Properties

Label 462.2.k.a.89.1
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 89.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 462.89
Dual form 462.2.k.a.353.1

$q$-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 \(0.448714\pi\)
−0.935021 + 0.354593i \(0.884620\pi\)
\(6\) 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 0.951727 0.306944i \(-0.0993066\pi\)
−0.741685 + 0.670748i \(0.765973\pi\)
\(18\) 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 0.204046 0.978961i \(-0.434591\pi\)
−0.745782 + 0.666190i \(0.767924\pi\)
\(24\) 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 \(0.0898515\pi\)
−0.960424 + 0.278543i \(0.910149\pi\)
\(30\) 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 \(-0.318045\pi\)
0.541002 + 0.841021i \(0.318045\pi\)
\(42\) 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 −0.795926 0.605393i \(-0.793016\pi\)
0.922249 + 0.386596i \(0.126349\pi\)
\(48\) −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 \(-0.877147\pi\)
0.137212 0.990542i \(-0.456186\pi\)
\(60\) −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 \(0.349356\pi\)
−0.455792 + 0.890086i \(0.650644\pi\)
\(72\) 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 \(-0.100483\pi\)
0.950586 + 0.310460i \(0.100483\pi\)
\(84\) −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 \(-0.647659\pi\)
0.998218 0.0596775i \(-0.0190072\pi\)
\(90\) 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 0.707327 0.706887i \(-0.249901\pi\)
−0.965845 + 0.259120i \(0.916568\pi\)
\(102\) 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 0.227345 0.973814i \(-0.426996\pi\)
−0.729676 + 0.683793i \(0.760329\pi\)
\(108\) −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 \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −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 0.346235 0.938148i \(-0.387460\pi\)
0.985577 + 0.169226i \(0.0541268\pi\)
\(138\) −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 0.145519 0.989355i \(-0.453515\pi\)
−0.784047 + 0.620701i \(0.786848\pi\)
\(150\) −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 \(-0.112482\pi\)
0.938211 + 0.346064i \(0.112482\pi\)
\(168\) 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 \(0.456644\pi\)
−0.925897 + 0.377776i \(0.876689\pi\)
\(174\) 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 −0.899525 0.436870i \(-0.856087\pi\)
−0.0714220 + 0.997446i \(0.522754\pi\)
\(180\) 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 \(0.103888\pi\)
−0.947211 + 0.320612i \(0.896112\pi\)
\(198\) −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 0.985332 0.170648i \(-0.0545860\pi\)
−0.640451 + 0.767999i \(0.721253\pi\)
\(228\) 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 \(0.0121086\pi\)
0.532574 + 0.846383i \(0.321225\pi\)
\(234\) −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 \(0.0621637\pi\)
−0.980991 + 0.194054i \(0.937836\pi\)
\(240\) 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 \(-0.624985\pi\)
−0.382641 + 0.923897i \(0.624985\pi\)
\(252\) −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 −0.981335 0.192304i \(-0.938404\pi\)
0.657208 + 0.753709i \(0.271737\pi\)
\(258\) 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 0.0646755 0.997906i \(-0.479399\pi\)
0.896550 + 0.442943i \(0.146065\pi\)
\(264\) −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 0.996176 0.0873736i \(-0.0278474\pi\)
−0.573756 + 0.819027i \(0.694514\pi\)
\(270\) −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 \(-0.852346\pi\)
0.894328 0.447412i \(-0.147654\pi\)
\(282\) −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 \(-0.581407\pi\)
−0.252969 + 0.967474i \(0.581407\pi\)
\(294\) 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 \(0.0537373\pi\)
−0.347382 + 0.937724i \(0.612929\pi\)
\(312\) −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 0.638774 0.769395i \(-0.279442\pi\)
−0.346929 + 0.937892i \(0.612775\pi\)
\(318\) 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 0.175457 0.984487i \(-0.443860\pi\)
0.940319 + 0.340293i \(0.110526\pi\)
\(348\) −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 0.816244 0.577708i \(-0.196053\pi\)
−0.908431 + 0.418034i \(0.862719\pi\)
\(354\) −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 0.356572 0.934268i \(-0.383946\pi\)
−0.630814 + 0.775934i \(0.717279\pi\)
\(360\) −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 \(-0.562287\pi\)
0.946715 0.322073i \(-0.104380\pi\)
\(384\) 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 −0.840091 0.542445i \(-0.817499\pi\)
0.0497253 + 0.998763i \(0.484165\pi\)
\(390\) 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 −0.118686 0.992932i \(-0.537868\pi\)
−0.919247 + 0.393680i \(0.871202\pi\)
\(402\) 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 \(-0.513471\pi\)
−0.0423081 + 0.999105i \(0.513471\pi\)
\(420\) 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 −0.228373 0.973574i \(-0.573341\pi\)
0.728953 + 0.684564i \(0.240007\pi\)
\(432\) 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 0.673596 0.739100i \(-0.264749\pi\)
−0.303281 + 0.952901i \(0.598082\pi\)
\(444\) −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 \(-0.908618\pi\)
0.959073 0.283158i \(-0.0913819\pi\)
\(450\) −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 \(-0.564638\pi\)
−0.201674 + 0.979453i \(0.564638\pi\)
\(462\) −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 −0.988072 0.153993i \(-0.950787\pi\)
0.627398 + 0.778699i \(0.284120\pi\)
\(468\) 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 0.597493 0.801874i \(-0.296164\pi\)
−0.993190 + 0.116507i \(0.962830\pi\)
\(480\) −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 \(-0.763305\pi\)
0.736038 0.676941i \(-0.236695\pi\)
\(492\) −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 \(-0.373808\pi\)
0.386142 + 0.922440i \(0.373808\pi\)
\(504\) 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 −0.932528 0.361098i \(-0.882402\pi\)
0.778984 + 0.627044i \(0.215735\pi\)
\(510\) 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 0.611564 0.791195i \(-0.290541\pi\)
−0.990977 + 0.134033i \(0.957207\pi\)
\(522\) 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 0.247964 0.968769i \(-0.420239\pi\)
0.962961 + 0.269642i \(0.0869053\pi\)
\(558\) 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 \(0.0614977\pi\)
−0.324420 + 0.945913i \(0.605169\pi\)
\(564\) 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 −0.419984 0.907532i \(-0.637964\pi\)
−0.995937 + 0.0900490i \(0.971298\pi\)
\(570\) −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 \(-0.568802\pi\)
−0.214468 + 0.976731i \(0.568802\pi\)
\(588\) −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 \(-0.626675\pi\)
0.992118 0.125307i \(-0.0399915\pi\)
\(594\) −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 −0.860393 0.509631i \(-0.829782\pi\)
0.0111569 + 0.999938i \(0.496449\pi\)
\(600\) −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 \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 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 \(0.730174\pi\)
−0.980163 + 0.198194i \(0.936492\pi\)
\(642\) −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 0.745622 0.666369i \(-0.232153\pi\)
−0.949904 + 0.312543i \(0.898819\pi\)
\(648\) −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 0.394872 0.918736i \(-0.370789\pi\)
−0.598213 + 0.801337i \(0.704122\pi\)
\(654\) −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 \(0.0750921\pi\)
−0.972302 + 0.233727i \(0.924908\pi\)
\(660\) 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 \(-0.586978\pi\)
0.968826 0.247744i \(-0.0796891\pi\)
\(678\) −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 −0.979073 0.203510i \(-0.934765\pi\)
−0.313291 + 0.949657i \(0.601432\pi\)
\(684\) 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 \(-0.981957\pi\)
0.998394 0.0566542i \(-0.0180433\pi\)
\(702\) 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 \(-0.648321\pi\)
0.998340 0.0576013i \(-0.0183452\pi\)
\(720\) 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 \(0.229595\pi\)
−0.750953 + 0.660356i \(0.770405\pi\)
\(744\) 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 \(-0.617261\pi\)
0.987979 0.154590i \(-0.0494055\pi\)
\(762\) 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 0.714111 0.700032i \(-0.246831\pi\)
−0.963301 + 0.268422i \(0.913498\pi\)
\(774\) 2.59808 1.50000i 0.0933859 0.0539164i
\(775\) −21.0000 12.1244i −0.754342 0.435520i
\(776\) −15.5885