Properties

Label 722.2.c.d.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.d.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 −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −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 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) −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 0.999167 0.0408130i \(-0.0129948\pi\)
−0.534928 + 0.844897i \(0.679661\pi\)
\(30\) 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 −0.363905 0.931436i \(-0.618557\pi\)
0.988600 0.150567i \(-0.0481100\pi\)
\(42\) 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 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) −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 \(0.597400\pi\)
−0.675178 + 0.737655i \(0.735933\pi\)
\(60\) −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 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) 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 −0.919244 0.393688i \(-0.871199\pi\)
0.800566 + 0.599245i \(0.204532\pi\)
\(72\) 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 \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 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 −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) −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 \(-0.595519\pi\)
−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 −0.243276 0.969957i \(-0.578222\pi\)
0.961645 0.274296i \(-0.0884447\pi\)
\(110\) 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 −0.920514 0.390709i \(-0.872230\pi\)
0.121894 0.992543i \(-0.461103\pi\)
\(128\) −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 \(-0.474068\pi\)
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 −0.823359 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 0.999169 0.0407502i \(-0.0129748\pi\)
−0.534875 + 0.844931i \(0.679641\pi\)
\(168\) 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 −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −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 \(-0.861958\pi\)
0.0898051 0.995959i \(-0.471376\pi\)
\(182\) −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 −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) 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 \(0.546323\pi\)
−0.784364 + 0.620301i \(0.787010\pi\)
\(212\) 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 −0.999362 0.0357107i \(-0.988630\pi\)
0.530607 + 0.847618i \(0.321964\pi\)
\(224\) −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 −0.750867 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 0.965615 0.259975i \(-0.0837143\pi\)
−0.707953 + 0.706260i \(0.750381\pi\)
\(242\) 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 0.713878 0.700270i \(-0.246937\pi\)
−0.963391 + 0.268101i \(0.913604\pi\)
\(258\) −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 \(0.534134\pi\)
−0.807535 + 0.589819i \(0.799199\pi\)
\(270\) 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 0.960319 0.278906i \(-0.0899716\pi\)
−0.721699 + 0.692207i \(0.756638\pi\)
\(282\) 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 \(-0.415323\pi\)
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 −0.642447 0.766330i \(-0.722081\pi\)
0.984885 + 0.173210i \(0.0554140\pi\)
\(308\) −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 \(0.107272\pi\)
−0.185514 + 0.982642i \(0.559395\pi\)
\(318\) −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 0.0112091 0.999937i \(-0.496432\pi\)
0.860366 0.509676i \(-0.170235\pi\)
\(338\) 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 \(-0.229677\pi\)
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 −0.315214 0.949021i \(-0.602076\pi\)
0.979483 0.201527i \(-0.0645904\pi\)
\(384\) 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 −0.748697 0.662912i \(-0.769320\pi\)
0.948447 + 0.316934i \(0.102654\pi\)
\(402\) 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 0.999980 0.00637586i \(-0.00202951\pi\)
−0.505511 + 0.862820i \(0.668696\pi\)
\(410\) 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 −0.663026 0.748596i \(-0.730728\pi\)
0.979817 + 0.199899i \(0.0640614\pi\)
\(422\) −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 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) −7.00000 12.1244i −0.336399 0.582659i 0.647354 0.762190i \(-0.275876\pi\)
−0.983752 + 0.179530i \(0.942542\pi\)
\(434\) 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 −0.999661 0.0260459i \(-0.991708\pi\)
0.522387 + 0.852709i \(0.325042\pi\)
\(440\) 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 \(-0.424175\pi\)
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 −0.330581 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 \(-0.514429\pi\)
−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 −0.355370 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 \(0.0648436\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(510\) −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 −0.986718 0.162446i \(-0.948062\pi\)
0.352677 0.935745i \(-0.385272\pi\)
\(524\) 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 \(-0.962392\pi\)
0.394432 0.918925i \(-0.370941\pi\)
\(548\) 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 \(-0.774121\pi\)
−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 −0.715226 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 \(-0.552170\pi\)
−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 0.286300 + 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 \(0.478013\pi\)
−0.898470 + 0.439034i \(0.855321\pi\)
\(642\) −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 0.813216 0.581962i \(-0.197715\pi\)
−0.910602 + 0.413284i \(0.864382\pi\)
\(660\) −4.00000 + 6.92820i −0.155700 + 0.269680i
\(661\) 11.5000 + 19.9186i 0.447298 + 0.774743i 0.998209 0.0598209i \(-0.0190530\pi\)
−0.550911 + 0.834564i \(0.685720\pi\)
\(662\) −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 −0.470664 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 −0.681141 0.732152i \(-0.738516\pi\)
0.974633 + 0.223810i \(0.0718494\pi\)
\(744\) −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 \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) 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 0.773680 0.633577i \(-0.218414\pi\)
−0.935534 + 0.353238i \(0.885081\pi\)
\(774\) 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
\(782\) 1.50000 2.59808i 0.0536399 0.0929070i
\(783\) 12.5000 + 21.6506i 0.446714 + 0.773731i
\(784\) −1.00000 + 1.73205i −0.0357143 + 0.0618590i
\(785\) −4.00000 6.92820i −0.142766 0.247278i
\(786\) −12.0000 −0.428026
\(787\) −17.0000 −0.605985 −0.302992 0.952993i \(-0.597986\pi\)
−0.302992 + 0.952993i \(0.597986\pi\)
\(788\) −4.00000 6.92820i −0.142494 0.246807i
\(789\) 12.0000 + 20.7846i 0.427211 + 0.739952i
\(790\) 40.0000 1.42314
\(791\) 42.0000 1.49335
\(792\) 2.00000 + 3.46410i 0.0710669 + 0.123091i
\(793\) 1.00000 1.73205i 0.0355110 0.0615069i
\(794\) −4.00000 6.92820i −0.141955