Properties

Label 722.2.c.f.429.1
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
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: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 429.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.f.653.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-2.00000 - 3.46410i) q^{10} +2.00000 q^{11} +1.00000 q^{12} +(-0.500000 - 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{14} +(2.00000 + 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +2.00000 q^{18} -4.00000 q^{20} +(-1.50000 + 2.59808i) q^{21} +(1.00000 - 1.73205i) q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-5.50000 - 9.52628i) q^{25} -1.00000 q^{26} -5.00000 q^{27} +(-1.50000 - 2.59808i) q^{28} +(-2.50000 - 4.33013i) q^{29} +4.00000 q^{30} +8.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(1.50000 + 2.59808i) q^{34} +(6.00000 - 10.3923i) q^{35} +(1.00000 - 1.73205i) q^{36} +2.00000 q^{37} +1.00000 q^{39} +(-2.00000 + 3.46410i) q^{40} +(-4.00000 + 6.92820i) q^{41} +(1.50000 + 2.59808i) q^{42} +(-2.00000 + 3.46410i) q^{43} +(-1.00000 - 1.73205i) q^{44} +8.00000 q^{45} +1.00000 q^{46} +(-4.00000 - 6.92820i) q^{47} +(-0.500000 - 0.866025i) q^{48} +2.00000 q^{49} -11.0000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-2.50000 + 4.33013i) q^{54} +(4.00000 - 6.92820i) q^{55} -3.00000 q^{56} -5.00000 q^{58} +(7.50000 - 12.9904i) q^{59} +(2.00000 - 3.46410i) q^{60} +(-1.00000 - 1.73205i) q^{61} +(4.00000 - 6.92820i) q^{62} +(3.00000 + 5.19615i) q^{63} +1.00000 q^{64} -4.00000 q^{65} +(1.00000 + 1.73205i) q^{66} +(1.50000 + 2.59808i) q^{67} +3.00000 q^{68} -1.00000 q^{69} +(-6.00000 - 10.3923i) q^{70} +(1.00000 - 1.73205i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(-4.50000 + 7.79423i) q^{73} +(1.00000 - 1.73205i) q^{74} +11.0000 q^{75} +6.00000 q^{77} +(0.500000 - 0.866025i) q^{78} +(-5.00000 + 8.66025i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.00000 + 6.92820i) q^{82} -6.00000 q^{83} +3.00000 q^{84} +(6.00000 + 10.3923i) q^{85} +(2.00000 + 3.46410i) q^{86} +5.00000 q^{87} -2.00000 q^{88} +(4.00000 - 6.92820i) q^{90} +(-1.50000 - 2.59808i) q^{91} +(0.500000 - 0.866025i) q^{92} +(-4.00000 + 6.92820i) q^{93} -8.00000 q^{94} -1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(1.00000 - 1.73205i) q^{98} +(2.00000 + 3.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} + 4q^{5} + q^{6} + 6q^{7} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} + 4q^{5} + q^{6} + 6q^{7} - 2q^{8} + 2q^{9} - 4q^{10} + 4q^{11} + 2q^{12} - q^{13} + 3q^{14} + 4q^{15} - q^{16} - 3q^{17} + 4q^{18} - 8q^{20} - 3q^{21} + 2q^{22} + q^{23} + q^{24} - 11q^{25} - 2q^{26} - 10q^{27} - 3q^{28} - 5q^{29} + 8q^{30} + 16q^{31} + q^{32} - 2q^{33} + 3q^{34} + 12q^{35} + 2q^{36} + 4q^{37} + 2q^{39} - 4q^{40} - 8q^{41} + 3q^{42} - 4q^{43} - 2q^{44} + 16q^{45} + 2q^{46} - 8q^{47} - q^{48} + 4q^{49} - 22q^{50} - 3q^{51} - q^{52} - q^{53} - 5q^{54} + 8q^{55} - 6q^{56} - 10q^{58} + 15q^{59} + 4q^{60} - 2q^{61} + 8q^{62} + 6q^{63} + 2q^{64} - 8q^{65} + 2q^{66} + 3q^{67} + 6q^{68} - 2q^{69} - 12q^{70} + 2q^{71} - 2q^{72} - 9q^{73} + 2q^{74} + 22q^{75} + 12q^{77} + q^{78} - 10q^{79} + 4q^{80} - q^{81} + 8q^{82} - 12q^{83} + 6q^{84} + 12q^{85} + 4q^{86} + 10q^{87} - 4q^{88} + 8q^{90} - 3q^{91} + q^{92} - 8q^{93} - 16q^{94} - 2q^{96} - 2q^{97} + 2q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) −2.00000 3.46410i −0.632456 1.09545i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000 0.288675
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 1.50000 2.59808i 0.400892 0.694365i
\(15\) 2.00000 + 3.46410i 0.516398 + 0.894427i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 2.00000 0.471405
\(19\) 0 0
\(20\) −4.00000 −0.894427
\(21\) −1.50000 + 2.59808i −0.327327 + 0.566947i
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) −1.00000 −0.196116
\(27\) −5.00000 −0.962250
\(28\) −1.50000 2.59808i −0.283473 0.490990i
\(29\) −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i \(-0.320339\pi\)
−0.999167 + 0.0408130i \(0.987005\pi\)
\(30\) 4.00000 0.730297
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) 1.50000 + 2.59808i 0.257248 + 0.445566i
\(35\) 6.00000 10.3923i 1.01419 1.75662i
\(36\) 1.00000 1.73205i 0.166667 0.288675i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) −2.00000 + 3.46410i −0.316228 + 0.547723i
\(41\) −4.00000 + 6.92820i −0.624695 + 1.08200i 0.363905 + 0.931436i \(0.381443\pi\)
−0.988600 + 0.150567i \(0.951890\pi\)
\(42\) 1.50000 + 2.59808i 0.231455 + 0.400892i
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 8.00000 1.19257
\(46\) 1.00000 0.147442
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 2.00000 0.285714
\(50\) −11.0000 −1.55563
\(51\) −1.50000 2.59808i −0.210042 0.363803i
\(52\) −0.500000 + 0.866025i −0.0693375 + 0.120096i
\(53\) −0.500000 0.866025i −0.0686803 0.118958i 0.829640 0.558298i \(-0.188546\pi\)
−0.898321 + 0.439340i \(0.855212\pi\)
\(54\) −2.50000 + 4.33013i −0.340207 + 0.589256i
\(55\) 4.00000 6.92820i 0.539360 0.934199i
\(56\) −3.00000 −0.400892
\(57\) 0 0
\(58\) −5.00000 −0.656532
\(59\) 7.50000 12.9904i 0.976417 1.69120i 0.301239 0.953549i \(-0.402600\pi\)
0.675178 0.737655i \(-0.264067\pi\)
\(60\) 2.00000 3.46410i 0.258199 0.447214i
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 4.00000 6.92820i 0.508001 0.879883i
\(63\) 3.00000 + 5.19615i 0.377964 + 0.654654i
\(64\) 1.00000 0.125000
\(65\) −4.00000 −0.496139
\(66\) 1.00000 + 1.73205i 0.123091 + 0.213201i
\(67\) 1.50000 + 2.59808i 0.183254 + 0.317406i 0.942987 0.332830i \(-0.108004\pi\)
−0.759733 + 0.650236i \(0.774670\pi\)
\(68\) 3.00000 0.363803
\(69\) −1.00000 −0.120386
\(70\) −6.00000 10.3923i −0.717137 1.24212i
\(71\) 1.00000 1.73205i 0.118678 0.205557i −0.800566 0.599245i \(-0.795468\pi\)
0.919244 + 0.393688i \(0.128801\pi\)
\(72\) −1.00000 1.73205i −0.117851 0.204124i
\(73\) −4.50000 + 7.79423i −0.526685 + 0.912245i 0.472831 + 0.881153i \(0.343232\pi\)
−0.999517 + 0.0310925i \(0.990101\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 11.0000 1.27017
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) 0.500000 0.866025i 0.0566139 0.0980581i
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) 2.00000 + 3.46410i 0.223607 + 0.387298i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.00000 + 6.92820i 0.441726 + 0.765092i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 3.00000 0.327327
\(85\) 6.00000 + 10.3923i 0.650791 + 1.12720i
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 5.00000 0.536056
\(88\) −2.00000 −0.213201
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 4.00000 6.92820i 0.421637 0.730297i
\(91\) −1.50000 2.59808i −0.157243 0.272352i
\(92\) 0.500000 0.866025i 0.0521286 0.0902894i
\(93\) −4.00000 + 6.92820i −0.414781 + 0.718421i
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 1.00000 1.73205i 0.101015 0.174964i
\(99\) 2.00000 + 3.46410i 0.201008 + 0.348155i
\(100\) −5.50000 + 9.52628i −0.550000 + 0.952628i
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) −3.00000 −0.297044
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) 0.500000 + 0.866025i 0.0490290 + 0.0849208i
\(105\) 6.00000 + 10.3923i 0.585540 + 1.01419i
\(106\) −1.00000 −0.0971286
\(107\) 7.00000 0.676716 0.338358 0.941018i \(-0.390129\pi\)
0.338358 + 0.941018i \(0.390129\pi\)
\(108\) 2.50000 + 4.33013i 0.240563 + 0.416667i
\(109\) −7.50000 + 12.9904i −0.718370 + 1.24425i 0.243276 + 0.969957i \(0.421778\pi\)
−0.961645 + 0.274296i \(0.911555\pi\)
\(110\) −4.00000 6.92820i −0.381385 0.660578i
\(111\) −1.00000 + 1.73205i −0.0949158 + 0.164399i
\(112\) −1.50000 + 2.59808i −0.141737 + 0.245495i
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) −2.50000 + 4.33013i −0.232119 + 0.402042i
\(117\) 1.00000 1.73205i 0.0924500 0.160128i
\(118\) −7.50000 12.9904i −0.690431 1.19586i
\(119\) −4.50000 + 7.79423i −0.412514 + 0.714496i
\(120\) −2.00000 3.46410i −0.182574 0.316228i
\(121\) −7.00000 −0.636364
\(122\) −2.00000 −0.181071
\(123\) −4.00000 6.92820i −0.360668 0.624695i
\(124\) −4.00000 6.92820i −0.359211 0.622171i
\(125\) −24.0000 −2.14663
\(126\) 6.00000 0.534522
\(127\) 9.00000 + 15.5885i 0.798621 + 1.38325i 0.920514 + 0.390709i \(0.127770\pi\)
−0.121894 + 0.992543i \(0.538897\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) −2.00000 + 3.46410i −0.175412 + 0.303822i
\(131\) −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 2.00000 0.174078
\(133\) 0 0
\(134\) 3.00000 0.259161
\(135\) −10.0000 + 17.3205i −0.860663 + 1.49071i
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 8.50000 + 14.7224i 0.726204 + 1.25782i 0.958477 + 0.285171i \(0.0920506\pi\)
−0.232273 + 0.972651i \(0.574616\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) −12.0000 −1.01419
\(141\) 8.00000 0.673722
\(142\) −1.00000 1.73205i −0.0839181 0.145350i
\(143\) −1.00000 1.73205i −0.0836242 0.144841i
\(144\) −2.00000 −0.166667
\(145\) −20.0000 −1.66091
\(146\) 4.50000 + 7.79423i 0.372423 + 0.645055i
\(147\) −1.00000 + 1.73205i −0.0824786 + 0.142857i
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 5.50000 9.52628i 0.449073 0.777817i
\(151\) −2.00000 −0.162758 −0.0813788 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 3.00000 5.19615i 0.241747 0.418718i
\(155\) 16.0000 27.7128i 1.28515 2.22595i
\(156\) −0.500000 0.866025i −0.0400320 0.0693375i
\(157\) 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i \(-0.807902\pi\)
0.903167 + 0.429289i \(0.141236\pi\)
\(158\) 5.00000 + 8.66025i 0.397779 + 0.688973i
\(159\) 1.00000 0.0793052
\(160\) 4.00000 0.316228
\(161\) 1.50000 + 2.59808i 0.118217 + 0.204757i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 8.00000 0.624695
\(165\) 4.00000 + 6.92820i 0.311400 + 0.539360i
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 1.50000 2.59808i 0.115728 0.200446i
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 12.0000 0.920358
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 2.50000 4.33013i 0.189525 0.328266i
\(175\) −16.5000 28.5788i −1.24728 2.16036i
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 7.50000 + 12.9904i 0.563735 + 0.976417i
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −4.00000 6.92820i −0.298142 0.516398i
\(181\) 11.0000 + 19.0526i 0.817624 + 1.41617i 0.907429 + 0.420206i \(0.138042\pi\)
−0.0898051 + 0.995959i \(0.528624\pi\)
\(182\) −3.00000 −0.222375
\(183\) 2.00000 0.147844
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) 4.00000 6.92820i 0.294086 0.509372i
\(186\) 4.00000 + 6.92820i 0.293294 + 0.508001i
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) −4.00000 + 6.92820i −0.291730 + 0.505291i
\(189\) −15.0000 −1.09109
\(190\) 0 0
\(191\) 7.00000 0.506502 0.253251 0.967401i \(-0.418500\pi\)
0.253251 + 0.967401i \(0.418500\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −3.00000 + 5.19615i −0.215945 + 0.374027i −0.953564 0.301189i \(-0.902616\pi\)
0.737620 + 0.675216i \(0.235950\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 2.00000 3.46410i 0.143223 0.248069i
\(196\) −1.00000 1.73205i −0.0714286 0.123718i
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 4.00000 0.284268
\(199\) 12.5000 + 21.6506i 0.886102 + 1.53477i 0.844446 + 0.535641i \(0.179930\pi\)
0.0416556 + 0.999132i \(0.486737\pi\)
\(200\) 5.50000 + 9.52628i 0.388909 + 0.673610i
\(201\) −3.00000 −0.211604
\(202\) −2.00000 −0.140720
\(203\) −7.50000 12.9904i −0.526397 0.911746i
\(204\) −1.50000 + 2.59808i −0.105021 + 0.181902i
\(205\) 16.0000 + 27.7128i 1.11749 + 1.93555i
\(206\) 3.00000 5.19615i 0.209020 0.362033i
\(207\) −1.00000 + 1.73205i −0.0695048 + 0.120386i
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 12.0000 0.828079
\(211\) 13.5000 23.3827i 0.929378 1.60973i 0.145014 0.989430i \(-0.453677\pi\)
0.784364 0.620301i \(-0.212990\pi\)
\(212\) −0.500000 + 0.866025i −0.0343401 + 0.0594789i
\(213\) 1.00000 + 1.73205i 0.0685189 + 0.118678i
\(214\) 3.50000 6.06218i 0.239255 0.414402i
\(215\) 8.00000 + 13.8564i 0.545595 + 0.944999i
\(216\) 5.00000 0.340207
\(217\) 24.0000 1.62923
\(218\) 7.50000 + 12.9904i 0.507964 + 0.879820i
\(219\) −4.50000 7.79423i −0.304082 0.526685i
\(220\) −8.00000 −0.539360
\(221\) 3.00000 0.201802
\(222\) 1.00000 + 1.73205i 0.0671156 + 0.116248i
\(223\) 7.00000 12.1244i 0.468755 0.811907i −0.530607 0.847618i \(-0.678036\pi\)
0.999362 + 0.0357107i \(0.0113695\pi\)
\(224\) 1.50000 + 2.59808i 0.100223 + 0.173591i
\(225\) 11.0000 19.0526i 0.733333 1.27017i
\(226\) −7.00000 + 12.1244i −0.465633 + 0.806500i
\(227\) 17.0000 1.12833 0.564165 0.825662i \(-0.309198\pi\)
0.564165 + 0.825662i \(0.309198\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 2.00000 3.46410i 0.131876 0.228416i
\(231\) −3.00000 + 5.19615i −0.197386 + 0.341882i
\(232\) 2.50000 + 4.33013i 0.164133 + 0.284287i
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −1.00000 1.73205i −0.0653720 0.113228i
\(235\) −32.0000 −2.08745
\(236\) −15.0000 −0.976417
\(237\) −5.00000 8.66025i −0.324785 0.562544i
\(238\) 4.50000 + 7.79423i 0.291692 + 0.505225i
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) −4.00000 −0.258199
\(241\) −4.00000 6.92820i −0.257663 0.446285i 0.707953 0.706260i \(-0.249619\pi\)
−0.965615 + 0.259975i \(0.916286\pi\)
\(242\) −3.50000 + 6.06218i −0.224989 + 0.389692i
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) −1.00000 + 1.73205i −0.0640184 + 0.110883i
\(245\) 4.00000 6.92820i 0.255551 0.442627i
\(246\) −8.00000 −0.510061
\(247\) 0 0
\(248\) −8.00000 −0.508001
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) −12.0000 + 20.7846i −0.758947 + 1.31453i
\(251\) −1.00000 1.73205i −0.0631194 0.109326i 0.832739 0.553666i \(-0.186772\pi\)
−0.895858 + 0.444340i \(0.853438\pi\)
\(252\) 3.00000 5.19615i 0.188982 0.327327i
\(253\) 1.00000 + 1.73205i 0.0628695 + 0.108893i
\(254\) 18.0000 1.12942
\(255\) −12.0000 −0.751469
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.00000 + 6.92820i 0.249513 + 0.432169i 0.963391 0.268101i \(-0.0863961\pi\)
−0.713878 + 0.700270i \(0.753063\pi\)
\(258\) −4.00000 −0.249029
\(259\) 6.00000 0.372822
\(260\) 2.00000 + 3.46410i 0.124035 + 0.214834i
\(261\) 5.00000 8.66025i 0.309492 0.536056i
\(262\) 6.00000 + 10.3923i 0.370681 + 0.642039i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 1.00000 1.73205i 0.0615457 0.106600i
\(265\) −4.00000 −0.245718
\(266\) 0 0
\(267\) 0 0
\(268\) 1.50000 2.59808i 0.0916271 0.158703i
\(269\) 15.0000 25.9808i 0.914566 1.58408i 0.107031 0.994256i \(-0.465866\pi\)
0.807535 0.589819i \(-0.200801\pi\)
\(270\) 10.0000 + 17.3205i 0.608581 + 1.05409i
\(271\) −3.50000 + 6.06218i −0.212610 + 0.368251i −0.952531 0.304443i \(-0.901530\pi\)
0.739921 + 0.672694i \(0.234863\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) 3.00000 0.181568
\(274\) 17.0000 1.02701
\(275\) −11.0000 19.0526i −0.663325 1.14891i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 0 0
\(279\) 8.00000 + 13.8564i 0.478947 + 0.829561i
\(280\) −6.00000 + 10.3923i −0.358569 + 0.621059i
\(281\) −4.00000 6.92820i −0.238620 0.413302i 0.721699 0.692207i \(-0.243362\pi\)
−0.960319 + 0.278906i \(0.910028\pi\)
\(282\) 4.00000 6.92820i 0.238197 0.412568i
\(283\) 3.00000 5.19615i 0.178331 0.308879i −0.762978 0.646425i \(-0.776263\pi\)
0.941309 + 0.337546i \(0.109597\pi\)
\(284\) −2.00000 −0.118678
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) −12.0000 + 20.7846i −0.708338 + 1.22688i
\(288\) −1.00000 + 1.73205i −0.0589256 + 0.102062i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) −10.0000 + 17.3205i −0.587220 + 1.01710i
\(291\) −1.00000 1.73205i −0.0586210 0.101535i
\(292\) 9.00000 0.526685
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 1.00000 + 1.73205i 0.0583212 + 0.101015i
\(295\) −30.0000 51.9615i −1.74667 3.02532i
\(296\) −2.00000 −0.116248
\(297\) −10.0000 −0.580259
\(298\) 0 0
\(299\) 0.500000 0.866025i 0.0289157 0.0500835i
\(300\) −5.50000 9.52628i −0.317543 0.550000i
\(301\) −6.00000 + 10.3923i −0.345834 + 0.599002i
\(302\) −1.00000 + 1.73205i −0.0575435 + 0.0996683i
\(303\) 2.00000 0.114897
\(304\) 0 0
\(305\) −8.00000 −0.458079
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) −6.00000 + 10.3923i −0.342438 + 0.593120i −0.984885 0.173210i \(-0.944586\pi\)
0.642447 + 0.766330i \(0.277919\pi\)
\(308\) −3.00000 5.19615i −0.170941 0.296078i
\(309\) −3.00000 + 5.19615i −0.170664 + 0.295599i
\(310\) −16.0000 27.7128i −0.908739 1.57398i
\(311\) 7.00000 0.396934 0.198467 0.980108i \(-0.436404\pi\)
0.198467 + 0.980108i \(0.436404\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −14.5000 25.1147i −0.819588 1.41957i −0.905986 0.423308i \(-0.860869\pi\)
0.0863973 0.996261i \(-0.472465\pi\)
\(314\) −1.00000 1.73205i −0.0564333 0.0977453i
\(315\) 24.0000 1.35225
\(316\) 10.0000 0.562544
\(317\) −13.5000 23.3827i −0.758236 1.31330i −0.943750 0.330661i \(-0.892728\pi\)
0.185514 0.982642i \(-0.440605\pi\)
\(318\) 0.500000 0.866025i 0.0280386 0.0485643i
\(319\) −5.00000 8.66025i −0.279946 0.484881i
\(320\) 2.00000 3.46410i 0.111803 0.193649i
\(321\) −3.50000 + 6.06218i −0.195351 + 0.338358i
\(322\) 3.00000 0.167183
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −5.50000 + 9.52628i −0.305085 + 0.528423i
\(326\) −8.00000 + 13.8564i −0.443079 + 0.767435i
\(327\) −7.50000 12.9904i −0.414751 0.718370i
\(328\) 4.00000 6.92820i 0.220863 0.382546i
\(329\) −12.0000 20.7846i −0.661581 1.14589i
\(330\) 8.00000 0.440386
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) −12.0000 −0.656611
\(335\) 12.0000 0.655630
\(336\) −1.50000 2.59808i −0.0818317 0.141737i
\(337\) −16.0000 + 27.7128i −0.871576 + 1.50961i −0.0112091 + 0.999937i \(0.503568\pi\)
−0.860366 + 0.509676i \(0.829765\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 7.00000 12.1244i 0.380188 0.658505i
\(340\) 6.00000 10.3923i 0.325396 0.563602i
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 2.00000 3.46410i 0.107833 0.186772i
\(345\) −2.00000 + 3.46410i −0.107676 + 0.186501i
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) 1.00000 1.73205i 0.0536828 0.0929814i −0.837935 0.545770i \(-0.816237\pi\)
0.891618 + 0.452788i \(0.149571\pi\)
\(348\) −2.50000 4.33013i −0.134014 0.232119i
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) −33.0000 −1.76392
\(351\) 2.50000 + 4.33013i 0.133440 + 0.231125i
\(352\) 1.00000 + 1.73205i 0.0533002 + 0.0923186i
\(353\) 9.00000 0.479022 0.239511 0.970894i \(-0.423013\pi\)
0.239511 + 0.970894i \(0.423013\pi\)
\(354\) 15.0000 0.797241
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) 0 0
\(357\) −4.50000 7.79423i −0.238165 0.412514i
\(358\) 0 0
\(359\) 7.50000 12.9904i 0.395835 0.685606i −0.597372 0.801964i \(-0.703789\pi\)
0.993207 + 0.116358i \(0.0371219\pi\)
\(360\) −8.00000 −0.421637
\(361\) 0 0
\(362\) 22.0000 1.15629
\(363\) 3.50000 6.06218i 0.183702 0.318182i
\(364\) −1.50000 + 2.59808i −0.0786214 + 0.136176i
\(365\) 18.0000 + 31.1769i 0.942163 + 1.63187i
\(366\) 1.00000 1.73205i 0.0522708 0.0905357i
\(367\) −14.0000 24.2487i −0.730794 1.26577i −0.956544 0.291587i \(-0.905817\pi\)
0.225750 0.974185i \(-0.427517\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −16.0000 −0.832927
\(370\) −4.00000 6.92820i −0.207950 0.360180i
\(371\) −1.50000 2.59808i −0.0778761 0.134885i
\(372\) 8.00000 0.414781
\(373\) −29.0000 −1.50156 −0.750782 0.660551i \(-0.770323\pi\)
−0.750782 + 0.660551i \(0.770323\pi\)
\(374\) 3.00000 + 5.19615i 0.155126 + 0.268687i
\(375\) 12.0000 20.7846i 0.619677 1.07331i
\(376\) 4.00000 + 6.92820i 0.206284 + 0.357295i
\(377\) −2.50000 + 4.33013i −0.128757 + 0.223013i
\(378\) −7.50000 + 12.9904i −0.385758 + 0.668153i
\(379\) −15.0000 −0.770498 −0.385249 0.922813i \(-0.625884\pi\)
−0.385249 + 0.922813i \(0.625884\pi\)
\(380\) 0 0
\(381\) −18.0000 −0.922168
\(382\) 3.50000 6.06218i 0.179076 0.310168i
\(383\) −13.0000 + 22.5167i −0.664269 + 1.15055i 0.315214 + 0.949021i \(0.397924\pi\)
−0.979483 + 0.201527i \(0.935410\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 12.0000 20.7846i 0.611577 1.05928i
\(386\) 3.00000 + 5.19615i 0.152696 + 0.264477i
\(387\) −8.00000 −0.406663
\(388\) 2.00000 0.101535
\(389\) 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i \(0.108394\pi\)
−0.182047 + 0.983290i \(0.558272\pi\)
\(390\) −2.00000 3.46410i −0.101274 0.175412i
\(391\) −3.00000 −0.151717
\(392\) −2.00000 −0.101015
\(393\) −6.00000 10.3923i −0.302660 0.524222i
\(394\) 4.00000 6.92820i 0.201517 0.349038i
\(395\) 20.0000 + 34.6410i 1.00631 + 1.74298i
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) −4.00000 + 6.92820i −0.200754 + 0.347717i −0.948772 0.315963i \(-0.897673\pi\)
0.748017 + 0.663679i \(0.231006\pi\)
\(398\) 25.0000 1.25314
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) −4.00000 + 6.92820i −0.199750 + 0.345978i −0.948447 0.316934i \(-0.897346\pi\)
0.748697 + 0.662912i \(0.230680\pi\)
\(402\) −1.50000 + 2.59808i −0.0748132 + 0.129580i
\(403\) −4.00000 6.92820i −0.199254 0.345118i
\(404\) −1.00000 + 1.73205i −0.0497519 + 0.0861727i
\(405\) 2.00000 + 3.46410i 0.0993808 + 0.172133i
\(406\) −15.0000 −0.744438
\(407\) 4.00000 0.198273
\(408\) 1.50000 + 2.59808i 0.0742611 + 0.128624i
\(409\) −10.0000 17.3205i −0.494468 0.856444i 0.505511 0.862820i \(-0.331304\pi\)
−0.999980 + 0.00637586i \(0.997970\pi\)
\(410\) 32.0000 1.58037
\(411\) −17.0000 −0.838548
\(412\) −3.00000 5.19615i −0.147799 0.255996i
\(413\) 22.5000 38.9711i 1.10715 1.91764i
\(414\) 1.00000 + 1.73205i 0.0491473 + 0.0851257i
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 6.00000 10.3923i 0.292770 0.507093i
\(421\) −6.50000 + 11.2583i −0.316791 + 0.548697i −0.979817 0.199899i \(-0.935939\pi\)
0.663026 + 0.748596i \(0.269272\pi\)
\(422\) −13.5000 23.3827i −0.657170 1.13825i
\(423\) 8.00000 13.8564i 0.388973 0.673722i
\(424\) 0.500000 + 0.866025i 0.0242821 + 0.0420579i
\(425\) 33.0000 1.60074
\(426\) 2.00000 0.0969003
\(427\) −3.00000 5.19615i −0.145180 0.251459i
\(428\) −3.50000 6.06218i −0.169179 0.293026i
\(429\) 2.00000 0.0965609
\(430\) 16.0000 0.771589
\(431\) −9.00000 15.5885i −0.433515 0.750870i 0.563658 0.826008i \(-0.309393\pi\)
−0.997173 + 0.0751385i \(0.976060\pi\)
\(432\) 2.50000 4.33013i 0.120281 0.208333i
\(433\) 7.00000 + 12.1244i 0.336399 + 0.582659i 0.983752 0.179530i \(-0.0574578\pi\)
−0.647354 + 0.762190i \(0.724124\pi\)
\(434\) 12.0000 20.7846i 0.576018 0.997693i
\(435\) 10.0000 17.3205i 0.479463 0.830455i
\(436\) 15.0000 0.718370
\(437\) 0 0
\(438\) −9.00000 −0.430037
\(439\) 10.0000 17.3205i 0.477274 0.826663i −0.522387 0.852709i \(-0.674958\pi\)
0.999661 + 0.0260459i \(0.00829161\pi\)
\(440\) −4.00000 + 6.92820i −0.190693 + 0.330289i
\(441\) 2.00000 + 3.46410i 0.0952381 + 0.164957i
\(442\) 1.50000 2.59808i 0.0713477 0.123578i
\(443\) 13.0000 + 22.5167i 0.617649 + 1.06980i 0.989914 + 0.141672i \(0.0452479\pi\)
−0.372265 + 0.928126i \(0.621419\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) −7.00000 12.1244i −0.331460 0.574105i
\(447\) 0 0
\(448\) 3.00000 0.141737
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) −11.0000 19.0526i −0.518545 0.898146i
\(451\) −8.00000 + 13.8564i −0.376705 + 0.652473i
\(452\) 7.00000 + 12.1244i 0.329252 + 0.570282i
\(453\) 1.00000 1.73205i 0.0469841 0.0813788i
\(454\) 8.50000 14.7224i 0.398925 0.690958i
\(455\) −12.0000 −0.562569
\(456\) 0 0
\(457\) −7.00000 −0.327446 −0.163723 0.986506i \(-0.552350\pi\)
−0.163723 + 0.986506i \(0.552350\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) 7.50000 12.9904i 0.350070 0.606339i
\(460\) −2.00000 3.46410i −0.0932505 0.161515i
\(461\) 14.0000 24.2487i 0.652045 1.12938i −0.330581 0.943778i \(-0.607245\pi\)
0.982626 0.185597i \(-0.0594220\pi\)
\(462\) 3.00000 + 5.19615i 0.139573 + 0.241747i
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 5.00000 0.232119
\(465\) 16.0000 + 27.7128i 0.741982 + 1.28515i
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −2.00000 −0.0925490 −0.0462745 0.998929i \(-0.514735\pi\)
−0.0462745 + 0.998929i \(0.514735\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 4.50000 + 7.79423i 0.207791 + 0.359904i
\(470\) −16.0000 + 27.7128i −0.738025 + 1.27830i
\(471\) 1.00000 + 1.73205i 0.0460776 + 0.0798087i
\(472\) −7.50000 + 12.9904i −0.345215 + 0.597931i
\(473\) −4.00000 + 6.92820i −0.183920 + 0.318559i
\(474\) −10.0000 −0.459315
\(475\) 0 0
\(476\) 9.00000 0.412514
\(477\) 1.00000 1.73205i 0.0457869 0.0793052i
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) 10.0000 + 17.3205i 0.456912 + 0.791394i 0.998796 0.0490589i \(-0.0156222\pi\)
−0.541884 + 0.840453i \(0.682289\pi\)
\(480\) −2.00000 + 3.46410i −0.0912871 + 0.158114i
\(481\) −1.00000 1.73205i −0.0455961 0.0789747i
\(482\) −8.00000 −0.364390
\(483\) −3.00000 −0.136505
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 4.00000 + 6.92820i 0.181631 + 0.314594i
\(486\) −16.0000 −0.725775
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 1.00000 + 1.73205i 0.0452679 + 0.0784063i
\(489\) 8.00000 13.8564i 0.361773 0.626608i
\(490\) −4.00000 6.92820i −0.180702 0.312984i
\(491\) 14.0000 24.2487i 0.631811 1.09433i −0.355370 0.934726i \(-0.615645\pi\)
0.987181 0.159603i \(-0.0510215\pi\)
\(492\) −4.00000 + 6.92820i −0.180334 + 0.312348i
\(493\) 15.0000 0.675566
\(494\) 0 0
\(495\) 16.0000 0.719147
\(496\) −4.00000 + 6.92820i −0.179605 + 0.311086i
\(497\) 3.00000 5.19615i 0.134568 0.233079i
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) −20.0000 + 34.6410i −0.895323 + 1.55074i −0.0619186 + 0.998081i \(0.519722\pi\)
−0.833404 + 0.552664i \(0.813611\pi\)
\(500\) 12.0000 + 20.7846i 0.536656 + 0.929516i
\(501\) 12.0000 0.536120
\(502\) −2.00000 −0.0892644
\(503\) −19.5000 33.7750i −0.869462 1.50595i −0.862547 0.505976i \(-0.831132\pi\)
−0.00691465 0.999976i \(-0.502201\pi\)
\(504\) −3.00000 5.19615i −0.133631 0.231455i
\(505\) −8.00000 −0.355995
\(506\) 2.00000 0.0889108
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 9.00000 15.5885i 0.399310 0.691626i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) −6.00000 + 10.3923i −0.265684 + 0.460179i
\(511\) −13.5000 + 23.3827i −0.597205 + 1.03439i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 8.00000 0.352865
\(515\) 12.0000 20.7846i 0.528783 0.915879i
\(516\) −2.00000 + 3.46410i −0.0880451 + 0.152499i
\(517\) −8.00000 13.8564i −0.351840 0.609404i
\(518\) 3.00000 5.19615i 0.131812 0.228306i
\(519\) −3.00000 5.19615i −0.131685 0.228086i
\(520\) 4.00000 0.175412
\(521\) 28.0000 1.22670 0.613351 0.789810i \(-0.289821\pi\)
0.613351 + 0.789810i \(0.289821\pi\)
\(522\) −5.00000 8.66025i −0.218844 0.379049i
\(523\) 14.5000 + 25.1147i 0.634041 + 1.09819i 0.986718 + 0.162446i \(0.0519382\pi\)
−0.352677 + 0.935745i \(0.614728\pi\)
\(524\) 12.0000 0.524222
\(525\) 33.0000 1.44024
\(526\) 12.0000 + 20.7846i 0.523225 + 0.906252i
\(527\) −12.0000 + 20.7846i −0.522728 + 0.905392i
\(528\) −1.00000 1.73205i −0.0435194 0.0753778i
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) −2.00000 + 3.46410i −0.0868744 + 0.150471i
\(531\) 30.0000 1.30189
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) 0 0
\(535\) 14.0000 24.2487i 0.605273 1.04836i
\(536\) −1.50000 2.59808i −0.0647901 0.112220i
\(537\) 0 0
\(538\) −15.0000 25.9808i −0.646696 1.12011i
\(539\) 4.00000 0.172292
\(540\) 20.0000 0.860663
\(541\) −1.00000 1.73205i −0.0429934 0.0744667i 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) 3.50000 + 6.06218i 0.150338 + 0.260393i
\(543\) −22.0000 −0.944110
\(544\) −3.00000 −0.128624
\(545\) 30.0000 + 51.9615i 1.28506 + 2.22579i
\(546\) 1.50000 2.59808i 0.0641941 0.111187i
\(547\) 14.0000 + 24.2487i 0.598597 + 1.03680i 0.993028 + 0.117875i \(0.0376081\pi\)
−0.394432 + 0.918925i \(0.629059\pi\)
\(548\) 8.50000 14.7224i 0.363102 0.628911i
\(549\) 2.00000 3.46410i 0.0853579 0.147844i
\(550\) −22.0000 −0.938083
\(551\) 0 0
\(552\) 1.00000 0.0425628
\(553\) −15.0000 + 25.9808i −0.637865 + 1.10481i
\(554\) 14.0000 24.2487i 0.594803 1.03023i
\(555\) 4.00000 + 6.92820i 0.169791 + 0.294086i
\(556\) 0 0
\(557\) −14.0000 24.2487i −0.593199 1.02745i −0.993798 0.111198i \(-0.964531\pi\)
0.400599 0.916253i \(-0.368802\pi\)
\(558\) 16.0000 0.677334
\(559\) 4.00000 0.169182
\(560\) 6.00000 + 10.3923i 0.253546 + 0.439155i
\(561\) −3.00000 5.19615i −0.126660 0.219382i
\(562\) −8.00000 −0.337460
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) −4.00000 6.92820i −0.168430 0.291730i
\(565\) −28.0000 + 48.4974i −1.17797 + 2.04030i
\(566\) −3.00000 5.19615i −0.126099 0.218411i
\(567\) −1.50000 + 2.59808i −0.0629941 + 0.109109i
\(568\) −1.00000 + 1.73205i −0.0419591 + 0.0726752i
\(569\) −40.0000 −1.67689 −0.838444 0.544988i \(-0.816534\pi\)
−0.838444 + 0.544988i \(0.816534\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) −1.00000 + 1.73205i −0.0418121 + 0.0724207i
\(573\) −3.50000 + 6.06218i −0.146215 + 0.253251i
\(574\) 12.0000 + 20.7846i 0.500870 + 0.867533i
\(575\) 5.50000 9.52628i 0.229366 0.397273i
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) −37.0000 −1.54033 −0.770165 0.637845i \(-0.779826\pi\)
−0.770165 + 0.637845i \(0.779826\pi\)
\(578\) 8.00000 0.332756
\(579\) −3.00000 5.19615i −0.124676 0.215945i
\(580\) 10.0000 + 17.3205i 0.415227 + 0.719195i
\(581\) −18.0000 −0.746766
\(582\) −2.00000 −0.0829027
\(583\) −1.00000 1.73205i −0.0414158 0.0717342i
\(584\) 4.50000 7.79423i 0.186211 0.322527i
\(585\) −4.00000 6.92820i −0.165380 0.286446i
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) 2.00000 0.0824786
\(589\) 0 0
\(590\) −60.0000 −2.47016
\(591\) −4.00000 + 6.92820i −0.164538 + 0.284988i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −17.0000 29.4449i −0.698106 1.20916i −0.969122 0.246581i \(-0.920693\pi\)
0.271016 0.962575i \(-0.412640\pi\)
\(594\) −5.00000 + 8.66025i −0.205152 + 0.355335i
\(595\) 18.0000 + 31.1769i 0.737928 + 1.27813i
\(596\) 0 0
\(597\) −25.0000 −1.02318
\(598\) −0.500000 0.866025i −0.0204465 0.0354144i
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) −11.0000 −0.449073
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 6.00000 + 10.3923i 0.244542 + 0.423559i
\(603\) −3.00000 + 5.19615i −0.122169 + 0.211604i
\(604\) 1.00000 + 1.73205i 0.0406894 + 0.0704761i
\(605\) −14.0000 + 24.2487i −0.569181 + 0.985850i
\(606\) 1.00000 1.73205i 0.0406222 0.0703598i
\(607\) 22.0000 0.892952 0.446476 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 0 0
\(609\) 15.0000 0.607831
\(610\) −4.00000 + 6.92820i −0.161955 + 0.280515i
\(611\) −4.00000 + 6.92820i −0.161823 + 0.280285i
\(612\) 3.00000 + 5.19615i 0.121268 + 0.210042i
\(613\) −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i \(0.407575\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) −32.0000 −1.29036
\(616\) −6.00000 −0.241747
\(617\) −9.00000 15.5885i −0.362326 0.627568i 0.626017 0.779809i \(-0.284684\pi\)
−0.988343 + 0.152242i \(0.951351\pi\)
\(618\) 3.00000 + 5.19615i 0.120678 + 0.209020i
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) −32.0000 −1.28515
\(621\) −2.50000 4.33013i −0.100322 0.173762i
\(622\) 3.50000 6.06218i 0.140337 0.243071i
\(623\) 0 0
\(624\) −0.500000 + 0.866025i −0.0200160 + 0.0346688i
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) −29.0000 −1.15907
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) −3.00000 + 5.19615i −0.119618 + 0.207184i
\(630\) 12.0000 20.7846i 0.478091 0.828079i
\(631\) −16.0000 27.7128i −0.636950 1.10323i −0.986098 0.166162i \(-0.946862\pi\)
0.349148 0.937067i \(-0.386471\pi\)
\(632\) 5.00000 8.66025i 0.198889 0.344486i
\(633\) 13.5000 + 23.3827i 0.536577 + 0.929378i
\(634\) −27.0000 −1.07231
\(635\) 72.0000 2.85723
\(636\) −0.500000 0.866025i −0.0198263 0.0343401i
\(637\) −1.00000 1.73205i −0.0396214 0.0686264i
\(638\) −10.0000 −0.395904
\(639\) 4.00000 0.158238
\(640\) −2.00000 3.46410i −0.0790569 0.136931i
\(641\) 21.0000 36.3731i 0.829450 1.43665i −0.0690201 0.997615i \(-0.521987\pi\)
0.898470 0.439034i \(-0.144679\pi\)
\(642\) 3.50000 + 6.06218i 0.138134 + 0.239255i
\(643\) 13.0000 22.5167i 0.512670 0.887970i −0.487222 0.873278i \(-0.661990\pi\)
0.999892 0.0146923i \(-0.00467688\pi\)
\(644\) 1.50000 2.59808i 0.0591083 0.102379i
\(645\) −16.0000 −0.629999
\(646\) 0 0
\(647\) 23.0000 0.904223 0.452112 0.891961i \(-0.350671\pi\)
0.452112 + 0.891961i \(0.350671\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 15.0000 25.9808i 0.588802 1.01983i
\(650\) 5.50000 + 9.52628i 0.215728 + 0.373651i
\(651\) −12.0000 + 20.7846i −0.470317 + 0.814613i
\(652\) 8.00000 + 13.8564i 0.313304 + 0.542659i
\(653\) −36.0000 −1.40879 −0.704394 0.709809i \(-0.748781\pi\)
−0.704394 + 0.709809i \(0.748781\pi\)
\(654\) −15.0000 −0.586546
\(655\) 24.0000 + 41.5692i 0.937758 + 1.62424i
\(656\) −4.00000 6.92820i −0.156174 0.270501i
\(657\) −18.0000 −0.702247
\(658\) −24.0000 −0.935617
\(659\) 2.50000 + 4.33013i 0.0973862 + 0.168678i 0.910602 0.413284i \(-0.135618\pi\)
−0.813216 + 0.581962i \(0.802285\pi\)
\(660\) 4.00000 6.92820i 0.155700 0.269680i
\(661\) −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i \(-0.314280\pi\)
−0.998209 + 0.0598209i \(0.980947\pi\)
\(662\) −8.50000 + 14.7224i −0.330362 + 0.572204i
\(663\) −1.50000 + 2.59808i −0.0582552 + 0.100901i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 2.50000 4.33013i 0.0968004 0.167663i
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) 7.00000 + 12.1244i 0.270636 + 0.468755i
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) −2.00000 3.46410i −0.0772091 0.133730i
\(672\) −3.00000 −0.115728
\(673\) −44.0000 −1.69608 −0.848038 0.529936i \(-0.822216\pi\)
−0.848038 + 0.529936i \(0.822216\pi\)
\(674\) 16.0000 + 27.7128i 0.616297 + 1.06746i
\(675\) 27.5000 + 47.6314i 1.05848 + 1.83333i
\(676\) −12.0000 −0.461538
\(677\) −13.0000 −0.499631 −0.249815 0.968294i \(-0.580370\pi\)
−0.249815 + 0.968294i \(0.580370\pi\)
\(678\) −7.00000 12.1244i −0.268833 0.465633i
\(679\) −3.00000 + 5.19615i −0.115129 + 0.199410i
\(680\) −6.00000 10.3923i −0.230089 0.398527i
\(681\) −8.50000 + 14.7224i −0.325721 + 0.564165i
\(682\) 8.00000 13.8564i 0.306336 0.530589i
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) 68.0000 2.59815
\(686\) −7.50000 + 12.9904i −0.286351 + 0.495975i
\(687\) 5.00000 8.66025i 0.190762 0.330409i
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −0.500000 + 0.866025i −0.0190485 + 0.0329929i
\(690\) 2.00000 + 3.46410i 0.0761387 + 0.131876i
\(691\) 42.0000 1.59776 0.798878 0.601494i \(-0.205427\pi\)
0.798878 + 0.601494i \(0.205427\pi\)
\(692\) 6.00000 0.228086
\(693\) 6.00000 + 10.3923i 0.227921 + 0.394771i
\(694\) −1.00000 1.73205i −0.0379595 0.0657477i
\(695\) 0 0
\(696\) −5.00000 −0.189525
\(697\) −12.0000 20.7846i −0.454532 0.787273i
\(698\) 5.00000 8.66025i 0.189253 0.327795i
\(699\) 3.00000 + 5.19615i 0.113470 + 0.196537i
\(700\) −16.5000 + 28.5788i −0.623641 + 1.08018i
\(701\) 14.0000 24.2487i 0.528773 0.915861i −0.470664 0.882312i \(-0.655986\pi\)
0.999437 0.0335489i \(-0.0106809\pi\)
\(702\) 5.00000 0.188713
\(703\) 0 0
\(704\) 2.00000 0.0753778
\(705\) 16.0000 27.7128i 0.602595 1.04372i
\(706\) 4.50000 7.79423i 0.169360 0.293340i
\(707\) −3.00000 5.19615i −0.112827 0.195421i
\(708\) 7.50000 12.9904i 0.281867 0.488208i
\(709\) 15.0000 + 25.9808i 0.563337 + 0.975728i 0.997202 + 0.0747503i \(0.0238160\pi\)
−0.433865 + 0.900978i \(0.642851\pi\)
\(710\) −8.00000 −0.300235
\(711\) −20.0000 −0.750059
\(712\) 0 0
\(713\) 4.00000 + 6.92820i 0.149801 + 0.259463i
\(714\) −9.00000 −0.336817
\(715\) −8.00000 −0.299183
\(716\) 0 0
\(717\) −7.50000 + 12.9904i −0.280093 + 0.485135i
\(718\) −7.50000 12.9904i −0.279898 0.484797i
\(719\) 2.50000 4.33013i 0.0932343 0.161486i −0.815636 0.578565i \(-0.803613\pi\)
0.908870 + 0.417079i \(0.136946\pi\)
\(720\) −4.00000 + 6.92820i −0.149071 + 0.258199i
\(721\) 18.0000 0.670355
\(722\) 0 0
\(723\) 8.00000 0.297523
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) −27.5000 + 47.6314i −1.02132 + 1.76899i
\(726\) −3.50000 6.06218i −0.129897 0.224989i
\(727\) 8.50000 14.7224i 0.315248 0.546025i −0.664243 0.747517i \(-0.731246\pi\)
0.979490 + 0.201492i \(0.0645791\pi\)
\(728\) 1.50000 + 2.59808i 0.0555937 + 0.0962911i
\(729\) 13.0000 0.481481
\(730\) 36.0000 1.33242
\(731\) −6.00000 10.3923i −0.221918 0.384373i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) −36.0000 −1.32969 −0.664845 0.746981i \(-0.731502\pi\)
−0.664845 + 0.746981i \(0.731502\pi\)
\(734\) −28.0000 −1.03350
\(735\) 4.00000 + 6.92820i 0.147542 + 0.255551i
\(736\) −0.500000 + 0.866025i −0.0184302 + 0.0319221i
\(737\) 3.00000 + 5.19615i 0.110506 + 0.191403i
\(738\) −8.00000 + 13.8564i −0.294484 + 0.510061i
\(739\) 20.0000 34.6410i 0.735712 1.27429i −0.218698 0.975793i \(-0.570181\pi\)
0.954410 0.298498i \(-0.0964856\pi\)
\(740\) −8.00000 −0.294086
\(741\) 0 0
\(742\) −3.00000 −0.110133
\(743\) −8.00000 + 13.8564i −0.293492 + 0.508342i −0.974633 0.223810i \(-0.928151\pi\)
0.681141 + 0.732152i \(0.261484\pi\)
\(744\) 4.00000 6.92820i 0.146647 0.254000i
\(745\) 0 0
\(746\) −14.5000 + 25.1147i −0.530883 + 0.919516i
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) 6.00000 0.219382
\(749\) 21.0000 0.767323
\(750\) −12.0000 20.7846i −0.438178 0.758947i
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) 8.00000 0.291730
\(753\) 2.00000 0.0728841
\(754\) 2.50000 + 4.33013i 0.0910446 + 0.157694i
\(755\) −4.00000 + 6.92820i −0.145575 + 0.252143i
\(756\) 7.50000 + 12.9904i 0.272772 + 0.472456i
\(757\) 1.00000 1.73205i 0.0363456 0.0629525i −0.847280 0.531146i \(-0.821762\pi\)
0.883626 + 0.468193i \(0.155095\pi\)
\(758\) −7.50000 + 12.9904i −0.272412 + 0.471832i
\(759\) −2.00000 −0.0725954
\(760\) 0 0
\(761\) 27.0000 0.978749 0.489375 0.872074i \(-0.337225\pi\)
0.489375 + 0.872074i \(0.337225\pi\)
\(762\) −9.00000 + 15.5885i −0.326036 + 0.564710i
\(763\) −22.5000 + 38.9711i −0.814555 + 1.41085i
\(764\) −3.50000 6.06218i −0.126626 0.219322i
\(765\) −12.0000 + 20.7846i −0.433861 + 0.751469i
\(766\) 13.0000 + 22.5167i 0.469709 + 0.813560i
\(767\) −15.0000 −0.541619
\(768\) 1.00000 0.0360844
\(769\) 17.5000 + 30.3109i 0.631066 + 1.09304i 0.987334 + 0.158655i \(0.0507157\pi\)
−0.356268 + 0.934384i \(0.615951\pi\)
\(770\) −12.0000 20.7846i −0.432450 0.749025i
\(771\) −8.00000 −0.288113
\(772\) 6.00000 0.215945
\(773\) 4.50000 + 7.79423i 0.161854 + 0.280339i 0.935534 0.353238i \(-0.114919\pi\)
−0.773680 + 0.633577i \(0.781586\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) −44.0000 76.2102i −1.58053 2.73755i
\(776\) 1.00000 1.73205i 0.0358979 0.0621770i
\(777\) −3.00000 + 5.19615i −0.107624 + 0.186411i
\(778\) 30.0000 1.07555
\(779\) 0 0
\(780\) −4.00000 −0.143223