Properties

Label 722.2.c.d.653.1
Level $722$
Weight $2$
Character 722.653
Analytic conductor $5.765$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 653.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 722.653
Dual form 722.2.c.d.429.1

$q$-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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i \(0.185750\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) 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 \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) −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 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) −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 −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) 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 \(-0.679661\pi\)
0.999167 + 0.0408130i \(0.0129948\pi\)
\(30\) 4.00000 0.730297
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −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 \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 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 0.988600 + 0.150567i \(0.0481100\pi\)
−0.363905 + 0.931436i \(0.618557\pi\)
\(42\) 1.50000 2.59808i 0.231455 0.400892i
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) −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 0.411606 + 0.911362i \(0.364968\pi\)
−0.995066 + 0.0992202i \(0.968365\pi\)
\(48\) 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 \(-0.811454\pi\)
0.898321 + 0.439340i \(0.144788\pi\)
\(54\) −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 −0.675178 0.737655i \(-0.735933\pi\)
−0.301239 0.953549i \(-0.597400\pi\)
\(60\) −2.00000 3.46410i −0.258199 0.447214i
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 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 \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) 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 \(-0.204532\pi\)
−0.919244 + 0.393688i \(0.871199\pi\)
\(72\) 1.00000 1.73205i 0.117851 0.204124i
\(73\) −4.50000 7.79423i −0.526685 0.912245i −0.999517 0.0310925i \(-0.990101\pi\)
0.472831 0.881153i \(-0.343232\pi\)
\(74\) 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 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) −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 \(-0.134291\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) −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 −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) −3.00000 −0.297044
\(103\) −6.00000 −0.591198 −0.295599 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 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 \(-0.609871\pi\)
−0.338358 + 0.941018i \(0.609871\pi\)
\(108\) −2.50000 + 4.33013i −0.240563 + 0.416667i
\(109\) 7.50000 + 12.9904i 0.718370 + 1.24425i 0.961645 + 0.274296i \(0.0884447\pi\)
−0.243276 + 0.969957i \(0.578222\pi\)
\(110\) 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 \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 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 0.121894 + 0.992543i \(0.461103\pi\)
−0.920514 + 0.390709i \(0.872230\pi\)
\(128\) −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 −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) −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 −0.232273 0.972651i \(-0.574616\pi\)
0.958477 0.285171i \(-0.0920506\pi\)
\(138\) −0.500000 0.866025i −0.0425628 0.0737210i
\(139\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 5.50000 + 9.52628i 0.449073 + 0.777817i
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 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 0.903167 0.429289i \(-0.141236\pi\)
−0.823359 + 0.567521i \(0.807902\pi\)
\(158\) 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 \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 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 \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) −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 0.0898051 + 0.995959i \(0.471376\pi\)
−0.907429 + 0.420206i \(0.861958\pi\)
\(182\) −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 \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) 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 0.0416556 0.999132i \(-0.486737\pi\)
0.844446 0.535641i \(-0.179930\pi\)
\(200\) −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 −0.784364 0.620301i \(-0.787010\pi\)
−0.145014 0.989430i \(-0.546323\pi\)
\(212\) 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 \(-0.321964\pi\)
−0.999362 + 0.0357107i \(0.988630\pi\)
\(224\) −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 \(-0.690802\pi\)
−0.564165 + 0.825662i \(0.690802\pi\)
\(228\) 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 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) −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 \(-0.750381\pi\)
0.965615 + 0.259975i \(0.0837143\pi\)
\(242\) 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 −0.895858 0.444340i \(-0.853438\pi\)
0.832739 + 0.553666i \(0.186772\pi\)
\(252\) 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 \(-0.913604\pi\)
0.713878 + 0.700270i \(0.246937\pi\)
\(258\) −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 −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 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 −0.807535 0.589819i \(-0.799199\pi\)
−0.107031 0.994256i \(-0.534134\pi\)
\(270\) 10.0000 17.3205i 0.608581 1.05409i
\(271\) −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i \(-0.234863\pi\)
−0.952531 + 0.304443i \(0.901530\pi\)
\(272\) −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 \(-0.756638\pi\)
0.960319 + 0.278906i \(0.0899716\pi\)
\(282\) 4.00000 + 6.92820i 0.238197 + 0.412568i
\(283\) 3.00000 + 5.19615i 0.178331 + 0.308879i 0.941309 0.337546i \(-0.109597\pi\)
−0.762978 + 0.646425i \(0.776263\pi\)
\(284\) 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 \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 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 \(-0.0554140\pi\)
−0.642447 + 0.766330i \(0.722081\pi\)
\(308\) −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 0.0863973 + 0.996261i \(0.472465\pi\)
−0.905986 + 0.423308i \(0.860869\pi\)
\(314\) 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 −0.185514 0.982642i \(-0.559395\pi\)
0.943750 0.330661i \(-0.107272\pi\)
\(318\) −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 \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 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 0.860366 + 0.509676i \(0.170235\pi\)
0.0112091 + 0.999937i \(0.496432\pi\)
\(338\) 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 0.891618 0.452788i \(-0.149571\pi\)
−0.837935 + 0.545770i \(0.816237\pi\)
\(348\) −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 0.993207 0.116358i \(-0.0371219\pi\)
−0.597372 + 0.801964i \(0.703789\pi\)
\(360\) 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 0.225750 + 0.974185i \(0.427517\pi\)
−0.956544 + 0.291587i \(0.905817\pi\)
\(368\) −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 \(-0.229677\pi\)
0.750782 + 0.660551i \(0.229677\pi\)
\(374\) −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 \(-0.374116\pi\)
0.385249 + 0.922813i \(0.374116\pi\)
\(380\) 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 0.979483 + 0.201527i \(0.0645904\pi\)
−0.315214 + 0.949021i \(0.602076\pi\)
\(384\) 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 −0.182047 0.983290i \(-0.558272\pi\)
0.942578 0.333987i \(-0.108394\pi\)
\(390\) 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 0.748017 0.663679i \(-0.231006\pi\)
−0.948772 + 0.315963i \(0.897673\pi\)
\(398\) −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 \(-0.102654\pi\)
−0.748697 + 0.662912i \(0.769320\pi\)
\(402\) 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 \(-0.668696\pi\)
0.999980 + 0.00637586i \(0.00202951\pi\)
\(410\) 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 \(-0.0640614\pi\)
−0.663026 + 0.748596i \(0.730728\pi\)
\(422\) −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 \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) −2.50000 4.33013i −0.120281 0.208333i
\(433\) −7.00000 + 12.1244i −0.336399 + 0.582659i −0.983752 0.179530i \(-0.942542\pi\)
0.647354 + 0.762190i \(0.275876\pi\)
\(434\) 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 \(-0.325042\pi\)
−0.999661 + 0.0260459i \(0.991708\pi\)
\(440\) 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 −0.372265 0.928126i \(-0.621419\pi\)
0.989914 0.141672i \(-0.0452479\pi\)
\(444\) 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 \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 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 0.982626 + 0.185597i \(0.0594220\pi\)
−0.330581 + 0.943778i \(0.607245\pi\)
\(462\) 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 −0.541884 0.840453i \(-0.682289\pi\)
0.998796 + 0.0490589i \(0.0156222\pi\)
\(480\) −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 \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) −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 0.987181 + 0.159603i \(0.0510215\pi\)
−0.355370 + 0.934726i \(0.615645\pi\)
\(492\) −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 −0.833404 0.552664i \(-0.813611\pi\)
−0.0619186 0.998081i \(-0.519722\pi\)
\(500\) 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 −0.00691465 + 0.999976i \(0.502201\pi\)
−0.862547 + 0.505976i \(0.831132\pi\)
\(504\) 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 −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) −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 \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) −5.00000 + 8.66025i −0.218844 + 0.379049i
\(523\) −14.5000 + 25.1147i −0.634041 + 1.09819i 0.352677 + 0.935745i \(0.385272\pi\)
−0.986718 + 0.162446i \(0.948062\pi\)
\(524\) 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 −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) −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 0.394432 + 0.918925i \(0.370941\pi\)
−0.993028 + 0.117875i \(0.962392\pi\)
\(548\) 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 0.400599 + 0.916253i \(0.368802\pi\)
−0.993798 + 0.111198i \(0.964531\pi\)
\(558\) 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 \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) 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 \(-0.183466\pi\)
0.838444 + 0.544988i \(0.183466\pi\)
\(570\) 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 0.962872 0.269957i \(-0.0870095\pi\)
−0.715226 + 0.698893i \(0.753676\pi\)
\(588\) −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 0.271016 + 0.962575i \(0.412640\pi\)
−0.969122 + 0.246581i \(0.920693\pi\)
\(594\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) −11.0000 −0.449073
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) −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 \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 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 −0.972924 0.231127i \(-0.925759\pi\)
0.286300 0.958140i \(-0.407575\pi\)
\(614\) 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 −0.988343 0.152242i \(-0.951351\pi\)
0.626017 + 0.779809i \(0.284684\pi\)
\(618\) −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 0.349148 + 0.937067i \(0.386471\pi\)
−0.986098 + 0.166162i \(0.946862\pi\)
\(632\) 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 −0.898470 0.439034i \(-0.855321\pi\)
0.0690201 0.997615i \(-0.478013\pi\)
\(642\) −3.50000 + 6.06218i −0.138134 + 0.239255i
\(643\) 13.0000 + 22.5167i 0.512670 + 0.887970i 0.999892 + 0.0146923i \(0.00467688\pi\)
−0.487222 + 0.873278i \(0.661990\pi\)
\(644\) 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 \(-0.864382\pi\)
0.813216 + 0.581962i \(0.197715\pi\)
\(660\) −4.00000 6.92820i −0.155700 0.269680i
\(661\) 11.5000 19.9186i 0.447298 0.774743i −0.550911 0.834564i \(-0.685720\pi\)
0.998209 + 0.0598209i \(0.0190530\pi\)
\(662\) −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 \(-0.177784\pi\)
0.848038 + 0.529936i \(0.177784\pi\)
\(674\) 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 \(-0.419630\pi\)
0.249815 + 0.968294i \(0.419630\pi\)
\(678\) 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 \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 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 0.999437 + 0.0335489i \(0.0106809\pi\)
−0.470664 + 0.882312i \(0.655986\pi\)
\(702\) −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 −0.433865 0.900978i \(-0.642851\pi\)
0.997202 0.0747503i \(-0.0238160\pi\)
\(710\) −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 0.908870 0.417079i \(-0.136946\pi\)
−0.815636 + 0.578565i \(0.803613\pi\)
\(720\) −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 0.979490 0.201492i \(-0.0645791\pi\)
−0.664243 + 0.747517i \(0.731246\pi\)
\(728\) 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 0.954410 + 0.298498i \(0.0964856\pi\)
−0.218698 + 0.975793i \(0.570181\pi\)
\(740\) 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 \(-0.0718494\pi\)
−0.681141 + 0.732152i \(0.738516\pi\)
\(744\) −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 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 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 0.883626 0.468193i \(-0.155095\pi\)
−0.847280 + 0.531146i \(0.821762\pi\)
\(758\) −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 −0.356268 0.934384i \(-0.615951\pi\)
0.987334 0.158655i \(-0.0507157\pi\)
\(770\) 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 \(-0.885081\pi\)
0.773680 + 0.633577i \(0.218414\pi\)
\(774\) 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
\(781\) −2.00000 3.46410i −0.0715656 0.123955i