)
−0.183559 + 0.983009i \(0.558762\pi\)
\(602\) 5.00000 25.9808i 0.203785 1.05890i
\(603\) −5.00000 −0.203616
\(604\) 16.0000 27.7128i 0.651031 1.12762i
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) −2.00000 3.46410i −0.0812444 0.140720i
\(607\) −11.5000 + 19.9186i −0.466771 + 0.808470i −0.999279 0.0379540i \(-0.987916\pi\)
0.532509 + 0.846424i \(0.321249\pi\)
\(608\) −8.00000 −0.324443
\(609\) 8.00000 + 6.92820i 0.324176 + 0.280745i
\(610\) −40.0000 −1.61955
\(611\) 3.00000 5.19615i 0.121367 0.210214i
\(612\) 0 0
\(613\) −17.0000 29.4449i −0.686624 1.18927i −0.972924 0.231127i \(-0.925759\pi\)
0.286300 0.958140i \(-0.407575\pi\)
\(614\) 17.0000 29.4449i 0.686064 1.18830i
\(615\) 20.0000 0.806478
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 7.00000 12.1244i 0.281581 0.487713i
\(619\) 14.5000 + 25.1147i 0.582804 + 1.00945i 0.995145 + 0.0984169i \(0.0313779\pi\)
−0.412341 + 0.911030i \(0.635289\pi\)
\(620\) 18.0000 + 31.1769i 0.722897 + 1.25210i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 8.00000 41.5692i 0.320513 1.66544i
\(624\) −4.00000 −0.160128
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 1.00000 + 1.73205i 0.0399680 + 0.0692267i
\(627\) 1.00000 + 1.73205i 0.0399362 + 0.0691714i
\(628\) 14.0000 24.2487i 0.558661 0.967629i
\(629\) 0 0
\(630\) 10.0000 3.46410i 0.398410 0.138013i
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) −2.00000 3.46410i −0.0794929 0.137686i
\(634\) −24.0000 41.5692i −0.953162 1.65092i
\(635\) −15.0000 + 25.9808i −0.595257 + 1.03102i
\(636\) 24.0000 0.951662
\(637\) 5.50000 4.33013i 0.217918 0.171566i
\(638\) −16.0000 −0.633446
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 0 0
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 8.00000 13.8564i 0.315735 0.546869i
\(643\) −19.0000 −0.749287 −0.374643 0.927169i \(-0.622235\pi\)
−0.374643 + 0.927169i \(0.622235\pi\)
\(644\) 0 0
\(645\) −10.0000 −0.393750
\(646\) 0 0
\(647\) −1.00000 1.73205i −0.0393141 0.0680939i 0.845699 0.533660i \(-0.179184\pi\)
−0.885013 + 0.465566i \(0.845851\pi\)
\(648\) 0 0
\(649\) −12.0000 + 20.7846i −0.471041 + 0.815867i
\(650\) −2.00000 −0.0784465
\(651\) 4.50000 23.3827i 0.176369 0.916440i
\(652\) 8.00000 0.313304
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) −9.00000 15.5885i −0.351928 0.609557i
\(655\) −14.0000 24.2487i −0.547025 0.947476i
\(656\) −20.0000 + 34.6410i −0.780869 + 1.35250i
\(657\) −3.00000 −0.117041
\(658\) −24.0000 20.7846i −0.935617 0.810268i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) −4.00000 + 6.92820i −0.155700 + 0.269680i
\(661\) 20.5000 + 35.5070i 0.797358 + 1.38106i 0.921331 + 0.388778i \(0.127103\pi\)
−0.123974 + 0.992286i \(0.539564\pi\)
\(662\) 25.0000 + 43.3013i 0.971653 + 1.68295i
\(663\) 0 0
\(664\) 0 0
\(665\) −4.00000 3.46410i −0.155113 0.134332i
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) 14.0000 + 24.2487i 0.541676 + 0.938211i
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) −10.0000 + 17.3205i −0.386334 + 0.669150i
\(671\) −20.0000 −0.772091
\(672\) −4.00000 + 20.7846i −0.154303 + 0.801784i
\(673\) −41.0000 −1.58043 −0.790217 0.612827i \(-0.790032\pi\)
−0.790217 + 0.612827i \(0.790032\pi\)
\(674\) −13.0000 + 22.5167i −0.500741 + 0.867309i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 12.0000 + 20.7846i 0.461538 + 0.799408i
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 20.0000 0.768095
\(679\) 15.0000 5.19615i 0.575647 0.199410i
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) 18.0000 + 31.1769i 0.689256 + 1.19383i
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) −1.00000 + 1.73205i −0.0382360 + 0.0662266i
\(685\) 24.0000 0.916993
\(686\) −17.0000 32.9090i −0.649063 1.25647i
\(687\) −19.0000 −0.724895
\(688\) 10.0000 17.3205i 0.381246 0.660338i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) 18.5000 32.0429i 0.703773 1.21897i −0.263359 0.964698i \(-0.584830\pi\)
0.967132 0.254273i \(-0.0818362\pi\)
\(692\) 16.0000 0.608229
\(693\) 5.00000 1.73205i 0.189934 0.0657952i
\(694\) 64.0000 2.42941
\(695\) −3.00000 + 5.19615i −0.113796 + 0.197101i
\(696\) 0 0
\(697\) 0 0
\(698\) 14.0000 24.2487i 0.529908 0.917827i
\(699\) 6.00000 0.226941
\(700\) −1.00000 + 5.19615i −0.0377964 + 0.196396i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −1.00000 + 1.73205i −0.0377426 + 0.0653720i
\(703\) −1.50000 2.59808i −0.0565736 0.0979883i
\(704\) −8.00000 13.8564i −0.301511 0.522233i
\(705\) −6.00000 + 10.3923i −0.225973 + 0.391397i
\(706\) 68.0000 2.55921
\(707\) 4.00000 + 3.46410i 0.150435 + 0.130281i
\(708\) −24.0000 −0.901975
\(709\) −15.0000 + 25.9808i −0.563337 + 0.975728i 0.433865 + 0.900978i \(0.357149\pi\)
−0.997202 + 0.0747503i \(0.976184\pi\)
\(710\) −12.0000 20.7846i −0.450352 0.780033i
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) −2.00000 + 3.46410i −0.0747435 + 0.129460i
\(717\) −3.00000 5.19615i −0.112037 0.194054i
\(718\) −20.0000 34.6410i −0.746393 1.29279i
\(719\) 9.00000 15.5885i 0.335643 0.581351i −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 8.00000 0.298142
\(721\) −3.50000 + 18.1865i −0.130347 + 0.677302i
\(722\) −36.0000 −1.33978
\(723\) −7.00000 + 12.1244i −0.260333 + 0.450910i
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) 2.00000 + 3.46410i 0.0742781 + 0.128654i
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) −13.0000 −0.482143 −0.241072 0.970507i \(-0.577499\pi\)
−0.241072 + 0.970507i \(0.577499\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −6.00000 + 10.3923i −0.222070 + 0.384636i
\(731\) 0 0
\(732\) −10.0000 17.3205i −0.369611 0.640184i
\(733\) 7.50000 12.9904i 0.277019 0.479811i −0.693624 0.720338i \(-0.743987\pi\)
0.970642 + 0.240527i \(0.0773202\pi\)
\(734\) −18.0000 −0.664392
\(735\) −11.0000 + 8.66025i −0.405741 + 0.319438i
\(736\) 0 0
\(737\) −5.00000 + 8.66025i −0.184177 + 0.319005i
\(738\) 10.0000 + 17.3205i 0.368105 + 0.637577i
\(739\) 7.50000 + 12.9904i 0.275892 + 0.477859i 0.970360 0.241665i \(-0.0776935\pi\)
−0.694468 + 0.719524i \(0.744360\pi\)
\(740\) 6.00000 10.3923i 0.220564 0.382029i
\(741\) 1.00000 0.0367359
\(742\) −60.0000 + 20.7846i −2.20267 + 0.763027i
\(743\) 42.0000 1.54083 0.770415 0.637542i \(-0.220049\pi\)
0.770415 + 0.637542i \(0.220049\pi\)
\(744\) 0 0
\(745\) −12.0000 20.7846i −0.439646 0.761489i
\(746\) −23.0000 39.8372i −0.842090 1.45854i
\(747\) −3.00000 + 5.19615i −0.109764 + 0.190117i
\(748\) 0 0
\(749\) −4.00000 + 20.7846i −0.146157 + 0.759453i
\(750\) 24.0000 0.876356
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) −12.0000 20.7846i −0.437595 0.757937i
\(753\) 4.00000 + 6.92820i 0.145768 + 0.252478i
\(754\) −4.00000 + 6.92820i −0.145671 + 0.252310i
\(755\) 32.0000 1.16460
\(756\) 4.00000 + 3.46410i 0.145479 + 0.125988i
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −3.00000 + 5.19615i −0.108965 + 0.188733i
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 41.5692i 0.869999 1.50688i 0.00800331 0.999968i \(-0.497452\pi\)
0.861996 0.506915i \(-0.169214\pi\)
\(762\) −30.0000 −1.08679
\(763\) 18.0000 + 15.5885i 0.651644 + 0.564340i
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) 12.0000 + 20.7846i 0.433578 + 0.750978i
\(767\) 6.00000 + 10.3923i 0.216647 + 0.375244i
\(768\) −8.00000 + 13.8564i −0.288675 + 0.500000i
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 4.00000 20.7846i 0.144150 0.749025i
\(771\) 26.0000 0.936367
\(772\) −11.0000 + 19.0526i −0.395899 + 0.685717i
\(773\) 17.0000 + 29.4449i 0.611448 + 1.05906i 0.990997 + 0.133887i \(0.0427458\pi\)
−0.379549 + 0.925172i \(0.623921\pi\)
\(774\) −5.00000 8.66025i −0.179721 0.311286i
\(775\) 4.50000 7.79423i 0.161645 0.279977i
\(776\) 0 0
\(777\) −7.50000 + 2.59808i −0.269061 + 0.0932055i
\(778\) −12.0000 −0.430221
\(779\) 5.00000 8.66025i 0.179144 0.310286i
\(780\) 2.00000 + 3.46410i 0.0716115 + 0.124035i
\(781\) −6.00000 10.3923i −0.214697 0.371866i
\(782\) 0 0