Properties

Label 462.2.k.a.89.2
Level $462$
Weight $2$
Character 462.89
Analytic conductor $3.689$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 462.89
Dual form 462.2.k.a.353.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.73205 - 3.00000i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.73205 - 3.00000i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.866025 - 1.50000i) q^{12} -3.46410i q^{13} +(0.866025 + 2.50000i) q^{14} -6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.866025 - 1.50000i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(-1.50000 - 0.866025i) q^{19} +3.46410 q^{20} +(0.866025 - 4.50000i) q^{21} +1.00000 q^{22} +(2.59808 + 1.50000i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-3.50000 - 6.06218i) q^{25} +(1.73205 - 3.00000i) q^{26} +5.19615 q^{27} +(-0.500000 + 2.59808i) q^{28} -3.00000i q^{29} +(-5.19615 - 3.00000i) q^{30} +(3.00000 - 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} -1.73205i q^{34} +(8.66025 - 3.00000i) q^{35} -3.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(-0.866025 - 1.50000i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(3.00000 + 1.73205i) q^{40} -6.92820 q^{41} +(3.00000 - 3.46410i) q^{42} +1.00000 q^{43} +(0.866025 + 0.500000i) q^{44} +(5.19615 + 9.00000i) q^{45} +(1.50000 + 2.59808i) q^{46} +(-0.866025 + 1.50000i) q^{47} +1.73205 q^{48} +(1.00000 + 6.92820i) q^{49} -7.00000i q^{50} +(-1.50000 + 2.59808i) q^{51} +(3.00000 - 1.73205i) q^{52} +(4.50000 + 2.59808i) q^{54} -3.46410i q^{55} +(-1.73205 + 2.00000i) q^{56} +3.00000i q^{57} +(1.50000 - 2.59808i) q^{58} +(6.06218 + 10.5000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(9.00000 + 5.19615i) q^{61} +3.46410 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-10.3923 - 6.00000i) q^{65} +(-0.866025 - 1.50000i) q^{66} +(8.00000 + 13.8564i) q^{67} +(0.866025 - 1.50000i) q^{68} -5.19615i q^{69} +(9.00000 + 1.73205i) q^{70} -15.0000i q^{71} +(-2.59808 - 1.50000i) q^{72} +(-12.0000 + 6.92820i) q^{73} +(-6.06218 + 3.50000i) q^{74} +(-6.06218 + 10.5000i) q^{75} -1.73205i q^{76} +(2.59808 + 0.500000i) q^{77} -6.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(1.73205 + 3.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 3.46410i) q^{82} -17.3205 q^{83} +(4.33013 - 1.50000i) q^{84} -6.00000 q^{85} +(0.866025 + 0.500000i) q^{86} +(-4.50000 + 2.59808i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-5.19615 + 9.00000i) q^{89} +10.3923i q^{90} +(6.00000 - 6.92820i) q^{91} +3.00000i q^{92} +(-5.19615 - 3.00000i) q^{93} +(-1.50000 + 0.866025i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(1.50000 + 0.866025i) q^{96} -15.5885i q^{97} +(-2.59808 + 6.50000i) q^{98} +3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 8q^{7} - 6q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 8q^{7} - 6q^{9} + 12q^{10} - 24q^{15} - 2q^{16} - 6q^{19} + 4q^{22} + 6q^{24} - 14q^{25} - 2q^{28} + 12q^{31} - 6q^{33} - 12q^{36} - 14q^{37} + 12q^{40} + 12q^{42} + 4q^{43} + 6q^{46} + 4q^{49} - 6q^{51} + 12q^{52} + 18q^{54} + 6q^{58} - 12q^{60} + 36q^{61} - 30q^{63} - 4q^{64} + 32q^{67} + 36q^{70} - 48q^{73} - 24q^{78} - 16q^{79} - 18q^{81} - 24q^{82} - 24q^{85} - 18q^{87} + 2q^{88} + 24q^{91} - 6q^{94} + 6q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.866025 1.50000i −0.500000 0.866025i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.73205 3.00000i 0.774597 1.34164i −0.160424 0.987048i \(-0.551286\pi\)
0.935021 0.354593i \(-0.115380\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) 3.00000 1.73205i 0.948683 0.547723i
\(11\) 0.866025 0.500000i 0.261116 0.150756i
\(12\) 0.866025 1.50000i 0.250000 0.433013i
\(13\) 3.46410i 0.960769i −0.877058 0.480384i \(-0.840497\pi\)
0.877058 0.480384i \(-0.159503\pi\)
\(14\) 0.866025 + 2.50000i 0.231455 + 0.668153i
\(15\) −6.00000 −1.54919
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.866025 1.50000i −0.210042 0.363803i 0.741685 0.670748i \(-0.234027\pi\)
−0.951727 + 0.306944i \(0.900693\pi\)
\(18\) −2.59808 + 1.50000i −0.612372 + 0.353553i
\(19\) −1.50000 0.866025i −0.344124 0.198680i 0.317970 0.948101i \(-0.396999\pi\)
−0.662094 + 0.749421i \(0.730332\pi\)
\(20\) 3.46410 0.774597
\(21\) 0.866025 4.50000i 0.188982 0.981981i
\(22\) 1.00000 0.213201
\(23\) 2.59808 + 1.50000i 0.541736 + 0.312772i 0.745782 0.666190i \(-0.232076\pi\)
−0.204046 + 0.978961i \(0.565409\pi\)
\(24\) 1.50000 0.866025i 0.306186 0.176777i
\(25\) −3.50000 6.06218i −0.700000 1.21244i
\(26\) 1.73205 3.00000i 0.339683 0.588348i
\(27\) 5.19615 1.00000
\(28\) −0.500000 + 2.59808i −0.0944911 + 0.490990i
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) −5.19615 3.00000i −0.948683 0.547723i
\(31\) 3.00000 1.73205i 0.538816 0.311086i −0.205783 0.978598i \(-0.565974\pi\)
0.744599 + 0.667512i \(0.232641\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −1.50000 0.866025i −0.261116 0.150756i
\(34\) 1.73205i 0.297044i
\(35\) 8.66025 3.00000i 1.46385 0.507093i
\(36\) −3.00000 −0.500000
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) −0.866025 1.50000i −0.140488 0.243332i
\(39\) −5.19615 + 3.00000i −0.832050 + 0.480384i
\(40\) 3.00000 + 1.73205i 0.474342 + 0.273861i
\(41\) −6.92820 −1.08200 −0.541002 0.841021i \(-0.681955\pi\)
−0.541002 + 0.841021i \(0.681955\pi\)
\(42\) 3.00000 3.46410i 0.462910 0.534522i
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0.866025 + 0.500000i 0.130558 + 0.0753778i
\(45\) 5.19615 + 9.00000i 0.774597 + 1.34164i
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) −0.866025 + 1.50000i −0.126323 + 0.218797i −0.922249 0.386596i \(-0.873651\pi\)
0.795926 + 0.605393i \(0.206984\pi\)
\(48\) 1.73205 0.250000
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 7.00000i 0.989949i
\(51\) −1.50000 + 2.59808i −0.210042 + 0.363803i
\(52\) 3.00000 1.73205i 0.416025 0.240192i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 3.46410i 0.467099i
\(56\) −1.73205 + 2.00000i −0.231455 + 0.267261i
\(57\) 3.00000i 0.397360i
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 6.06218 + 10.5000i 0.789228 + 1.36698i 0.926440 + 0.376442i \(0.122853\pi\)
−0.137212 + 0.990542i \(0.543814\pi\)
\(60\) −3.00000 5.19615i −0.387298 0.670820i
\(61\) 9.00000 + 5.19615i 1.15233 + 0.665299i 0.949454 0.313905i \(-0.101637\pi\)
0.202878 + 0.979204i \(0.434971\pi\)
\(62\) 3.46410 0.439941
\(63\) −7.50000 + 2.59808i −0.944911 + 0.327327i
\(64\) −1.00000 −0.125000
\(65\) −10.3923 6.00000i −1.28901 0.744208i
\(66\) −0.866025 1.50000i −0.106600 0.184637i
\(67\) 8.00000 + 13.8564i 0.977356 + 1.69283i 0.671932 + 0.740613i \(0.265465\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) 0.866025 1.50000i 0.105021 0.181902i
\(69\) 5.19615i 0.625543i
\(70\) 9.00000 + 1.73205i 1.07571 + 0.207020i
\(71\) 15.0000i 1.78017i −0.455792 0.890086i \(-0.650644\pi\)
0.455792 0.890086i \(-0.349356\pi\)
\(72\) −2.59808 1.50000i −0.306186 0.176777i
\(73\) −12.0000 + 6.92820i −1.40449 + 0.810885i −0.994850 0.101361i \(-0.967680\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −6.06218 + 3.50000i −0.704714 + 0.406867i
\(75\) −6.06218 + 10.5000i −0.700000 + 1.21244i
\(76\) 1.73205i 0.198680i
\(77\) 2.59808 + 0.500000i 0.296078 + 0.0569803i
\(78\) −6.00000 −0.679366
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 1.73205 + 3.00000i 0.193649 + 0.335410i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −6.00000 3.46410i −0.662589 0.382546i
\(83\) −17.3205 −1.90117 −0.950586 0.310460i \(-0.899517\pi\)
−0.950586 + 0.310460i \(0.899517\pi\)
\(84\) 4.33013 1.50000i 0.472456 0.163663i
\(85\) −6.00000 −0.650791
\(86\) 0.866025 + 0.500000i 0.0933859 + 0.0539164i
\(87\) −4.50000 + 2.59808i −0.482451 + 0.278543i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −5.19615 + 9.00000i −0.550791 + 0.953998i 0.447427 + 0.894321i \(0.352341\pi\)
−0.998218 + 0.0596775i \(0.980993\pi\)
\(90\) 10.3923i 1.09545i
\(91\) 6.00000 6.92820i 0.628971 0.726273i
\(92\) 3.00000i 0.312772i
\(93\) −5.19615 3.00000i −0.538816 0.311086i
\(94\) −1.50000 + 0.866025i −0.154713 + 0.0893237i
\(95\) −5.19615 + 3.00000i −0.533114 + 0.307794i
\(96\) 1.50000 + 0.866025i 0.153093 + 0.0883883i
\(97\) 15.5885i 1.58277i −0.611319 0.791384i \(-0.709361\pi\)
0.611319 0.791384i \(-0.290639\pi\)
\(98\) −2.59808 + 6.50000i −0.262445 + 0.656599i
\(99\) 3.00000i 0.301511i
\(100\) 3.50000 6.06218i 0.350000 0.606218i
\(101\) 2.59808 + 4.50000i 0.258518 + 0.447767i 0.965845 0.259120i \(-0.0834325\pi\)
−0.707327 + 0.706887i \(0.750099\pi\)
\(102\) −2.59808 + 1.50000i −0.257248 + 0.148522i
\(103\) 15.0000 + 8.66025i 1.47799 + 0.853320i 0.999691 0.0248745i \(-0.00791862\pi\)
0.478303 + 0.878195i \(0.341252\pi\)
\(104\) 3.46410 0.339683
\(105\) −12.0000 10.3923i −1.17108 1.01419i
\(106\) 0 0
\(107\) 5.19615 + 3.00000i 0.502331 + 0.290021i 0.729676 0.683793i \(-0.239671\pi\)
−0.227345 + 0.973814i \(0.573004\pi\)
\(108\) 2.59808 + 4.50000i 0.250000 + 0.433013i
\(109\) −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i \(-0.888782\pi\)
0.173316 0.984866i \(-0.444552\pi\)
\(110\) 1.73205 3.00000i 0.165145 0.286039i
\(111\) 12.1244 1.15079
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) −1.50000 + 2.59808i −0.140488 + 0.243332i
\(115\) 9.00000 5.19615i 0.839254 0.484544i
\(116\) 2.59808 1.50000i 0.241225 0.139272i
\(117\) 9.00000 + 5.19615i 0.832050 + 0.480384i
\(118\) 12.1244i 1.11614i
\(119\) 0.866025 4.50000i 0.0793884 0.412514i
\(120\) 6.00000i 0.547723i
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 5.19615 + 9.00000i 0.470438 + 0.814822i
\(123\) 6.00000 + 10.3923i 0.541002 + 0.937043i
\(124\) 3.00000 + 1.73205i 0.269408 + 0.155543i
\(125\) −6.92820 −0.619677
\(126\) −7.79423 1.50000i −0.694365 0.133631i
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −0.866025 1.50000i −0.0762493 0.132068i
\(130\) −6.00000 10.3923i −0.526235 0.911465i
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 1.73205i 0.150756i
\(133\) −1.50000 4.33013i −0.130066 0.375470i
\(134\) 16.0000i 1.38219i
\(135\) 9.00000 15.5885i 0.774597 1.34164i
\(136\) 1.50000 0.866025i 0.128624 0.0742611i
\(137\) −15.5885 + 9.00000i −1.33181 + 0.768922i −0.985577 0.169226i \(-0.945873\pi\)
−0.346235 + 0.938148i \(0.612540\pi\)
\(138\) 2.59808 4.50000i 0.221163 0.383065i
\(139\) 1.73205i 0.146911i −0.997299 0.0734553i \(-0.976597\pi\)
0.997299 0.0734553i \(-0.0234026\pi\)
\(140\) 6.92820 + 6.00000i 0.585540 + 0.507093i
\(141\) 3.00000 0.252646
\(142\) 7.50000 12.9904i 0.629386 1.09013i
\(143\) −1.73205 3.00000i −0.144841 0.250873i
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) −9.00000 5.19615i −0.747409 0.431517i
\(146\) −13.8564 −1.14676
\(147\) 9.52628 7.50000i 0.785714 0.618590i
\(148\) −7.00000 −0.575396
\(149\) 7.79423 + 4.50000i 0.638528 + 0.368654i 0.784047 0.620701i \(-0.213152\pi\)
−0.145519 + 0.989355i \(0.546485\pi\)
\(150\) −10.5000 + 6.06218i −0.857321 + 0.494975i
\(151\) 5.50000 + 9.52628i 0.447584 + 0.775238i 0.998228 0.0595022i \(-0.0189513\pi\)
−0.550645 + 0.834740i \(0.685618\pi\)
\(152\) 0.866025 1.50000i 0.0702439 0.121666i
\(153\) 5.19615 0.420084
\(154\) 2.00000 + 1.73205i 0.161165 + 0.139573i
\(155\) 12.0000i 0.963863i
\(156\) −5.19615 3.00000i −0.416025 0.240192i
\(157\) 4.50000 2.59808i 0.359139 0.207349i −0.309564 0.950879i \(-0.600183\pi\)
0.668703 + 0.743530i \(0.266850\pi\)
\(158\) −6.92820 + 4.00000i −0.551178 + 0.318223i
\(159\) 0 0
\(160\) 3.46410i 0.273861i
\(161\) 2.59808 + 7.50000i 0.204757 + 0.591083i
\(162\) 9.00000i 0.707107i
\(163\) −7.00000 + 12.1244i −0.548282 + 0.949653i 0.450110 + 0.892973i \(0.351385\pi\)
−0.998392 + 0.0566798i \(0.981949\pi\)
\(164\) −3.46410 6.00000i −0.270501 0.468521i
\(165\) −5.19615 + 3.00000i −0.404520 + 0.233550i
\(166\) −15.0000 8.66025i −1.16423 0.672166i
\(167\) −24.2487 −1.87642 −0.938211 0.346064i \(-0.887518\pi\)
−0.938211 + 0.346064i \(0.887518\pi\)
\(168\) 4.50000 + 0.866025i 0.347183 + 0.0668153i
\(169\) 1.00000 0.0769231
\(170\) −5.19615 3.00000i −0.398527 0.230089i
\(171\) 4.50000 2.59808i 0.344124 0.198680i
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) 10.3923 18.0000i 0.790112 1.36851i −0.135785 0.990738i \(-0.543356\pi\)
0.925897 0.377776i \(-0.123311\pi\)
\(174\) −5.19615 −0.393919
\(175\) 3.50000 18.1865i 0.264575 1.37477i
\(176\) 1.00000i 0.0753778i
\(177\) 10.5000 18.1865i 0.789228 1.36698i
\(178\) −9.00000 + 5.19615i −0.674579 + 0.389468i
\(179\) 12.9904 7.50000i 0.970947 0.560576i 0.0714220 0.997446i \(-0.477246\pi\)
0.899525 + 0.436870i \(0.143913\pi\)
\(180\) −5.19615 + 9.00000i −0.387298 + 0.670820i
\(181\) 13.8564i 1.02994i 0.857209 + 0.514969i \(0.172197\pi\)
−0.857209 + 0.514969i \(0.827803\pi\)
\(182\) 8.66025 3.00000i 0.641941 0.222375i
\(183\) 18.0000i 1.33060i
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) 12.1244 + 21.0000i 0.891400 + 1.54395i
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) −1.50000 0.866025i −0.109691 0.0633300i
\(188\) −1.73205 −0.126323
\(189\) 10.3923 + 9.00000i 0.755929 + 0.654654i
\(190\) −6.00000 −0.435286
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0.866025 + 1.50000i 0.0625000 + 0.108253i
\(193\) −2.00000 3.46410i −0.143963 0.249351i 0.785022 0.619467i \(-0.212651\pi\)
−0.928986 + 0.370116i \(0.879318\pi\)
\(194\) 7.79423 13.5000i 0.559593 0.969244i
\(195\) 20.7846i 1.48842i
\(196\) −5.50000 + 4.33013i −0.392857 + 0.309295i
\(197\) 9.00000i 0.641223i −0.947211 0.320612i \(-0.896112\pi\)
0.947211 0.320612i \(-0.103888\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) −9.00000 + 5.19615i −0.637993 + 0.368345i −0.783841 0.620962i \(-0.786742\pi\)
0.145848 + 0.989307i \(0.453409\pi\)
\(200\) 6.06218 3.50000i 0.428661 0.247487i
\(201\) 13.8564 24.0000i 0.977356 1.69283i
\(202\) 5.19615i 0.365600i
\(203\) 5.19615 6.00000i 0.364698 0.421117i
\(204\) −3.00000 −0.210042
\(205\) −12.0000 + 20.7846i −0.838116 + 1.45166i
\(206\) 8.66025 + 15.0000i 0.603388 + 1.04510i
\(207\) −7.79423 + 4.50000i −0.541736 + 0.312772i
\(208\) 3.00000 + 1.73205i 0.208013 + 0.120096i
\(209\) −1.73205 −0.119808
\(210\) −5.19615 15.0000i −0.358569 1.03510i
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) −22.5000 + 12.9904i −1.54167 + 0.890086i
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 1.73205 3.00000i 0.118125 0.204598i
\(216\) 5.19615i 0.353553i
\(217\) 9.00000 + 1.73205i 0.610960 + 0.117579i
\(218\) 16.0000i 1.08366i
\(219\) 20.7846 + 12.0000i 1.40449 + 0.810885i
\(220\) 3.00000 1.73205i 0.202260 0.116775i
\(221\) −5.19615 + 3.00000i −0.349531 + 0.201802i
\(222\) 10.5000 + 6.06218i 0.704714 + 0.406867i
\(223\) 10.3923i 0.695920i −0.937509 0.347960i \(-0.886874\pi\)
0.937509 0.347960i \(-0.113126\pi\)
\(224\) −2.59808 0.500000i −0.173591 0.0334077i
\(225\) 21.0000 1.40000
\(226\) −3.00000 + 5.19615i −0.199557 + 0.345643i
\(227\) −5.19615 9.00000i −0.344881 0.597351i 0.640451 0.767999i \(-0.278747\pi\)
−0.985332 + 0.170648i \(0.945414\pi\)
\(228\) −2.59808 + 1.50000i −0.172062 + 0.0993399i
\(229\) −12.0000 6.92820i −0.792982 0.457829i 0.0480291 0.998846i \(-0.484706\pi\)
−0.841011 + 0.541017i \(0.818039\pi\)
\(230\) 10.3923 0.685248
\(231\) −1.50000 4.33013i −0.0986928 0.284901i
\(232\) 3.00000 0.196960
\(233\) −23.3827 13.5000i −1.53185 0.884414i −0.999277 0.0380310i \(-0.987891\pi\)
−0.532574 0.846383i \(-0.678775\pi\)
\(234\) 5.19615 + 9.00000i 0.339683 + 0.588348i
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) −6.06218 + 10.5000i −0.394614 + 0.683492i
\(237\) 13.8564 0.900070
\(238\) 3.00000 3.46410i 0.194461 0.224544i
\(239\) 6.00000i 0.388108i −0.980991 0.194054i \(-0.937836\pi\)
0.980991 0.194054i \(-0.0621637\pi\)
\(240\) 3.00000 5.19615i 0.193649 0.335410i
\(241\) 18.0000 10.3923i 1.15948 0.669427i 0.208302 0.978065i \(-0.433206\pi\)
0.951180 + 0.308637i \(0.0998729\pi\)
\(242\) 0.866025 0.500000i 0.0556702 0.0321412i
\(243\) −7.79423 + 13.5000i −0.500000 + 0.866025i
\(244\) 10.3923i 0.665299i
\(245\) 22.5167 + 9.00000i 1.43854 + 0.574989i
\(246\) 12.0000i 0.765092i
\(247\) −3.00000 + 5.19615i −0.190885 + 0.330623i
\(248\) 1.73205 + 3.00000i 0.109985 + 0.190500i
\(249\) 15.0000 + 25.9808i 0.950586 + 1.64646i
\(250\) −6.00000 3.46410i −0.379473 0.219089i
\(251\) 12.1244 0.765283 0.382641 0.923897i \(-0.375015\pi\)
0.382641 + 0.923897i \(0.375015\pi\)
\(252\) −6.00000 5.19615i −0.377964 0.327327i
\(253\) 3.00000 0.188608
\(254\) 9.52628 + 5.50000i 0.597732 + 0.345101i
\(255\) 5.19615 + 9.00000i 0.325396 + 0.563602i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.19615 9.00000i 0.324127 0.561405i −0.657208 0.753709i \(-0.728263\pi\)
0.981335 + 0.192304i \(0.0615961\pi\)
\(258\) 1.73205i 0.107833i
\(259\) −17.5000 + 6.06218i −1.08740 + 0.376685i
\(260\) 12.0000i 0.744208i
\(261\) 7.79423 + 4.50000i 0.482451 + 0.278543i
\(262\) 0 0
\(263\) −15.5885 + 9.00000i −0.961225 + 0.554964i −0.896550 0.442943i \(-0.853935\pi\)
−0.0646755 + 0.997906i \(0.520601\pi\)
\(264\) 0.866025 1.50000i 0.0533002 0.0923186i
\(265\) 0 0
\(266\) 0.866025 4.50000i 0.0530994 0.275913i
\(267\) 18.0000 1.10158
\(268\) −8.00000 + 13.8564i −0.488678 + 0.846415i
\(269\) −6.92820 12.0000i −0.422420 0.731653i 0.573756 0.819027i \(-0.305486\pi\)
−0.996176 + 0.0873736i \(0.972153\pi\)
\(270\) 15.5885 9.00000i 0.948683 0.547723i
\(271\) −9.00000 5.19615i −0.546711 0.315644i 0.201083 0.979574i \(-0.435554\pi\)
−0.747794 + 0.663930i \(0.768887\pi\)
\(272\) 1.73205 0.105021
\(273\) −15.5885 3.00000i −0.943456 0.181568i
\(274\) −18.0000 −1.08742
\(275\) −6.06218 3.50000i −0.365563 0.211058i
\(276\) 4.50000 2.59808i 0.270868 0.156386i
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) 0.866025 1.50000i 0.0519408 0.0899640i
\(279\) 10.3923i 0.622171i
\(280\) 3.00000 + 8.66025i 0.179284 + 0.517549i
\(281\) 15.0000i 0.894825i 0.894328 + 0.447412i \(0.147654\pi\)
−0.894328 + 0.447412i \(0.852346\pi\)
\(282\) 2.59808 + 1.50000i 0.154713 + 0.0893237i
\(283\) 15.0000 8.66025i 0.891657 0.514799i 0.0171732 0.999853i \(-0.494533\pi\)
0.874484 + 0.485054i \(0.161200\pi\)
\(284\) 12.9904 7.50000i 0.770837 0.445043i
\(285\) 9.00000 + 5.19615i 0.533114 + 0.307794i
\(286\) 3.46410i 0.204837i
\(287\) −13.8564 12.0000i −0.817918 0.708338i
\(288\) 3.00000i 0.176777i
\(289\) 7.00000 12.1244i 0.411765 0.713197i
\(290\) −5.19615 9.00000i −0.305129 0.528498i
\(291\) −23.3827 + 13.5000i −1.37072 + 0.791384i
\(292\) −12.0000 6.92820i −0.702247 0.405442i
\(293\) 8.66025 0.505937 0.252969 0.967474i \(-0.418593\pi\)
0.252969 + 0.967474i \(0.418593\pi\)
\(294\) 12.0000 1.73205i 0.699854 0.101015i
\(295\) 42.0000 2.44533
\(296\) −6.06218 3.50000i −0.352357 0.203433i
\(297\) 4.50000 2.59808i 0.261116 0.150756i
\(298\) 4.50000 + 7.79423i 0.260678 + 0.451508i
\(299\) 5.19615 9.00000i 0.300501 0.520483i
\(300\) −12.1244 −0.700000
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) 11.0000i 0.632979i
\(303\) 4.50000 7.79423i 0.258518 0.447767i
\(304\) 1.50000 0.866025i 0.0860309 0.0496700i
\(305\) 31.1769 18.0000i 1.78518 1.03068i
\(306\) 4.50000 + 2.59808i 0.257248 + 0.148522i
\(307\) 17.3205i 0.988534i −0.869310 0.494267i \(-0.835437\pi\)
0.869310 0.494267i \(-0.164563\pi\)
\(308\) 0.866025 + 2.50000i 0.0493464 + 0.142451i
\(309\) 30.0000i 1.70664i
\(310\) 6.00000 10.3923i 0.340777 0.590243i
\(311\) −11.2583 19.5000i −0.638401 1.10574i −0.985784 0.168020i \(-0.946263\pi\)
0.347382 0.937724i \(-0.387071\pi\)
\(312\) −3.00000 5.19615i −0.169842 0.294174i
\(313\) −25.5000 14.7224i −1.44135 0.832161i −0.443406 0.896321i \(-0.646230\pi\)
−0.997940 + 0.0641600i \(0.979563\pi\)
\(314\) 5.19615 0.293236
\(315\) −5.19615 + 27.0000i −0.292770 + 1.52128i
\(316\) −8.00000 −0.450035
\(317\) −5.19615 3.00000i −0.291845 0.168497i 0.346929 0.937892i \(-0.387225\pi\)
−0.638774 + 0.769395i \(0.720558\pi\)
\(318\) 0 0
\(319\) −1.50000 2.59808i −0.0839839 0.145464i
\(320\) −1.73205 + 3.00000i −0.0968246 + 0.167705i
\(321\) 10.3923i 0.580042i
\(322\) −1.50000 + 7.79423i −0.0835917 + 0.434355i
\(323\) 3.00000i 0.166924i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) −21.0000 + 12.1244i −1.16487 + 0.672538i
\(326\) −12.1244 + 7.00000i −0.671506 + 0.387694i
\(327\) −13.8564 + 24.0000i −0.766261 + 1.32720i
\(328\) 6.92820i 0.382546i
\(329\) −4.33013 + 1.50000i −0.238728 + 0.0826977i
\(330\) −6.00000 −0.330289
\(331\) −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) −8.66025 15.0000i −0.475293 0.823232i
\(333\) −10.5000 18.1865i −0.575396 0.996616i
\(334\) −21.0000 12.1244i −1.14907 0.663415i
\(335\) 55.4256 3.02823
\(336\) 3.46410 + 3.00000i 0.188982 + 0.163663i
\(337\) 4.00000 0.217894 0.108947 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) 9.00000 5.19615i 0.488813 0.282216i
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) 1.73205 3.00000i 0.0937958 0.162459i
\(342\) 5.19615 0.280976
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 1.00000i 0.0539164i
\(345\) −15.5885 9.00000i −0.839254 0.484544i
\(346\) 18.0000 10.3923i 0.967686 0.558694i
\(347\) −20.7846 + 12.0000i −1.11578 + 0.644194i −0.940319 0.340293i \(-0.889474\pi\)
−0.175457 + 0.984487i \(0.556140\pi\)
\(348\) −4.50000 2.59808i −0.241225 0.139272i
\(349\) 20.7846i 1.11257i −0.830990 0.556287i \(-0.812225\pi\)
0.830990 0.556287i \(-0.187775\pi\)
\(350\) 12.1244 14.0000i 0.648074 0.748331i
\(351\) 18.0000i 0.960769i
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 1.73205 + 3.00000i 0.0921878 + 0.159674i 0.908431 0.418034i \(-0.137281\pi\)
−0.816244 + 0.577708i \(0.803947\pi\)
\(354\) 18.1865 10.5000i 0.966603 0.558069i
\(355\) −45.0000 25.9808i −2.38835 1.37892i
\(356\) −10.3923 −0.550791
\(357\) −7.50000 + 2.59808i −0.396942 + 0.137505i
\(358\) 15.0000 0.792775
\(359\) 5.19615 + 3.00000i 0.274242 + 0.158334i 0.630814 0.775934i \(-0.282721\pi\)
−0.356572 + 0.934268i \(0.616054\pi\)
\(360\) −9.00000 + 5.19615i −0.474342 + 0.273861i
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) −6.92820 + 12.0000i −0.364138 + 0.630706i
\(363\) −1.73205 −0.0909091
\(364\) 9.00000 + 1.73205i 0.471728 + 0.0907841i
\(365\) 48.0000i 2.51243i
\(366\) 9.00000 15.5885i 0.470438 0.814822i
\(367\) −6.00000 + 3.46410i −0.313197 + 0.180825i −0.648356 0.761337i \(-0.724543\pi\)
0.335159 + 0.942162i \(0.391210\pi\)
\(368\) −2.59808 + 1.50000i −0.135434 + 0.0781929i
\(369\) 10.3923 18.0000i 0.541002 0.937043i
\(370\) 24.2487i 1.26063i
\(371\) 0 0
\(372\) 6.00000i 0.311086i
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) −0.866025 1.50000i −0.0447811 0.0775632i
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) −1.50000 0.866025i −0.0773566 0.0446619i
\(377\) −10.3923 −0.535231
\(378\) 4.50000 + 12.9904i 0.231455 + 0.668153i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −5.19615 3.00000i −0.266557 0.153897i
\(381\) −9.52628 16.5000i −0.488046 0.845321i
\(382\) 0 0
\(383\) −14.7224 + 25.5000i −0.752281 + 1.30299i 0.194434 + 0.980916i \(0.437713\pi\)
−0.946715 + 0.322073i \(0.895620\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 6.00000 6.92820i 0.305788 0.353094i
\(386\) 4.00000i 0.203595i
\(387\) −1.50000 + 2.59808i −0.0762493 + 0.132068i
\(388\) 13.5000 7.79423i 0.685359 0.395692i
\(389\) 15.5885 9.00000i 0.790366 0.456318i −0.0497253 0.998763i \(-0.515835\pi\)
0.840091 + 0.542445i \(0.182501\pi\)
\(390\) −10.3923 + 18.0000i −0.526235 + 0.911465i
\(391\) 5.19615i 0.262781i
\(392\) −6.92820 + 1.00000i −0.349927 + 0.0505076i
\(393\) 0 0
\(394\) 4.50000 7.79423i 0.226707 0.392668i
\(395\) 13.8564 + 24.0000i 0.697191 + 1.20757i
\(396\) −2.59808 + 1.50000i −0.130558 + 0.0753778i
\(397\) −1.50000 0.866025i −0.0752828 0.0434646i 0.461886 0.886939i \(-0.347173\pi\)
−0.537169 + 0.843475i \(0.680506\pi\)
\(398\) −10.3923 −0.520919
\(399\) −5.19615 + 6.00000i −0.260133 + 0.300376i
\(400\) 7.00000 0.350000
\(401\) 20.7846 + 12.0000i 1.03793 + 0.599251i 0.919247 0.393680i \(-0.128798\pi\)
0.118686 + 0.992932i \(0.462132\pi\)
\(402\) 24.0000 13.8564i 1.19701 0.691095i
\(403\) −6.00000 10.3923i −0.298881 0.517678i
\(404\) −2.59808 + 4.50000i −0.129259 + 0.223883i
\(405\) −31.1769 −1.54919
\(406\) 7.50000 2.59808i 0.372219 0.128940i
\(407\) 7.00000i 0.346977i
\(408\) −2.59808 1.50000i −0.128624 0.0742611i
\(409\) 12.0000 6.92820i 0.593362 0.342578i −0.173064 0.984911i \(-0.555367\pi\)
0.766426 + 0.642333i \(0.222033\pi\)
\(410\) −20.7846 + 12.0000i −1.02648 + 0.592638i
\(411\) 27.0000 + 15.5885i 1.33181 + 0.768922i
\(412\) 17.3205i 0.853320i
\(413\) −6.06218 + 31.5000i −0.298300 + 1.55001i
\(414\) −9.00000 −0.442326
\(415\) −30.0000 + 51.9615i −1.47264 + 2.55069i
\(416\) 1.73205 + 3.00000i 0.0849208 + 0.147087i
\(417\) −2.59808 + 1.50000i −0.127228 + 0.0734553i
\(418\) −1.50000 0.866025i −0.0733674 0.0423587i
\(419\) 1.73205 0.0846162 0.0423081 0.999105i \(-0.486529\pi\)
0.0423081 + 0.999105i \(0.486529\pi\)
\(420\) 3.00000 15.5885i 0.146385 0.760639i
\(421\) 5.00000 0.243685 0.121843 0.992549i \(-0.461120\pi\)
0.121843 + 0.992549i \(0.461120\pi\)
\(422\) 3.46410 + 2.00000i 0.168630 + 0.0973585i
\(423\) −2.59808 4.50000i −0.126323 0.218797i
\(424\) 0 0
\(425\) −6.06218 + 10.5000i −0.294059 + 0.509325i
\(426\) −25.9808 −1.25877
\(427\) 9.00000 + 25.9808i 0.435541 + 1.25730i
\(428\) 6.00000i 0.290021i
\(429\) −3.00000 + 5.19615i −0.144841 + 0.250873i
\(430\) 3.00000 1.73205i 0.144673 0.0835269i
\(431\) −10.3923 + 6.00000i −0.500580 + 0.289010i −0.728953 0.684564i \(-0.759993\pi\)
0.228373 + 0.973574i \(0.426659\pi\)
\(432\) −2.59808 + 4.50000i −0.125000 + 0.216506i
\(433\) 8.66025i 0.416185i −0.978109 0.208093i \(-0.933274\pi\)
0.978109 0.208093i \(-0.0667255\pi\)
\(434\) 6.92820 + 6.00000i 0.332564 + 0.288009i
\(435\) 18.0000i 0.863034i
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) −2.59808 4.50000i −0.124283 0.215264i
\(438\) 12.0000 + 20.7846i 0.573382 + 0.993127i
\(439\) 13.5000 + 7.79423i 0.644320 + 0.371998i 0.786277 0.617875i \(-0.212006\pi\)
−0.141957 + 0.989873i \(0.545339\pi\)
\(440\) 3.46410 0.165145
\(441\) −19.5000 7.79423i −0.928571 0.371154i
\(442\) −6.00000 −0.285391
\(443\) −7.79423 4.50000i −0.370315 0.213801i 0.303281 0.952901i \(-0.401918\pi\)
−0.673596 + 0.739100i \(0.735251\pi\)
\(444\) 6.06218 + 10.5000i 0.287698 + 0.498308i
\(445\) 18.0000 + 31.1769i 0.853282 + 1.47793i
\(446\) 5.19615 9.00000i 0.246045 0.426162i
\(447\) 15.5885i 0.737309i
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) 12.0000i 0.566315i 0.959073 + 0.283158i \(0.0913819\pi\)
−0.959073 + 0.283158i \(0.908618\pi\)
\(450\) 18.1865 + 10.5000i 0.857321 + 0.494975i
\(451\) −6.00000 + 3.46410i −0.282529 + 0.163118i
\(452\) −5.19615 + 3.00000i −0.244406 + 0.141108i
\(453\) 9.52628 16.5000i 0.447584 0.775238i
\(454\) 10.3923i 0.487735i
\(455\) −10.3923 30.0000i −0.487199 1.40642i
\(456\) −3.00000 −0.140488
\(457\) 16.0000 27.7128i 0.748448 1.29635i −0.200118 0.979772i \(-0.564132\pi\)
0.948566 0.316579i \(-0.102534\pi\)
\(458\) −6.92820 12.0000i −0.323734 0.560723i
\(459\) −4.50000 7.79423i −0.210042 0.363803i
\(460\) 9.00000 + 5.19615i 0.419627 + 0.242272i
\(461\) 8.66025 0.403348 0.201674 0.979453i \(-0.435362\pi\)
0.201674 + 0.979453i \(0.435362\pi\)
\(462\) 0.866025 4.50000i 0.0402911 0.209359i
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 2.59808 + 1.50000i 0.120613 + 0.0696358i
\(465\) −18.0000 + 10.3923i −0.834730 + 0.481932i
\(466\) −13.5000 23.3827i −0.625375 1.08318i
\(467\) 7.79423 13.5000i 0.360674 0.624705i −0.627398 0.778699i \(-0.715880\pi\)
0.988072 + 0.153993i \(0.0492134\pi\)
\(468\) 10.3923i 0.480384i
\(469\) −8.00000 + 41.5692i −0.369406 + 1.91949i
\(470\) 6.00000i 0.276759i
\(471\) −7.79423 4.50000i −0.359139 0.207349i
\(472\) −10.5000 + 6.06218i −0.483302 + 0.279034i
\(473\) 0.866025 0.500000i 0.0398199 0.0229900i
\(474\) 12.0000 + 6.92820i 0.551178 + 0.318223i
\(475\) 12.1244i 0.556304i
\(476\) 4.33013 1.50000i 0.198471 0.0687524i
\(477\) 0 0
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) 8.66025 + 15.0000i 0.395697 + 0.685367i 0.993190 0.116507i \(-0.0371697\pi\)
−0.597493 + 0.801874i \(0.703836\pi\)
\(480\) 5.19615 3.00000i 0.237171 0.136931i
\(481\) 21.0000 + 12.1244i 0.957518 + 0.552823i
\(482\) 20.7846 0.946713
\(483\) 9.00000 10.3923i 0.409514 0.472866i
\(484\) 1.00000 0.0454545
\(485\) −46.7654 27.0000i −2.12351 1.22601i
\(486\) −13.5000 + 7.79423i −0.612372 + 0.353553i
\(487\) 13.0000 + 22.5167i 0.589086 + 1.02033i 0.994352 + 0.106129i \(0.0338455\pi\)
−0.405266 + 0.914199i \(0.632821\pi\)
\(488\) −5.19615 + 9.00000i −0.235219 + 0.407411i
\(489\) 24.2487 1.09656
\(490\) 15.0000 + 19.0526i 0.677631 + 0.860707i
\(491\) 30.0000i 1.35388i 0.736038 + 0.676941i \(0.236695\pi\)
−0.736038 + 0.676941i \(0.763305\pi\)
\(492\) −6.00000 + 10.3923i −0.270501 + 0.468521i
\(493\) −4.50000 + 2.59808i −0.202670 + 0.117011i
\(494\) −5.19615 + 3.00000i −0.233786 + 0.134976i
\(495\) 9.00000 + 5.19615i 0.404520 + 0.233550i
\(496\) 3.46410i 0.155543i
\(497\) 25.9808 30.0000i 1.16540 1.34568i
\(498\) 30.0000i 1.34433i
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) −3.46410 6.00000i −0.154919 0.268328i
\(501\) 21.0000 + 36.3731i 0.938211 + 1.62503i
\(502\) 10.5000 + 6.06218i 0.468638 + 0.270568i
\(503\) −17.3205 −0.772283 −0.386142 0.922440i \(-0.626192\pi\)
−0.386142 + 0.922440i \(0.626192\pi\)
\(504\) −2.59808 7.50000i −0.115728 0.334077i
\(505\) 18.0000 0.800989
\(506\) 2.59808 + 1.50000i 0.115499 + 0.0666831i
\(507\) −0.866025 1.50000i −0.0384615 0.0666173i
\(508\) 5.50000 + 9.52628i 0.244023 + 0.422660i
\(509\) 3.46410 6.00000i 0.153544 0.265945i −0.778984 0.627044i \(-0.784265\pi\)
0.932528 + 0.361098i \(0.117598\pi\)
\(510\) 10.3923i 0.460179i
\(511\) −36.0000 6.92820i −1.59255 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) −7.79423 4.50000i −0.344124 0.198680i
\(514\) 9.00000 5.19615i 0.396973 0.229192i
\(515\) 51.9615 30.0000i 2.28970 1.32196i
\(516\) 0.866025 1.50000i 0.0381246 0.0660338i
\(517\) 1.73205i 0.0761755i
\(518\) −18.1865 3.50000i −0.799070 0.153781i
\(519\) −36.0000 −1.58022
\(520\) 6.00000 10.3923i 0.263117 0.455733i
\(521\) 8.66025 + 15.0000i 0.379413 + 0.657162i 0.990977 0.134033i \(-0.0427928\pi\)
−0.611564 + 0.791195i \(0.709459\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) −15.0000 8.66025i −0.655904 0.378686i 0.134810 0.990871i \(-0.456957\pi\)
−0.790715 + 0.612185i \(0.790291\pi\)
\(524\) 0 0
\(525\) −30.3109 + 10.5000i −1.32288 + 0.458258i
\(526\) −18.0000 −0.784837
\(527\) −5.19615 3.00000i −0.226348 0.130682i
\(528\) 1.50000 0.866025i 0.0652791 0.0376889i
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) 0 0
\(531\) −36.3731 −1.57846
\(532\) 3.00000 3.46410i 0.130066 0.150188i
\(533\) 24.0000i 1.03956i
\(534\) 15.5885 + 9.00000i 0.674579 + 0.389468i
\(535\) 18.0000 10.3923i 0.778208 0.449299i
\(536\) −13.8564 + 8.00000i −0.598506 + 0.345547i
\(537\) −22.5000 12.9904i −0.970947 0.560576i
\(538\) 13.8564i 0.597392i
\(539\) 4.33013 + 5.50000i 0.186512 + 0.236902i
\(540\) 18.0000 0.774597
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) −5.19615 9.00000i −0.223194 0.386583i
\(543\) 20.7846 12.0000i 0.891953 0.514969i
\(544\) 1.50000 + 0.866025i 0.0643120 + 0.0371305i
\(545\) −55.4256 −2.37417
\(546\) −12.0000 10.3923i −0.513553 0.444750i
\(547\) −25.0000 −1.06892 −0.534461 0.845193i \(-0.679486\pi\)
−0.534461 + 0.845193i \(0.679486\pi\)
\(548\) −15.5885 9.00000i −0.665906 0.384461i
\(549\) −27.0000 + 15.5885i −1.15233 + 0.665299i
\(550\) −3.50000 6.06218i −0.149241 0.258492i
\(551\) −2.59808 + 4.50000i −0.110682 + 0.191706i
\(552\) 5.19615 0.221163
\(553\) −20.0000 + 6.92820i −0.850487 + 0.294617i
\(554\) 8.00000i 0.339887i
\(555\) 21.0000 36.3731i 0.891400 1.54395i
\(556\) 1.50000 0.866025i 0.0636142 0.0367277i
\(557\) −28.5788 + 16.5000i −1.21092 + 0.699127i −0.962961 0.269642i \(-0.913095\pi\)
−0.247964 + 0.968769i \(0.579761\pi\)
\(558\) −5.19615 + 9.00000i −0.219971 + 0.381000i
\(559\) 3.46410i 0.146516i
\(560\) −1.73205 + 9.00000i −0.0731925 + 0.380319i
\(561\) 3.00000i 0.126660i
\(562\) −7.50000 + 12.9904i −0.316368 + 0.547966i
\(563\) −15.5885 27.0000i −0.656975 1.13791i −0.981395 0.192001i \(-0.938502\pi\)
0.324420 0.945913i \(-0.394831\pi\)
\(564\) 1.50000 + 2.59808i 0.0631614 + 0.109399i
\(565\) 18.0000 + 10.3923i 0.757266 + 0.437208i
\(566\) 17.3205 0.728035
\(567\) 4.50000 23.3827i 0.188982 0.981981i
\(568\) 15.0000 0.629386
\(569\) 33.7750 + 19.5000i 1.41592 + 0.817483i 0.995937 0.0900490i \(-0.0287024\pi\)
0.419984 + 0.907532i \(0.362036\pi\)
\(570\) 5.19615 + 9.00000i 0.217643 + 0.376969i
\(571\) −11.5000 19.9186i −0.481260 0.833567i 0.518509 0.855072i \(-0.326487\pi\)
−0.999769 + 0.0215055i \(0.993154\pi\)
\(572\) 1.73205 3.00000i 0.0724207 0.125436i
\(573\) 0 0
\(574\) −6.00000 17.3205i −0.250435 0.722944i
\(575\) 21.0000i 0.875761i
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −24.0000 + 13.8564i −0.999133 + 0.576850i −0.907992 0.418988i \(-0.862385\pi\)
−0.0911414 + 0.995838i \(0.529052\pi\)
\(578\) 12.1244 7.00000i 0.504307 0.291162i
\(579\) −3.46410 + 6.00000i −0.143963 + 0.249351i
\(580\) 10.3923i 0.431517i
\(581\) −34.6410 30.0000i −1.43715 1.24461i
\(582\) −27.0000 −1.11919
\(583\) 0 0
\(584\) −6.92820 12.0000i −0.286691 0.496564i
\(585\) 31.1769 18.0000i 1.28901 0.744208i
\(586\) 7.50000 + 4.33013i 0.309822 + 0.178876i
\(587\) 10.3923 0.428936 0.214468 0.976731i \(-0.431198\pi\)
0.214468 + 0.976731i \(0.431198\pi\)
\(588\) 11.2583 + 4.50000i 0.464286 + 0.185577i
\(589\) −6.00000 −0.247226
\(590\) 36.3731 + 21.0000i 1.49746 + 0.864556i
\(591\) −13.5000 + 7.79423i −0.555316 + 0.320612i
\(592\) −3.50000 6.06218i −0.143849 0.249154i
\(593\) −14.7224 + 25.5000i −0.604578 + 1.04716i 0.387540 + 0.921853i \(0.373325\pi\)
−0.992118 + 0.125307i \(0.960009\pi\)
\(594\) 5.19615 0.213201
\(595\) −12.0000 10.3923i −0.491952 0.426043i
\(596\) 9.00000i 0.368654i
\(597\) 15.5885 + 9.00000i 0.637993 + 0.368345i
\(598\) 9.00000 5.19615i 0.368037 0.212486i
\(599\) 20.7846 12.0000i 0.849236 0.490307i −0.0111569 0.999938i \(-0.503551\pi\)
0.860393 + 0.509631i \(0.170218\pi\)
\(600\) −10.5000 6.06218i −0.428661 0.247487i
\(601\) 6.92820i 0.282607i −0.989966 0.141304i \(-0.954871\pi\)
0.989966 0.141304i \(-0.0451294\pi\)
\(602\) 0.866025 + 2.50000i 0.0352966 + 0.101892i
\(603\) −48.0000 −1.95471
\(604\) −5.50000 + 9.52628i −0.223792 + 0.387619i
\(605\) −1.73205 3.00000i −0.0704179 0.121967i
\(606\) 7.79423 4.50000i 0.316619 0.182800i
\(607\) 33.0000 + 19.0526i 1.33943 + 0.773320i 0.986723 0.162415i \(-0.0519282\pi\)
0.352706 + 0.935734i \(0.385262\pi\)
\(608\) 1.73205 0.0702439
\(609\) −13.5000 2.59808i −0.547048 0.105279i
\(610\) 36.0000 1.45760
\(611\) 5.19615 + 3.00000i 0.210214 + 0.121367i
\(612\) 2.59808 + 4.50000i 0.105021 + 0.181902i
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 8.66025 15.0000i 0.349499 0.605351i
\(615\) 41.5692 1.67623
\(616\) −0.500000 + 2.59808i −0.0201456 + 0.104679i
\(617\) 12.0000i 0.483102i 0.970388 + 0.241551i \(0.0776561\pi\)
−0.970388 + 0.241551i \(0.922344\pi\)
\(618\) 15.0000 25.9808i 0.603388 1.04510i
\(619\) 33.0000 19.0526i 1.32638 0.765787i 0.341644 0.939829i \(-0.389016\pi\)
0.984738 + 0.174042i \(0.0556830\pi\)
\(620\) 10.3923 6.00000i 0.417365 0.240966i
\(621\) 13.5000 + 7.79423i 0.541736 + 0.312772i
\(622\) 22.5167i 0.902836i
\(623\) −25.9808 + 9.00000i −1.04090 + 0.360577i
\(624\) 6.00000i 0.240192i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −14.7224 25.5000i −0.588427 1.01918i
\(627\) 1.50000 + 2.59808i 0.0599042 + 0.103757i
\(628\) 4.50000 + 2.59808i 0.179570 + 0.103675i
\(629\) 12.1244 0.483430
\(630\) −18.0000 + 20.7846i −0.717137 + 0.828079i
\(631\) −22.0000 −0.875806 −0.437903 0.899022i \(-0.644279\pi\)
−0.437903 + 0.899022i \(0.644279\pi\)
\(632\) −6.92820 4.00000i −0.275589 0.159111i
\(633\) −3.46410 6.00000i −0.137686 0.238479i
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 19.0526 33.0000i 0.756078 1.30957i
\(636\) 0 0
\(637\) 24.0000 3.46410i 0.950915 0.137253i
\(638\) 3.00000i 0.118771i
\(639\) 38.9711 + 22.5000i 1.54167 + 0.890086i
\(640\) −3.00000 + 1.73205i −0.118585 + 0.0684653i
\(641\) 41.5692 24.0000i 1.64189 0.947943i 0.661723 0.749749i \(-0.269826\pi\)
0.980163 0.198194i \(-0.0635077\pi\)
\(642\) 5.19615 9.00000i 0.205076 0.355202i
\(643\) 34.6410i 1.36611i −0.730368 0.683054i \(-0.760651\pi\)
0.730368 0.683054i \(-0.239349\pi\)
\(644\) −5.19615 + 6.00000i −0.204757 + 0.236433i
\(645\) −6.00000 −0.236250
\(646\) −1.50000 + 2.59808i −0.0590167 + 0.102220i
\(647\) 5.19615 + 9.00000i 0.204282 + 0.353827i 0.949904 0.312543i \(-0.101181\pi\)
−0.745622 + 0.666369i \(0.767847\pi\)
\(648\) 7.79423 4.50000i 0.306186 0.176777i
\(649\) 10.5000 + 6.06218i 0.412161 + 0.237961i
\(650\) −24.2487 −0.951113
\(651\) −5.19615 15.0000i −0.203653 0.587896i
\(652\) −14.0000 −0.548282
\(653\) 5.19615 + 3.00000i 0.203341 + 0.117399i 0.598213 0.801337i \(-0.295878\pi\)
−0.394872 + 0.918736i \(0.629211\pi\)
\(654\) −24.0000 + 13.8564i −0.938474 + 0.541828i
\(655\) 0 0
\(656\) 3.46410 6.00000i 0.135250 0.234261i
\(657\) 41.5692i 1.62177i
\(658\) −4.50000 0.866025i −0.175428 0.0337612i
\(659\) 12.0000i 0.467454i −0.972302 0.233727i \(-0.924908\pi\)
0.972302 0.233727i \(-0.0750921\pi\)
\(660\) −5.19615 3.00000i −0.202260 0.116775i
\(661\) 25.5000 14.7224i 0.991835 0.572636i 0.0860127 0.996294i \(-0.472587\pi\)
0.905822 + 0.423658i \(0.139254\pi\)
\(662\) −8.66025 + 5.00000i −0.336590 + 0.194331i
\(663\) 9.00000 + 5.19615i 0.349531 + 0.201802i
\(664\) 17.3205i 0.672166i
\(665\) −15.5885 3.00000i −0.604494 0.116335i
\(666\) 21.0000i 0.813733i
\(667\) 4.50000 7.79423i 0.174241 0.301794i
\(668\) −12.1244 21.0000i −0.469105 0.812514i
\(669\) −15.5885 + 9.00000i −0.602685 + 0.347960i
\(670\) 48.0000 + 27.7128i 1.85440 + 1.07064i
\(671\) 10.3923 0.401190
\(672\) 1.50000 + 4.33013i 0.0578638 + 0.167038i
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 3.46410 + 2.00000i 0.133432 + 0.0770371i
\(675\) −18.1865 31.5000i −0.700000 1.21244i
\(676\) 0.500000 + 0.866025i 0.0192308 + 0.0333087i
\(677\) −18.1865 + 31.5000i −0.698965 + 1.21064i 0.269860 + 0.962899i \(0.413022\pi\)
−0.968826 + 0.247744i \(0.920311\pi\)
\(678\) 10.3923 0.399114
\(679\) 27.0000 31.1769i 1.03616 1.19646i
\(680\) 6.00000i 0.230089i
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) 3.00000 1.73205i 0.114876 0.0663237i
\(683\) 33.7750 19.5000i 1.29236 0.746147i 0.313291 0.949657i \(-0.398568\pi\)
0.979073 + 0.203510i \(0.0652350\pi\)
\(684\) 4.50000 + 2.59808i 0.172062 + 0.0993399i
\(685\) 62.3538i 2.38242i
\(686\) −16.4545 + 8.50000i −0.628235 + 0.324532i
\(687\) 24.0000i 0.915657i
\(688\) −0.500000 + 0.866025i −0.0190623 + 0.0330169i
\(689\) 0 0
\(690\) −9.00000 15.5885i −0.342624 0.593442i
\(691\) 3.00000 + 1.73205i 0.114125 + 0.0658903i 0.555976 0.831198i \(-0.312345\pi\)
−0.441851 + 0.897089i \(0.645678\pi\)
\(692\) 20.7846 0.790112
\(693\) −5.19615 + 6.00000i −0.197386 + 0.227921i
\(694\) −24.0000 −0.911028
\(695\) −5.19615 3.00000i −0.197101 0.113796i
\(696\) −2.59808 4.50000i −0.0984798 0.170572i
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) 10.3923 18.0000i 0.393355 0.681310i
\(699\) 46.7654i 1.76883i
\(700\) 17.5000 6.06218i 0.661438 0.229129i
\(701\) 3.00000i 0.113308i 0.998394 + 0.0566542i \(0.0180433\pi\)
−0.998394 + 0.0566542i \(0.981957\pi\)
\(702\) 9.00000 15.5885i 0.339683 0.588348i
\(703\) 10.5000 6.06218i 0.396015 0.228639i
\(704\) −0.866025 + 0.500000i −0.0326396 + 0.0188445i
\(705\) 5.19615 9.00000i 0.195698 0.338960i
\(706\) 3.46410i 0.130373i
\(707\) −2.59808 + 13.5000i −0.0977107 + 0.507720i
\(708\) 21.0000 0.789228
\(709\) 14.5000 25.1147i 0.544559 0.943204i −0.454076 0.890963i \(-0.650030\pi\)
0.998635 0.0522406i \(-0.0166363\pi\)
\(710\) −25.9808 45.0000i −0.975041 1.68882i
\(711\) −12.0000 20.7846i −0.450035 0.779484i
\(712\) −9.00000 5.19615i −0.337289 0.194734i
\(713\) 10.3923 0.389195
\(714\) −7.79423 1.50000i −0.291692 0.0561361i
\(715\) −12.0000 −0.448775
\(716\) 12.9904 + 7.50000i 0.485473 + 0.280288i
\(717\) −9.00000 + 5.19615i −0.336111 + 0.194054i
\(718\) 3.00000 + 5.19615i 0.111959 + 0.193919i
\(719\) −14.7224 + 25.5000i −0.549054 + 0.950990i 0.449286 + 0.893388i \(0.351679\pi\)
−0.998340 + 0.0576013i \(0.981655\pi\)
\(720\) −10.3923 −0.387298
\(721\) 15.0000 + 43.3013i 0.558629 + 1.61262i
\(722\) 16.0000i 0.595458i
\(723\) −31.1769 18.0000i −1.15948 0.669427i
\(724\) −12.0000 + 6.92820i −0.445976 + 0.257485i
\(725\) −18.1865 + 10.5000i −0.675431 + 0.389960i
\(726\) −1.50000 0.866025i −0.0556702 0.0321412i
\(727\) 17.3205i 0.642382i 0.947014 + 0.321191i \(0.104083\pi\)
−0.947014 + 0.321191i \(0.895917\pi\)
\(728\) 6.92820 + 6.00000i 0.256776 + 0.222375i
\(729\) 27.0000 1.00000
\(730\) −24.0000 + 41.5692i −0.888280 + 1.53855i
\(731\) −0.866025 1.50000i −0.0320311 0.0554795i
\(732\) 15.5885 9.00000i 0.576166 0.332650i
\(733\) 3.00000 + 1.73205i 0.110808 + 0.0639748i 0.554380 0.832264i \(-0.312956\pi\)
−0.443572 + 0.896239i \(0.646289\pi\)
\(734\) −6.92820 −0.255725
\(735\) −6.00000 41.5692i −0.221313 1.53330i
\(736\) −3.00000 −0.110581
\(737\) 13.8564 + 8.00000i 0.510407 + 0.294684i
\(738\) 18.0000 10.3923i 0.662589 0.382546i
\(739\) 14.0000 + 24.2487i 0.514998 + 0.892003i 0.999849 + 0.0174060i \(0.00554079\pi\)
−0.484850 + 0.874597i \(0.661126\pi\)
\(740\) −12.1244 + 21.0000i −0.445700 + 0.771975i
\(741\) 10.3923 0.381771
\(742\) 0 0
\(743\) 36.0000i 1.32071i −0.750953 0.660356i \(-0.770405\pi\)
0.750953 0.660356i \(-0.229595\pi\)
\(744\) 3.00000 5.19615i 0.109985 0.190500i
\(745\) 27.0000 15.5885i 0.989203 0.571117i
\(746\) −12.1244 + 7.00000i −0.443904 + 0.256288i
\(747\) 25.9808 45.0000i 0.950586 1.64646i
\(748\) 1.73205i 0.0633300i
\(749\) 5.19615 + 15.0000i 0.189863 + 0.548088i
\(750\) 12.0000i 0.438178i
\(751\) −26.0000 + 45.0333i −0.948753 + 1.64329i −0.200698 + 0.979653i \(0.564321\pi\)
−0.748056 + 0.663636i \(0.769012\pi\)
\(752\) −0.866025 1.50000i −0.0315807 0.0546994i
\(753\) −10.5000 18.1865i −0.382641 0.662754i
\(754\) −9.00000 5.19615i −0.327761 0.189233i
\(755\) 38.1051 1.38679
\(756\) −2.59808 + 13.5000i −0.0944911 + 0.490990i
\(757\) 13.0000 0.472493 0.236247 0.971693i \(-0.424083\pi\)
0.236247 + 0.971693i \(0.424083\pi\)
\(758\) −17.3205 10.0000i −0.629109 0.363216i
\(759\) −2.59808 4.50000i −0.0943042 0.163340i
\(760\) −3.00000 5.19615i −0.108821 0.188484i
\(761\) −17.3205 + 30.0000i −0.627868 + 1.08750i 0.360111 + 0.932910i \(0.382739\pi\)
−0.987979 + 0.154590i \(0.950594\pi\)
\(762\) 19.0526i 0.690201i
\(763\) 8.00000 41.5692i 0.289619 1.50491i
\(764\) 0 0
\(765\) 9.00000 15.5885i 0.325396 0.563602i
\(766\) −25.5000 + 14.7224i −0.921352 + 0.531943i
\(767\) 36.3731 21.0000i 1.31336 0.758266i
\(768\) −0.866025 + 1.50000i −0.0312500 + 0.0541266i
\(769\) 6.92820i 0.249837i 0.992167 + 0.124919i \(0.0398670\pi\)
−0.992167 + 0.124919i \(0.960133\pi\)
\(770\) 8.66025 3.00000i 0.312094 0.108112i
\(771\) −18.0000 −0.648254
\(772\) 2.00000 3.46410i 0.0719816 0.124676i
\(773\) 6.92820 + 12.0000i 0.249190 + 0.431610i 0.963301 0.268422i \(-0.0865023\pi\)
−0.714111 + 0.700032i \(0.753169\pi\)
\(774\) −2.59808 + 1.50000i −0.0933859 + 0.0539164i
\(775\) −21.0000 12.1244i −0.754342 0.435520i
\(776\) 15.5885