Properties

Label 546.2.bi.c.257.1
Level $546$
Weight $2$
Character 546.257
Analytic conductor $4.360$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bi (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.257
Dual form 546.2.bi.c.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(-3.00000 + 5.19615i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(-0.500000 - 2.59808i) q^{14} +(3.00000 + 5.19615i) q^{15} +1.00000 q^{16} +(1.50000 + 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(-1.50000 + 4.33013i) q^{21} +(-3.00000 + 5.19615i) q^{22} -3.46410i q^{23} +(-1.50000 - 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} +(-2.50000 + 2.59808i) q^{26} -5.19615i q^{27} +(-0.500000 - 2.59808i) q^{28} +(-6.00000 + 3.46410i) q^{29} +(3.00000 + 5.19615i) q^{30} +(-4.00000 - 6.92820i) q^{31} +1.00000 q^{32} +(9.00000 - 5.19615i) q^{33} +(-3.00000 + 8.66025i) q^{35} +(1.50000 + 2.59808i) q^{36} -8.66025i q^{37} +(2.50000 + 4.33013i) q^{38} +(6.00000 - 1.73205i) q^{39} +(-3.00000 - 1.73205i) q^{40} +(-9.00000 + 5.19615i) q^{41} +(-1.50000 + 4.33013i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{44} -10.3923i q^{45} -3.46410i q^{46} +(-6.00000 - 3.46410i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(3.50000 + 6.06218i) q^{50} +(-2.50000 + 2.59808i) q^{52} +(-3.00000 + 1.73205i) q^{53} -5.19615i q^{54} +(18.0000 - 10.3923i) q^{55} +(-0.500000 - 2.59808i) q^{56} -8.66025i q^{57} +(-6.00000 + 3.46410i) q^{58} +(3.00000 + 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(-4.00000 - 6.92820i) q^{62} +(6.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(12.0000 - 3.46410i) q^{65} +(9.00000 - 5.19615i) q^{66} +(-3.00000 - 1.73205i) q^{67} +(-3.00000 + 5.19615i) q^{69} +(-3.00000 + 8.66025i) q^{70} +(1.50000 + 2.59808i) q^{72} +(3.50000 + 6.06218i) q^{73} -8.66025i q^{74} -12.1244i q^{75} +(2.50000 + 4.33013i) q^{76} +(15.0000 + 5.19615i) q^{77} +(6.00000 - 1.73205i) q^{78} +(4.00000 - 6.92820i) q^{79} +(-3.00000 - 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-9.00000 + 5.19615i) q^{82} -3.46410i q^{83} +(-1.50000 + 4.33013i) q^{84} +(-0.500000 + 0.866025i) q^{86} +12.0000 q^{87} +(-3.00000 + 5.19615i) q^{88} -3.46410i q^{89} -10.3923i q^{90} +(8.00000 + 5.19615i) q^{91} -3.46410i q^{92} +13.8564i q^{93} +(-6.00000 - 3.46410i) q^{94} -17.3205i q^{95} +(-1.50000 - 0.866025i) q^{96} +(-3.50000 + 6.06218i) q^{97} +(-6.50000 + 2.59808i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 3q^{3} + 2q^{4} - 6q^{5} - 3q^{6} - q^{7} + 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 3q^{3} + 2q^{4} - 6q^{5} - 3q^{6} - q^{7} + 2q^{8} + 3q^{9} - 6q^{10} - 6q^{11} - 3q^{12} - 5q^{13} - q^{14} + 6q^{15} + 2q^{16} + 3q^{18} + 5q^{19} - 6q^{20} - 3q^{21} - 6q^{22} - 3q^{24} + 7q^{25} - 5q^{26} - q^{28} - 12q^{29} + 6q^{30} - 8q^{31} + 2q^{32} + 18q^{33} - 6q^{35} + 3q^{36} + 5q^{38} + 12q^{39} - 6q^{40} - 18q^{41} - 3q^{42} - q^{43} - 6q^{44} - 12q^{47} - 3q^{48} - 13q^{49} + 7q^{50} - 5q^{52} - 6q^{53} + 36q^{55} - q^{56} - 12q^{58} + 6q^{60} + 9q^{61} - 8q^{62} + 12q^{63} + 2q^{64} + 24q^{65} + 18q^{66} - 6q^{67} - 6q^{69} - 6q^{70} + 3q^{72} + 7q^{73} + 5q^{76} + 30q^{77} + 12q^{78} + 8q^{79} - 6q^{80} - 9q^{81} - 18q^{82} - 3q^{84} - q^{86} + 24q^{87} - 6q^{88} + 16q^{91} - 12q^{94} - 3q^{96} - 7q^{97} - 13q^{98} - 36q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) 1.00000 0.500000
\(5\) −3.00000 1.73205i −1.34164 0.774597i −0.354593 0.935021i \(-0.615380\pi\)
−0.987048 + 0.160424i \(0.948714\pi\)
\(6\) −1.50000 0.866025i −0.612372 0.353553i
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 1.00000 0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) −3.00000 1.73205i −0.948683 0.547723i
\(11\) −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) −1.50000 0.866025i −0.433013 0.250000i
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 3.00000 + 5.19615i 0.774597 + 1.34164i
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) −3.00000 1.73205i −0.670820 0.387298i
\(21\) −1.50000 + 4.33013i −0.327327 + 0.944911i
\(22\) −3.00000 + 5.19615i −0.639602 + 1.10782i
\(23\) 3.46410i 0.722315i −0.932505 0.361158i \(-0.882382\pi\)
0.932505 0.361158i \(-0.117618\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) 3.50000 + 6.06218i 0.700000 + 1.21244i
\(26\) −2.50000 + 2.59808i −0.490290 + 0.509525i
\(27\) 5.19615i 1.00000i
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) −6.00000 + 3.46410i −1.11417 + 0.643268i −0.939907 0.341431i \(-0.889088\pi\)
−0.174265 + 0.984699i \(0.555755\pi\)
\(30\) 3.00000 + 5.19615i 0.547723 + 0.948683i
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 1.00000 0.176777
\(33\) 9.00000 5.19615i 1.56670 0.904534i
\(34\) 0 0
\(35\) −3.00000 + 8.66025i −0.507093 + 1.46385i
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) 8.66025i 1.42374i −0.702313 0.711868i \(-0.747849\pi\)
0.702313 0.711868i \(-0.252151\pi\)
\(38\) 2.50000 + 4.33013i 0.405554 + 0.702439i
\(39\) 6.00000 1.73205i 0.960769 0.277350i
\(40\) −3.00000 1.73205i −0.474342 0.273861i
\(41\) −9.00000 + 5.19615i −1.40556 + 0.811503i −0.994956 0.100309i \(-0.968017\pi\)
−0.410608 + 0.911812i \(0.634683\pi\)
\(42\) −1.50000 + 4.33013i −0.231455 + 0.668153i
\(43\) −0.500000 + 0.866025i −0.0762493 + 0.132068i −0.901629 0.432511i \(-0.857628\pi\)
0.825380 + 0.564578i \(0.190961\pi\)
\(44\) −3.00000 + 5.19615i −0.452267 + 0.783349i
\(45\) 10.3923i 1.54919i
\(46\) 3.46410i 0.510754i
\(47\) −6.00000 3.46410i −0.875190 0.505291i −0.00612051 0.999981i \(-0.501948\pi\)
−0.869069 + 0.494690i \(0.835282\pi\)
\(48\) −1.50000 0.866025i −0.216506 0.125000i
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 3.50000 + 6.06218i 0.494975 + 0.857321i
\(51\) 0 0
\(52\) −2.50000 + 2.59808i −0.346688 + 0.360288i
\(53\) −3.00000 + 1.73205i −0.412082 + 0.237915i −0.691684 0.722200i \(-0.743131\pi\)
0.279602 + 0.960116i \(0.409797\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 18.0000 10.3923i 2.42712 1.40130i
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 8.66025i 1.14708i
\(58\) −6.00000 + 3.46410i −0.787839 + 0.454859i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 3.00000 + 5.19615i 0.387298 + 0.670820i
\(61\) 4.50000 2.59808i 0.576166 0.332650i −0.183442 0.983030i \(-0.558724\pi\)
0.759608 + 0.650381i \(0.225391\pi\)
\(62\) −4.00000 6.92820i −0.508001 0.879883i
\(63\) 6.00000 5.19615i 0.755929 0.654654i
\(64\) 1.00000 0.125000
\(65\) 12.0000 3.46410i 1.48842 0.429669i
\(66\) 9.00000 5.19615i 1.10782 0.639602i
\(67\) −3.00000 1.73205i −0.366508 0.211604i 0.305424 0.952217i \(-0.401202\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 0 0
\(69\) −3.00000 + 5.19615i −0.361158 + 0.625543i
\(70\) −3.00000 + 8.66025i −0.358569 + 1.03510i
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 8.66025i 1.00673i
\(75\) 12.1244i 1.40000i
\(76\) 2.50000 + 4.33013i 0.286770 + 0.496700i
\(77\) 15.0000 + 5.19615i 1.70941 + 0.592157i
\(78\) 6.00000 1.73205i 0.679366 0.196116i
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) −3.00000 1.73205i −0.335410 0.193649i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −9.00000 + 5.19615i −0.993884 + 0.573819i
\(83\) 3.46410i 0.380235i −0.981761 0.190117i \(-0.939113\pi\)
0.981761 0.190117i \(-0.0608868\pi\)
\(84\) −1.50000 + 4.33013i −0.163663 + 0.472456i
\(85\) 0 0
\(86\) −0.500000 + 0.866025i −0.0539164 + 0.0933859i
\(87\) 12.0000 1.28654
\(88\) −3.00000 + 5.19615i −0.319801 + 0.553912i
\(89\) 3.46410i 0.367194i −0.983002 0.183597i \(-0.941226\pi\)
0.983002 0.183597i \(-0.0587741\pi\)
\(90\) 10.3923i 1.09545i
\(91\) 8.00000 + 5.19615i 0.838628 + 0.544705i
\(92\) 3.46410i 0.361158i
\(93\) 13.8564i 1.43684i
\(94\) −6.00000 3.46410i −0.618853 0.357295i
\(95\) 17.3205i 1.77705i
\(96\) −1.50000 0.866025i −0.153093 0.0883883i
\(97\) −3.50000 + 6.06218i −0.355371 + 0.615521i −0.987181 0.159602i \(-0.948979\pi\)
0.631810 + 0.775123i \(0.282312\pi\)
\(98\) −6.50000 + 2.59808i −0.656599 + 0.262445i
\(99\) −18.0000 −1.80907
\(100\) 3.50000 + 6.06218i 0.350000 + 0.606218i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) 4.50000 + 2.59808i 0.443398 + 0.255996i 0.705038 0.709170i \(-0.250930\pi\)
−0.261640 + 0.965166i \(0.584263\pi\)
\(104\) −2.50000 + 2.59808i −0.245145 + 0.254762i
\(105\) 12.0000 10.3923i 1.17108 1.01419i
\(106\) −3.00000 + 1.73205i −0.291386 + 0.168232i
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 5.19615i 0.500000i
\(109\) −10.5000 + 6.06218i −1.00572 + 0.580651i −0.909935 0.414751i \(-0.863869\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 18.0000 10.3923i 1.71623 0.990867i
\(111\) −7.50000 + 12.9904i −0.711868 + 1.23299i
\(112\) −0.500000 2.59808i −0.0472456 0.245495i
\(113\) 6.00000 + 3.46410i 0.564433 + 0.325875i 0.754923 0.655814i \(-0.227674\pi\)
−0.190490 + 0.981689i \(0.561008\pi\)
\(114\) 8.66025i 0.811107i
\(115\) −6.00000 + 10.3923i −0.559503 + 0.969087i
\(116\) −6.00000 + 3.46410i −0.557086 + 0.321634i
\(117\) −10.5000 2.59808i −0.970725 0.240192i
\(118\) 0 0
\(119\) 0 0
\(120\) 3.00000 + 5.19615i 0.273861 + 0.474342i
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 4.50000 2.59808i 0.407411 0.235219i
\(123\) 18.0000 1.62301
\(124\) −4.00000 6.92820i −0.359211 0.622171i
\(125\) 6.92820i 0.619677i
\(126\) 6.00000 5.19615i 0.534522 0.462910i
\(127\) −0.500000 0.866025i −0.0443678 0.0768473i 0.842989 0.537931i \(-0.180794\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.50000 0.866025i 0.132068 0.0762493i
\(130\) 12.0000 3.46410i 1.05247 0.303822i
\(131\) 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) 9.00000 5.19615i 0.783349 0.452267i
\(133\) 10.0000 8.66025i 0.867110 0.750939i
\(134\) −3.00000 1.73205i −0.259161 0.149626i
\(135\) −9.00000 + 15.5885i −0.774597 + 1.34164i
\(136\) 0 0
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −3.00000 + 5.19615i −0.255377 + 0.442326i
\(139\) −3.00000 1.73205i −0.254457 0.146911i 0.367347 0.930084i \(-0.380266\pi\)
−0.621803 + 0.783174i \(0.713600\pi\)
\(140\) −3.00000 + 8.66025i −0.253546 + 0.731925i
\(141\) 6.00000 + 10.3923i 0.505291 + 0.875190i
\(142\) 0 0
\(143\) −6.00000 20.7846i −0.501745 1.73810i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 24.0000 1.99309
\(146\) 3.50000 + 6.06218i 0.289662 + 0.501709i
\(147\) 12.0000 + 1.73205i 0.989743 + 0.142857i
\(148\) 8.66025i 0.711868i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 12.1244i 0.989949i
\(151\) 3.00000 1.73205i 0.244137 0.140952i −0.372940 0.927855i \(-0.621650\pi\)
0.617076 + 0.786903i \(0.288317\pi\)
\(152\) 2.50000 + 4.33013i 0.202777 + 0.351220i
\(153\) 0 0
\(154\) 15.0000 + 5.19615i 1.20873 + 0.418718i
\(155\) 27.7128i 2.22595i
\(156\) 6.00000 1.73205i 0.480384 0.138675i
\(157\) −16.5000 + 9.52628i −1.31684 + 0.760280i −0.983220 0.182426i \(-0.941605\pi\)
−0.333624 + 0.942706i \(0.608272\pi\)
\(158\) 4.00000 6.92820i 0.318223 0.551178i
\(159\) 6.00000 0.475831
\(160\) −3.00000 1.73205i −0.237171 0.136931i
\(161\) −9.00000 + 1.73205i −0.709299 + 0.136505i
\(162\) −4.50000 + 7.79423i −0.353553 + 0.612372i
\(163\) 1.50000 0.866025i 0.117489 0.0678323i −0.440104 0.897947i \(-0.645058\pi\)
0.557593 + 0.830115i \(0.311725\pi\)
\(164\) −9.00000 + 5.19615i −0.702782 + 0.405751i
\(165\) −36.0000 −2.80260
\(166\) 3.46410i 0.268866i
\(167\) 3.00000 1.73205i 0.232147 0.134030i −0.379415 0.925227i \(-0.623875\pi\)
0.611562 + 0.791196i \(0.290541\pi\)
\(168\) −1.50000 + 4.33013i −0.115728 + 0.334077i
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 0 0
\(171\) −7.50000 + 12.9904i −0.573539 + 0.993399i
\(172\) −0.500000 + 0.866025i −0.0381246 + 0.0660338i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 12.0000 0.909718
\(175\) 14.0000 12.1244i 1.05830 0.916515i
\(176\) −3.00000 + 5.19615i −0.226134 + 0.391675i
\(177\) 0 0
\(178\) 3.46410i 0.259645i
\(179\) 21.0000 + 12.1244i 1.56961 + 0.906217i 0.996213 + 0.0869415i \(0.0277093\pi\)
0.573400 + 0.819275i \(0.305624\pi\)
\(180\) 10.3923i 0.774597i
\(181\) 15.5885i 1.15868i 0.815086 + 0.579340i \(0.196690\pi\)
−0.815086 + 0.579340i \(0.803310\pi\)
\(182\) 8.00000 + 5.19615i 0.592999 + 0.385164i
\(183\) −9.00000 −0.665299
\(184\) 3.46410i 0.255377i
\(185\) −15.0000 + 25.9808i −1.10282 + 1.91014i
\(186\) 13.8564i 1.01600i
\(187\) 0 0
\(188\) −6.00000 3.46410i −0.437595 0.252646i
\(189\) −13.5000 + 2.59808i −0.981981 + 0.188982i
\(190\) 17.3205i 1.25656i
\(191\) 18.0000 10.3923i 1.30243 0.751961i 0.321613 0.946871i \(-0.395775\pi\)
0.980821 + 0.194910i \(0.0624416\pi\)
\(192\) −1.50000 0.866025i −0.108253 0.0625000i
\(193\) −4.50000 2.59808i −0.323917 0.187014i 0.329220 0.944253i \(-0.393214\pi\)
−0.653137 + 0.757240i \(0.726548\pi\)
\(194\) −3.50000 + 6.06218i −0.251285 + 0.435239i
\(195\) −21.0000 5.19615i −1.50384 0.372104i
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −6.00000 10.3923i −0.427482 0.740421i 0.569166 0.822222i \(-0.307266\pi\)
−0.996649 + 0.0818013i \(0.973933\pi\)
\(198\) −18.0000 −1.27920
\(199\) 15.5885i 1.10504i 0.833501 + 0.552518i \(0.186333\pi\)
−0.833501 + 0.552518i \(0.813667\pi\)
\(200\) 3.50000 + 6.06218i 0.247487 + 0.428661i
\(201\) 3.00000 + 5.19615i 0.211604 + 0.366508i
\(202\) −3.00000 + 5.19615i −0.211079 + 0.365600i
\(203\) 12.0000 + 13.8564i 0.842235 + 0.972529i
\(204\) 0 0
\(205\) 36.0000 2.51435
\(206\) 4.50000 + 2.59808i 0.313530 + 0.181017i
\(207\) 9.00000 5.19615i 0.625543 0.361158i
\(208\) −2.50000 + 2.59808i −0.173344 + 0.180144i
\(209\) −30.0000 −2.07514
\(210\) 12.0000 10.3923i 0.828079 0.717137i
\(211\) −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i \(-0.221724\pi\)
−0.939156 + 0.343490i \(0.888391\pi\)
\(212\) −3.00000 + 1.73205i −0.206041 + 0.118958i
\(213\) 0 0
\(214\) 0 0
\(215\) 3.00000 1.73205i 0.204598 0.118125i
\(216\) 5.19615i 0.353553i
\(217\) −16.0000 + 13.8564i −1.08615 + 0.940634i
\(218\) −10.5000 + 6.06218i −0.711150 + 0.410582i
\(219\) 12.1244i 0.819288i
\(220\) 18.0000 10.3923i 1.21356 0.700649i
\(221\) 0 0
\(222\) −7.50000 + 12.9904i −0.503367 + 0.871857i
\(223\) −8.00000 13.8564i −0.535720 0.927894i −0.999128 0.0417488i \(-0.986707\pi\)
0.463409 0.886145i \(-0.346626\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) −10.5000 + 18.1865i −0.700000 + 1.21244i
\(226\) 6.00000 + 3.46410i 0.399114 + 0.230429i
\(227\) 10.3923i 0.689761i −0.938647 0.344881i \(-0.887919\pi\)
0.938647 0.344881i \(-0.112081\pi\)
\(228\) 8.66025i 0.573539i
\(229\) −14.5000 + 25.1147i −0.958187 + 1.65963i −0.231287 + 0.972886i \(0.574293\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) −6.00000 + 10.3923i −0.395628 + 0.685248i
\(231\) −18.0000 20.7846i −1.18431 1.36753i
\(232\) −6.00000 + 3.46410i −0.393919 + 0.227429i
\(233\) 6.00000 + 3.46410i 0.393073 + 0.226941i 0.683491 0.729959i \(-0.260461\pi\)
−0.290418 + 0.956900i \(0.593794\pi\)
\(234\) −10.5000 2.59808i −0.686406 0.169842i
\(235\) 12.0000 + 20.7846i 0.782794 + 1.35584i
\(236\) 0 0
\(237\) −12.0000 + 6.92820i −0.779484 + 0.450035i
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 3.00000 + 5.19615i 0.193649 + 0.335410i
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) −12.5000 21.6506i −0.803530 1.39176i
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 4.50000 2.59808i 0.288083 0.166325i
\(245\) 24.0000 + 3.46410i 1.53330 + 0.221313i
\(246\) 18.0000 1.14764
\(247\) −17.5000 4.33013i −1.11350 0.275519i
\(248\) −4.00000 6.92820i −0.254000 0.439941i
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 6.92820i 0.438178i
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) 6.00000 5.19615i 0.377964 0.327327i
\(253\) 18.0000 + 10.3923i 1.13165 + 0.653359i
\(254\) −0.500000 0.866025i −0.0313728 0.0543393i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 1.50000 0.866025i 0.0933859 0.0539164i
\(259\) −22.5000 + 4.33013i −1.39808 + 0.269061i
\(260\) 12.0000 3.46410i 0.744208 0.214834i
\(261\) −18.0000 10.3923i −1.11417 0.643268i
\(262\) 9.00000 15.5885i 0.556022 0.963058i
\(263\) −12.0000 6.92820i −0.739952 0.427211i 0.0821001 0.996624i \(-0.473837\pi\)
−0.822052 + 0.569413i \(0.807171\pi\)
\(264\) 9.00000 5.19615i 0.553912 0.319801i
\(265\) 12.0000 0.737154
\(266\) 10.0000 8.66025i 0.613139 0.530994i
\(267\) −3.00000 + 5.19615i −0.183597 + 0.317999i
\(268\) −3.00000 1.73205i −0.183254 0.105802i
\(269\) −12.0000 −0.731653 −0.365826 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) −9.00000 + 15.5885i −0.547723 + 0.948683i
\(271\) 1.00000 0.0607457 0.0303728 0.999539i \(-0.490331\pi\)
0.0303728 + 0.999539i \(0.490331\pi\)
\(272\) 0 0
\(273\) −7.50000 14.7224i −0.453921 0.891042i
\(274\) −6.00000 −0.362473
\(275\) −42.0000 −2.53270
\(276\) −3.00000 + 5.19615i −0.180579 + 0.312772i
\(277\) 17.0000 1.02143 0.510716 0.859750i \(-0.329381\pi\)
0.510716 + 0.859750i \(0.329381\pi\)
\(278\) −3.00000 1.73205i −0.179928 0.103882i
\(279\) 12.0000 20.7846i 0.718421 1.24434i
\(280\) −3.00000 + 8.66025i −0.179284 + 0.517549i
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 6.00000 + 10.3923i 0.357295 + 0.618853i
\(283\) −1.50000 0.866025i −0.0891657 0.0514799i 0.454754 0.890617i \(-0.349727\pi\)
−0.543920 + 0.839137i \(0.683060\pi\)
\(284\) 0 0
\(285\) −15.0000 + 25.9808i −0.888523 + 1.53897i
\(286\) −6.00000 20.7846i −0.354787 1.22902i
\(287\) 18.0000 + 20.7846i 1.06251 + 1.22688i
\(288\) 1.50000 + 2.59808i 0.0883883 + 0.153093i
\(289\) −17.0000 −1.00000
\(290\) 24.0000 1.40933
\(291\) 10.5000 6.06218i 0.615521 0.355371i
\(292\) 3.50000 + 6.06218i 0.204822 + 0.354762i
\(293\) −6.00000 3.46410i −0.350524 0.202375i 0.314392 0.949293i \(-0.398199\pi\)
−0.664916 + 0.746918i \(0.731533\pi\)
\(294\) 12.0000 + 1.73205i 0.699854 + 0.101015i
\(295\) 0 0
\(296\) 8.66025i 0.503367i
\(297\) 27.0000 + 15.5885i 1.56670 + 0.904534i
\(298\) −9.00000 15.5885i −0.521356 0.903015i
\(299\) 9.00000 + 8.66025i 0.520483 + 0.500835i
\(300\) 12.1244i 0.700000i
\(301\) 2.50000 + 0.866025i 0.144098 + 0.0499169i
\(302\) 3.00000 1.73205i 0.172631 0.0996683i
\(303\) 9.00000 5.19615i 0.517036 0.298511i
\(304\) 2.50000 + 4.33013i 0.143385 + 0.248350i
\(305\) −18.0000 −1.03068
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 15.0000 + 5.19615i 0.854704 + 0.296078i
\(309\) −4.50000 7.79423i −0.255996 0.443398i
\(310\) 27.7128i 1.57398i
\(311\) −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) 6.00000 1.73205i 0.339683 0.0980581i
\(313\) −28.5000 16.4545i −1.61092 0.930062i −0.989158 0.146852i \(-0.953086\pi\)
−0.621757 0.783210i \(-0.713581\pi\)
\(314\) −16.5000 + 9.52628i −0.931149 + 0.537599i
\(315\) −27.0000 + 5.19615i −1.52128 + 0.292770i
\(316\) 4.00000 6.92820i 0.225018 0.389742i
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 6.00000 0.336463
\(319\) 41.5692i 2.32743i
\(320\) −3.00000 1.73205i −0.167705 0.0968246i
\(321\) 0 0
\(322\) −9.00000 + 1.73205i −0.501550 + 0.0965234i
\(323\) 0 0
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) −24.5000 6.06218i −1.35902 0.336269i
\(326\) 1.50000 0.866025i 0.0830773 0.0479647i
\(327\) 21.0000 1.16130
\(328\) −9.00000 + 5.19615i −0.496942 + 0.286910i
\(329\) −6.00000 + 17.3205i −0.330791 + 0.954911i
\(330\) −36.0000 −1.98173
\(331\) −16.5000 + 9.52628i −0.906922 + 0.523612i −0.879440 0.476011i \(-0.842082\pi\)
−0.0274825 + 0.999622i \(0.508749\pi\)
\(332\) 3.46410i 0.190117i
\(333\) 22.5000 12.9904i 1.23299 0.711868i
\(334\) 3.00000 1.73205i 0.164153 0.0947736i
\(335\) 6.00000 + 10.3923i 0.327815 + 0.567792i
\(336\) −1.50000 + 4.33013i −0.0818317 + 0.236228i
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) −0.500000 12.9904i −0.0271964 0.706584i
\(339\) −6.00000 10.3923i −0.325875 0.564433i
\(340\) 0 0
\(341\) 48.0000 2.59935
\(342\) −7.50000 + 12.9904i −0.405554 + 0.702439i
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) 18.0000 10.3923i 0.969087 0.559503i
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 12.0000 0.643268
\(349\) −5.50000 9.52628i −0.294408 0.509930i 0.680439 0.732805i \(-0.261789\pi\)
−0.974847 + 0.222875i \(0.928456\pi\)
\(350\) 14.0000 12.1244i 0.748331 0.648074i
\(351\) 13.5000 + 12.9904i 0.720577 + 0.693375i
\(352\) −3.00000 + 5.19615i −0.159901 + 0.276956i
\(353\) −9.00000 5.19615i −0.479022 0.276563i 0.240987 0.970528i \(-0.422529\pi\)
−0.720009 + 0.693965i \(0.755862\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.46410i 0.183597i
\(357\) 0 0
\(358\) 21.0000 + 12.1244i 1.10988 + 0.640792i
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 10.3923i 0.547723i
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 15.5885i 0.819311i
\(363\) 43.3013i 2.27273i
\(364\) 8.00000 + 5.19615i 0.419314 + 0.272352i
\(365\) 24.2487i 1.26924i
\(366\) −9.00000 −0.470438
\(367\) 1.50000 + 0.866025i 0.0782994 + 0.0452062i 0.538639 0.842537i \(-0.318939\pi\)
−0.460339 + 0.887743i \(0.652272\pi\)
\(368\) 3.46410i 0.180579i
\(369\) −27.0000 15.5885i −1.40556 0.811503i
\(370\) −15.0000 + 25.9808i −0.779813 + 1.35068i
\(371\) 6.00000 + 6.92820i 0.311504 + 0.359694i
\(372\) 13.8564i 0.718421i
\(373\) 1.00000 + 1.73205i 0.0517780 + 0.0896822i 0.890753 0.454488i \(-0.150178\pi\)
−0.838975 + 0.544170i \(0.816844\pi\)
\(374\) 0 0
\(375\) −6.00000 + 10.3923i −0.309839 + 0.536656i
\(376\) −6.00000 3.46410i −0.309426 0.178647i
\(377\) 6.00000 24.2487i 0.309016 1.24887i
\(378\) −13.5000 + 2.59808i −0.694365 + 0.133631i
\(379\) −15.0000 + 8.66025i −0.770498 + 0.444847i −0.833052 0.553194i \(-0.813409\pi\)
0.0625541 + 0.998042i \(0.480075\pi\)
\(380\) 17.3205i 0.888523i
\(381\) 1.73205i 0.0887357i
\(382\) 18.0000 10.3923i 0.920960 0.531717i
\(383\) −18.0000 + 10.3923i −0.919757 + 0.531022i −0.883558 0.468323i \(-0.844859\pi\)
−0.0361995 + 0.999345i \(0.511525\pi\)
\(384\) −1.50000 0.866025i −0.0765466 0.0441942i
\(385\) −36.0000 41.5692i −1.83473 2.11856i
\(386\) −4.50000 2.59808i −0.229044 0.132239i
\(387\) −3.00000 −0.152499
\(388\) −3.50000 + 6.06218i −0.177686 + 0.307760i
\(389\) 9.00000 5.19615i 0.456318 0.263455i −0.254177 0.967158i \(-0.581804\pi\)
0.710495 + 0.703702i \(0.248471\pi\)
\(390\) −21.0000 5.19615i −1.06338 0.263117i
\(391\) 0 0
\(392\) −6.50000 + 2.59808i −0.328300 + 0.131223i
\(393\) −27.0000 + 15.5885i −1.36197 + 0.786334i
\(394\) −6.00000 10.3923i −0.302276 0.523557i
\(395\) −24.0000 + 13.8564i −1.20757 + 0.697191i
\(396\) −18.0000 −0.904534
\(397\) 5.50000 + 9.52628i 0.276037 + 0.478110i 0.970396 0.241518i \(-0.0776454\pi\)
−0.694359 + 0.719629i \(0.744312\pi\)
\(398\) 15.5885i 0.781379i
\(399\) −22.5000 + 4.33013i −1.12641 + 0.216777i
\(400\) 3.50000 + 6.06218i 0.175000 + 0.303109i
\(401\) −6.00000 −0.299626 −0.149813 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 3.00000 + 5.19615i 0.149626 + 0.259161i
\(403\) 28.0000 + 6.92820i 1.39478 + 0.345118i
\(404\) −3.00000 + 5.19615i −0.149256 + 0.258518i
\(405\) 27.0000 15.5885i 1.34164 0.774597i
\(406\) 12.0000 + 13.8564i 0.595550 + 0.687682i
\(407\) 45.0000 + 25.9808i 2.23057 + 1.28782i
\(408\) 0 0
\(409\) 19.0000 0.939490 0.469745 0.882802i \(-0.344346\pi\)
0.469745 + 0.882802i \(0.344346\pi\)
\(410\) 36.0000 1.77791
\(411\) 9.00000 + 5.19615i 0.443937 + 0.256307i
\(412\) 4.50000 + 2.59808i 0.221699 + 0.127998i
\(413\) 0 0
\(414\) 9.00000 5.19615i 0.442326 0.255377i
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) −2.50000 + 2.59808i −0.122573 + 0.127381i
\(417\) 3.00000 + 5.19615i 0.146911 + 0.254457i
\(418\) −30.0000 −1.46735
\(419\) −15.0000 25.9808i −0.732798 1.26924i −0.955683 0.294398i \(-0.904881\pi\)
0.222885 0.974845i \(-0.428453\pi\)
\(420\) 12.0000 10.3923i 0.585540 0.507093i
\(421\) 27.7128i 1.35064i 0.737525 + 0.675320i \(0.235994\pi\)
−0.737525 + 0.675320i \(0.764006\pi\)
\(422\) −2.50000 4.33013i −0.121698 0.210787i
\(423\) 20.7846i 1.01058i
\(424\) −3.00000 + 1.73205i −0.145693 + 0.0841158i
\(425\) 0 0
\(426\) 0 0
\(427\) −9.00000 10.3923i −0.435541 0.502919i
\(428\) 0 0
\(429\) −9.00000 + 36.3731i −0.434524 + 1.75611i
\(430\) 3.00000 1.73205i 0.144673 0.0835269i
\(431\) 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 18.0000 + 10.3923i 0.865025 + 0.499422i 0.865692 0.500577i \(-0.166879\pi\)
−0.000666943 1.00000i \(0.500212\pi\)
\(434\) −16.0000 + 13.8564i −0.768025 + 0.665129i
\(435\) −36.0000 20.7846i −1.72607 0.996546i
\(436\) −10.5000 + 6.06218i −0.502859 + 0.290326i
\(437\) 15.0000 8.66025i 0.717547 0.414276i
\(438\) 12.1244i 0.579324i
\(439\) 12.1244i 0.578664i 0.957229 + 0.289332i \(0.0934331\pi\)
−0.957229 + 0.289332i \(0.906567\pi\)
\(440\) 18.0000 10.3923i 0.858116 0.495434i
\(441\) −16.5000 12.9904i −0.785714 0.618590i
\(442\) 0 0
\(443\) 33.0000 + 19.0526i 1.56788 + 0.905214i 0.996416 + 0.0845852i \(0.0269565\pi\)
0.571461 + 0.820629i \(0.306377\pi\)
\(444\) −7.50000 + 12.9904i −0.355934 + 0.616496i
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) −8.00000 13.8564i −0.378811 0.656120i
\(447\) 31.1769i 1.47462i
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) 15.0000 25.9808i 0.707894 1.22611i −0.257743 0.966213i \(-0.582979\pi\)
0.965637 0.259895i \(-0.0836878\pi\)
\(450\) −10.5000 + 18.1865i −0.494975 + 0.857321i
\(451\) 62.3538i 2.93613i
\(452\) 6.00000 + 3.46410i 0.282216 + 0.162938i
\(453\) −6.00000 −0.281905
\(454\) 10.3923i 0.487735i
\(455\) −15.0000 29.4449i −0.703211 1.38040i
\(456\) 8.66025i 0.405554i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −14.5000 + 25.1147i −0.677541 + 1.17353i
\(459\) 0 0
\(460\) −6.00000 + 10.3923i −0.279751 + 0.484544i
\(461\) 18.0000 + 10.3923i 0.838344 + 0.484018i 0.856701 0.515814i \(-0.172510\pi\)
−0.0183573 + 0.999831i \(0.505844\pi\)
\(462\) −18.0000 20.7846i −0.837436 0.966988i
\(463\) 19.0526i 0.885448i 0.896658 + 0.442724i \(0.145988\pi\)
−0.896658 + 0.442724i \(0.854012\pi\)
\(464\) −6.00000 + 3.46410i −0.278543 + 0.160817i
\(465\) 24.0000 41.5692i 1.11297 1.92773i
\(466\) 6.00000 + 3.46410i 0.277945 + 0.160471i
\(467\) −9.00000 + 15.5885i −0.416470 + 0.721348i −0.995582 0.0939008i \(-0.970066\pi\)
0.579111 + 0.815249i \(0.303400\pi\)
\(468\) −10.5000 2.59808i −0.485363 0.120096i
\(469\) −3.00000 + 8.66025i −0.138527 + 0.399893i
\(470\) 12.0000 + 20.7846i 0.553519 + 0.958723i
\(471\) 33.0000 1.52056
\(472\) 0 0
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) −12.0000 + 6.92820i −0.551178 + 0.318223i
\(475\) −17.5000 + 30.3109i −0.802955 + 1.39076i
\(476\) 0 0
\(477\) −9.00000 5.19615i −0.412082 0.237915i
\(478\) −6.00000 −0.274434
\(479\) −6.00000 3.46410i −0.274147 0.158279i 0.356624 0.934248i \(-0.383928\pi\)
−0.630771 + 0.775969i \(0.717261\pi\)
\(480\) 3.00000 + 5.19615i 0.136931 + 0.237171i
\(481\) 22.5000 + 21.6506i 1.02591 + 0.987184i
\(482\) 26.0000 1.18427
\(483\) 15.0000 + 5.19615i 0.682524 + 0.236433i
\(484\) −12.5000 21.6506i −0.568182 0.984120i
\(485\) 21.0000 12.1244i 0.953561 0.550539i
\(486\) 13.5000 7.79423i 0.612372 0.353553i
\(487\) 15.5885i 0.706380i −0.935552 0.353190i \(-0.885097\pi\)
0.935552 0.353190i \(-0.114903\pi\)
\(488\) 4.50000 2.59808i 0.203705 0.117609i
\(489\) −3.00000 −0.135665
\(490\) 24.0000 + 3.46410i 1.08421 + 0.156492i
\(491\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 18.0000 0.811503
\(493\) 0 0
\(494\) −17.5000 4.33013i −0.787362 0.194822i
\(495\) 54.0000 + 31.1769i 2.42712 + 1.40130i
\(496\) −4.00000 6.92820i −0.179605 0.311086i
\(497\) 0 0
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) −7.50000 4.33013i −0.335746 0.193843i 0.322643 0.946521i \(-0.395429\pi\)
−0.658389 + 0.752678i \(0.728762\pi\)
\(500\) 6.92820i 0.309839i
\(501\) −6.00000 −0.268060
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) −15.0000 + 25.9808i −0.668817 + 1.15842i 0.309418 + 0.950926i \(0.399866\pi\)
−0.978235 + 0.207499i \(0.933468\pi\)
\(504\) 6.00000 5.19615i 0.267261 0.231455i
\(505\) 18.0000 10.3923i 0.800989 0.462451i
\(506\) 18.0000 + 10.3923i 0.800198 + 0.461994i
\(507\) −10.5000 + 19.9186i −0.466321 + 0.884615i
\(508\) −0.500000 0.866025i −0.0221839 0.0384237i
\(509\) 24.2487i 1.07481i −0.843326 0.537403i \(-0.819406\pi\)
0.843326 0.537403i \(-0.180594\pi\)
\(510\) 0 0
\(511\) 14.0000 12.1244i 0.619324 0.536350i
\(512\) 1.00000 0.0441942
\(513\) 22.5000 12.9904i 0.993399 0.573539i
\(514\) 18.0000 0.793946
\(515\) −9.00000 15.5885i −0.396587 0.686909i
\(516\) 1.50000 0.866025i 0.0660338 0.0381246i
\(517\) 36.0000 20.7846i 1.58328 0.914106i
\(518\) −22.5000 + 4.33013i −0.988593 + 0.190255i
\(519\) 10.3923i 0.456172i
\(520\) 12.0000 3.46410i 0.526235 0.151911i
\(521\) 6.00000 + 10.3923i 0.262865 + 0.455295i 0.967002 0.254769i \(-0.0819994\pi\)
−0.704137 + 0.710064i \(0.748666\pi\)
\(522\) −18.0000 10.3923i −0.787839 0.454859i
\(523\) 8.66025i 0.378686i 0.981911 + 0.189343i \(0.0606359\pi\)
−0.981911 + 0.189343i \(0.939364\pi\)
\(524\) 9.00000 15.5885i 0.393167 0.680985i
\(525\) −31.5000 + 6.06218i −1.37477 + 0.264575i
\(526\) −12.0000 6.92820i −0.523225 0.302084i
\(527\) 0 0
\(528\) 9.00000 5.19615i 0.391675 0.226134i
\(529\) 11.0000 0.478261
\(530\) 12.0000 0.521247
\(531\) 0 0
\(532\) 10.0000 8.66025i 0.433555 0.375470i
\(533\) 9.00000 36.3731i 0.389833 1.57549i
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 0 0
\(536\) −3.00000 1.73205i −0.129580 0.0748132i
\(537\) −21.0000 36.3731i −0.906217 1.56961i
\(538\) −12.0000 −0.517357
\(539\) 6.00000 41.5692i 0.258438 1.79051i
\(540\) −9.00000 + 15.5885i −0.387298 + 0.670820i
\(541\) 1.50000 + 0.866025i 0.0644900 + 0.0372333i 0.531898 0.846808i \(-0.321479\pi\)
−0.467408 + 0.884042i \(0.654812\pi\)
\(542\) 1.00000 0.0429537
\(543\) 13.5000 23.3827i 0.579340 1.00345i
\(544\) 0 0
\(545\) 42.0000 1.79908
\(546\) −7.50000 14.7224i −0.320970 0.630062i
\(547\) −25.0000 −1.06892 −0.534461 0.845193i \(-0.679486\pi\)
−0.534461 + 0.845193i \(0.679486\pi\)
\(548\) −6.00000 −0.256307
\(549\) 13.5000 + 7.79423i 0.576166 + 0.332650i
\(550\) −42.0000 −1.79089
\(551\) −30.0000 17.3205i −1.27804 0.737878i
\(552\) −3.00000 + 5.19615i −0.127688 + 0.221163i
\(553\) −20.0000 6.92820i −0.850487 0.294617i
\(554\) 17.0000 0.722261
\(555\) 45.0000 25.9808i 1.91014 1.10282i
\(556\) −3.00000 1.73205i −0.127228 0.0734553i
\(557\) 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) 12.0000 20.7846i 0.508001 0.879883i
\(559\) −1.00000 3.46410i −0.0422955 0.146516i
\(560\) −3.00000 + 8.66025i −0.126773 + 0.365963i
\(561\) 0 0
\(562\) 12.0000 0.506189
\(563\) 18.0000 0.758610 0.379305 0.925272i \(-0.376163\pi\)
0.379305 + 0.925272i \(0.376163\pi\)
\(564\) 6.00000 + 10.3923i 0.252646 + 0.437595i
\(565\) −12.0000 20.7846i −0.504844 0.874415i
\(566\) −1.50000 0.866025i −0.0630497 0.0364018i
\(567\) 22.5000 + 7.79423i 0.944911 + 0.327327i
\(568\) 0 0
\(569\) 27.7128i 1.16178i −0.813982 0.580891i \(-0.802704\pi\)
0.813982 0.580891i \(-0.197296\pi\)
\(570\) −15.0000 + 25.9808i −0.628281 + 1.08821i
\(571\) −9.50000 16.4545i −0.397563 0.688599i 0.595862 0.803087i \(-0.296811\pi\)
−0.993425 + 0.114488i \(0.963477\pi\)
\(572\) −6.00000 20.7846i −0.250873 0.869048i
\(573\) −36.0000 −1.50392
\(574\) 18.0000 + 20.7846i 0.751305 + 0.867533i
\(575\) 21.0000 12.1244i 0.875761 0.505621i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −18.5000 32.0429i −0.770165 1.33397i −0.937472 0.348060i \(-0.886840\pi\)
0.167307 0.985905i \(-0.446493\pi\)
\(578\) −17.0000 −0.707107
\(579\) 4.50000 + 7.79423i 0.187014 + 0.323917i
\(580\) 24.0000 0.996546
\(581\) −9.00000 + 1.73205i −0.373383 + 0.0718576i
\(582\) 10.5000 6.06218i 0.435239 0.251285i
\(583\) 20.7846i 0.860811i
\(584\) 3.50000 + 6.06218i 0.144831 + 0.250855i
\(585\) 27.0000 + 25.9808i 1.11631 + 1.07417i
\(586\) −6.00000 3.46410i −0.247858 0.143101i
\(587\) 39.0000 22.5167i 1.60970 0.929362i 0.620266 0.784391i \(-0.287025\pi\)
0.989436 0.144971i \(-0.0463088\pi\)
\(588\) 12.0000 + 1.73205i 0.494872 + 0.0714286i
\(589\) 20.0000 34.6410i 0.824086 1.42736i
\(590\) 0 0
\(591\) 20.7846i 0.854965i
\(592\) 8.66025i 0.355934i
\(593\) −6.00000 3.46410i −0.246390 0.142254i 0.371720 0.928345i \(-0.378768\pi\)
−0.618110 + 0.786091i \(0.712102\pi\)
\(594\) 27.0000 + 15.5885i 1.10782 + 0.639602i
\(595\) 0 0
\(596\) −9.00000 15.5885i −0.368654 0.638528i
\(597\) 13.5000 23.3827i 0.552518 0.956990i
\(598\) 9.00000 + 8.66025i 0.368037 + 0.354144i
\(599\) −24.0000 + 13.8564i −0.980613 + 0.566157i −0.902455 0.430784i \(-0.858237\pi\)
−0.0781581 + 0.996941i \(0.524904\pi\)
\(600\) 12.1244i 0.494975i
\(601\) 1.50000 0.866025i 0.0611863 0.0353259i −0.469095 0.883148i \(-0.655420\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 2.50000 + 0.866025i 0.101892 + 0.0352966i
\(603\) 10.3923i 0.423207i
\(604\) 3.00000 1.73205i 0.122068 0.0704761i
\(605\) 86.6025i 3.52089i
\(606\) 9.00000 5.19615i 0.365600 0.211079i
\(607\) −13.5000 + 7.79423i −0.547948 + 0.316358i −0.748294 0.663367i \(-0.769127\pi\)
0.200346 + 0.979725i \(0.435793\pi\)
\(608\) 2.50000 + 4.33013i 0.101388 + 0.175610i
\(609\) −6.00000 31.1769i −0.243132 1.26335i
\(610\) −18.0000 −0.728799
\(611\) 24.0000 6.92820i 0.970936 0.280285i
\(612\) 0 0
\(613\) 22.5000 + 12.9904i 0.908766 + 0.524677i 0.880034 0.474911i \(-0.157520\pi\)
0.0287324 + 0.999587i \(0.490853\pi\)
\(614\) −4.00000 −0.161427
\(615\) −54.0000 31.1769i −2.17749 1.25717i
\(616\) 15.0000 + 5.19615i 0.604367 + 0.209359i
\(617\) −18.0000 + 31.1769i −0.724653 + 1.25514i 0.234464 + 0.972125i \(0.424666\pi\)
−0.959117 + 0.283011i \(0.908667\pi\)
\(618\) −4.50000 7.79423i −0.181017 0.313530i
\(619\) 8.50000 + 14.7224i 0.341644 + 0.591744i 0.984738 0.174042i \(-0.0556830\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 27.7128i 1.11297i
\(621\) −18.0000 −0.722315
\(622\) −3.00000 5.19615i −0.120289 0.208347i
\(623\) −9.00000 + 1.73205i −0.360577 + 0.0693932i
\(624\) 6.00000 1.73205i 0.240192 0.0693375i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −28.5000 16.4545i −1.13909 0.657653i
\(627\) 45.0000 + 25.9808i 1.79713 + 1.03757i
\(628\) −16.5000 + 9.52628i −0.658422 + 0.380140i
\(629\) 0 0
\(630\) −27.0000 + 5.19615i −1.07571 + 0.207020i
\(631\) 22.5000 + 12.9904i 0.895711 + 0.517139i 0.875806 0.482663i \(-0.160330\pi\)
0.0199047 + 0.999802i \(0.493664\pi\)
\(632\) 4.00000 6.92820i 0.159111 0.275589i
\(633\) 8.66025i 0.344214i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 3.46410i 0.137469i
\(636\) 6.00000 0.237915
\(637\) 9.50000 23.3827i 0.376404 0.926456i
\(638\) 41.5692i 1.64574i
\(639\) 0 0
\(640\) −3.00000 1.73205i −0.118585 0.0684653i
\(641\) 38.1051i 1.50506i 0.658557 + 0.752531i \(0.271167\pi\)
−0.658557 + 0.752531i \(0.728833\pi\)
\(642\) 0 0
\(643\) −5.50000 + 9.52628i −0.216899 + 0.375680i −0.953858 0.300257i \(-0.902928\pi\)
0.736959 + 0.675937i \(0.236261\pi\)
\(644\) −9.00000 + 1.73205i −0.354650 + 0.0682524i
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) −18.0000 + 31.1769i −0.707653 + 1.22569i 0.258073 + 0.966126i \(0.416913\pi\)
−0.965726 + 0.259565i \(0.916421\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 0 0
\(650\) −24.5000 6.06218i −0.960969 0.237778i
\(651\) 36.0000 6.92820i 1.41095 0.271538i
\(652\) 1.50000 0.866025i 0.0587445 0.0339162i
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 21.0000 0.821165
\(655\) −54.0000 + 31.1769i −2.10995 + 1.21818i
\(656\) −9.00000 + 5.19615i −0.351391 + 0.202876i
\(657\) −10.5000 + 18.1865i −0.409644 + 0.709524i
\(658\) −6.00000 + 17.3205i −0.233904 + 0.675224i
\(659\) −24.0000 13.8564i −0.934907 0.539769i −0.0465470 0.998916i \(-0.514822\pi\)
−0.888360 + 0.459147i \(0.848155\pi\)
\(660\) −36.0000 −1.40130
\(661\) −25.0000 + 43.3013i −0.972387 + 1.68422i −0.284087 + 0.958799i \(0.591690\pi\)
−0.688301 + 0.725426i \(0.741643\pi\)
\(662\) −16.5000 + 9.52628i −0.641291 + 0.370249i
\(663\) 0 0
\(664\) 3.46410i 0.134433i
\(665\) −45.0000 + 8.66025i −1.74503 + 0.335830i
\(666\) 22.5000 12.9904i 0.871857 0.503367i
\(667\) 12.0000 + 20.7846i 0.464642 + 0.804783i
\(668\) 3.00000 1.73205i 0.116073 0.0670151i
\(669\) 27.7128i 1.07144i
\(670\) 6.00000 + 10.3923i 0.231800 + 0.401490i
\(671\) 31.1769i 1.20357i
\(672\) −1.50000 + 4.33013i −0.0578638 + 0.167038i
\(673\) −0.500000 0.866025i −0.0192736 0.0333828i 0.856228 0.516599i \(-0.172802\pi\)
−0.875501 + 0.483216i \(0.839469\pi\)
\(674\) 5.00000 0.192593
\(675\) 31.5000 18.1865i 1.21244 0.700000i
\(676\) −0.500000 12.9904i −0.0192308 0.499630i
\(677\) −9.00000 + 15.5885i −0.345898 + 0.599113i −0.985517 0.169580i \(-0.945759\pi\)
0.639618 + 0.768693i \(0.279092\pi\)
\(678\) −6.00000 10.3923i −0.230429 0.399114i
\(679\) 17.5000 + 6.06218i 0.671588 + 0.232645i
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) 48.0000 1.83801
\(683\) −18.0000 −0.688751 −0.344375 0.938832i \(-0.611909\pi\)
−0.344375 + 0.938832i \(0.611909\pi\)
\(684\) −7.50000 + 12.9904i −0.286770 + 0.496700i
\(685\) 18.0000 + 10.3923i 0.687745 + 0.397070i
\(686\) 10.0000 + 15.5885i 0.381802 + 0.595170i
\(687\) 43.5000 25.1147i 1.65963 0.958187i
\(688\) −0.500000 + 0.866025i −0.0190623 + 0.0330169i
\(689\) 3.00000 12.1244i 0.114291 0.461901i
\(690\) 18.0000 10.3923i 0.685248 0.395628i
\(691\) −17.0000 −0.646710 −0.323355 0.946278i \(-0.604811\pi\)
−0.323355 + 0.946278i \(0.604811\pi\)
\(692\) 3.00000 + 5.19615i 0.114043 + 0.197528i
\(693\) 9.00000 + 46.7654i 0.341882 + 1.77647i
\(694\) 0 0
\(695\) 6.00000 + 10.3923i 0.227593 + 0.394203i
\(696\) 12.0000 0.454859
\(697\) 0 0
\(698\) −5.50000 9.52628i −0.208178 0.360575i
\(699\) −6.00000 10.3923i −0.226941 0.393073i
\(700\) 14.0000 12.1244i 0.529150 0.458258i
\(701\) 13.8564i 0.523349i 0.965156 + 0.261675i \(0.0842747\pi\)
−0.965156 + 0.261675i \(0.915725\pi\)
\(702\) 13.5000 + 12.9904i 0.509525 + 0.490290i
\(703\) 37.5000 21.6506i 1.41434 0.816569i
\(704\) −3.00000 + 5.19615i −0.113067 + 0.195837i
\(705\) 41.5692i 1.56559i
\(706\) −9.00000 5.19615i −0.338719 0.195560i
\(707\) 15.0000 + 5.19615i 0.564133 + 0.195421i
\(708\) 0 0
\(709\) −34.5000 + 19.9186i −1.29567 + 0.748058i −0.979654 0.200694i \(-0.935680\pi\)
−0.316021 + 0.948752i \(0.602347\pi\)
\(710\) 0 0
\(711\) 24.0000 0.900070
\(712\) 3.46410i 0.129823i
\(713\) −24.0000 + 13.8564i −0.898807 + 0.518927i
\(714\) 0 0
\(715\) −18.0000 + 72.7461i −0.673162 + 2.72055i
\(716\) 21.0000 + 12.1244i 0.784807 + 0.453108i
\(717\) 9.00000 + 5.19615i 0.336111 + 0.194054i
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) 15.0000 + 25.9808i 0.559406 + 0.968919i 0.997546 + 0.0700124i \(0.0223039\pi\)
−0.438141 + 0.898906i \(0.644363\pi\)
\(720\) 10.3923i 0.387298i
\(721\) 4.50000 12.9904i 0.167589 0.483787i
\(722\) −3.00000 + 5.19615i −0.111648 + 0.193381i
\(723\) −39.0000 22.5167i −1.45043 0.837404i
\(724\) 15.5885i 0.579340i
\(725\) −42.0000 24.2487i −1.55984 0.900575i
\(726\) 43.3013i 1.60706i
\(727\) 10.3923i 0.385429i −0.981255 0.192715i \(-0.938271\pi\)
0.981255 0.192715i \(-0.0617292\pi\)
\(728\) 8.00000 + 5.19615i 0.296500 + 0.192582i
\(729\) −27.0000 −1.00000
\(730\) 24.2487i 0.897485i
\(731\) 0 0
\(732\) −9.00000 −0.332650
\(733\) 23.0000 39.8372i 0.849524 1.47142i −0.0321090 0.999484i \(-0.510222\pi\)
0.881633 0.471935i \(-0.156444\pi\)
\(734\) 1.50000 + 0.866025i 0.0553660 + 0.0319656i
\(735\) −33.0000 25.9808i −1.21722 0.958315i
\(736\) 3.46410i 0.127688i
\(737\) 18.0000 10.3923i 0.663039 0.382805i
\(738\) −27.0000 15.5885i −0.993884 0.573819i
\(739\) −28.5000 16.4545i −1.04839 0.605288i −0.126191 0.992006i \(-0.540275\pi\)
−0.922198 + 0.386718i \(0.873609\pi\)
\(740\) −15.0000 + 25.9808i −0.551411 + 0.955072i
\(741\) 22.5000 + 21.6506i 0.826558 + 0.795356i
\(742\) 6.00000 + 6.92820i 0.220267 + 0.254342i
\(743\) −15.0000 25.9808i −0.550297 0.953142i −0.998253 0.0590862i \(-0.981181\pi\)
0.447956 0.894055i \(-0.352152\pi\)
\(744\) 13.8564i 0.508001i
\(745\) 62.3538i 2.28447i
\(746\) 1.00000 + 1.73205i 0.0366126 + 0.0634149i
\(747\) 9.00000 5.19615i 0.329293 0.190117i
\(748\) 0 0
\(749\) 0 0
\(750\) −6.00000 + 10.3923i −0.219089 + 0.379473i
\(751\) −17.0000 −0.620339 −0.310169 0.950681i \(-0.600386\pi\)
−0.310169 + 0.950681i \(0.600386\pi\)
\(752\) −6.00000 3.46410i −0.218797 0.126323i
\(753\) −18.0000 + 10.3923i −0.655956 + 0.378717i
\(754\) 6.00000 24.2487i 0.218507 0.883086i
\(755\) −12.0000 −0.436725
\(756\) −13.5000 + 2.59808i −0.490990 + 0.0944911i
\(757\) −19.0000 32.9090i −0.690567 1.19610i −0.971652 0.236414i \(-0.924028\pi\)
0.281086 0.959683i \(-0.409305\pi\)
\(758\) −15.0000 + 8.66025i −0.544825 + 0.314555i
\(759\) −18.0000 31.1769i −0.653359 1.13165i
\(760\) 17.3205i 0.628281i
\(761\) 3.00000 1.73205i 0.108750 0.0627868i −0.444639 0.895710i \(-0.646668\pi\)
0.553388 + 0.832923i \(0.313335\pi\)
\(762\) 1.73205i 0.0627456i
\(763\) 21.0000 + 24.2487i 0.760251 + 0.877862i
\(764\) 18.0000 10.3923i 0.651217 0.375980i
\(765\) 0 0
\(766\) −18.0000 + 10.3923i −0.650366 + 0.375489i
\(767\) 0 0
\(768\) −1.50000 0.866025i −0.0541266 0.0312500i
\(769\) 0.500000 + 0.866025i 0.0180305 + 0.0312297i 0.874900 0.484304i \(-0.160927\pi\)
−0.856869 + 0.515534i \(0.827594\pi\)
\(770\) −36.0000 41.5692i −1.29735 1.49805i
\(771\) −27.0000 15.5885i −0.972381 0.561405i
\(772\) −4.50000 2.59808i −0.161959 0.0935068i
\(773\) 41.5692i 1.49514i −0.664183 0.747570i \(-0.731220\pi\)
0.664183 0.747570i \(-0.268780\pi\)
\(774\) −3.00000 −0.107833
\(775\) 28.0000 48.4974i 1.00579 1.74208i
\(776\) −3.50000 + 6.06218i −0.125643 + 0.217620i
\(7