Properties

Label 546.2.bi.c.17.1
Level $546$
Weight $2$
Character 546.17
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 17.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.17
Dual form 546.2.bi.c.257.1

$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

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

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 −0.987048 0.160424i \(-0.948714\pi\)
−0.354593 + 0.935021i \(0.615380\pi\)
\(6\) −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 −0.821541 0.570149i \(-0.806886\pi\)
−0.0829925 0.996550i \(-0.526448\pi\)
\(12\) −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 −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) −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 \(0.117618\pi\)
−0.932505 + 0.361158i \(0.882382\pi\)
\(24\) −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 −0.174265 0.984699i \(-0.555755\pi\)
−0.939907 + 0.341431i \(0.889088\pi\)
\(30\) 3.00000 5.19615i 0.547723 0.948683i
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) 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 \(0.252151\pi\)
−0.702313 + 0.711868i \(0.747849\pi\)
\(38\) 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 −0.410608 0.911812i \(-0.634683\pi\)
−0.994956 + 0.100309i \(0.968017\pi\)
\(42\) −1.50000 4.33013i −0.231455 0.668153i
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) −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 −0.869069 0.494690i \(-0.835282\pi\)
−0.00612051 + 0.999981i \(0.501948\pi\)
\(48\) −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 0.279602 0.960116i \(-0.409797\pi\)
−0.691684 + 0.722200i \(0.743131\pi\)
\(54\) 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 0.759608 0.650381i \(-0.225391\pi\)
−0.183442 + 0.983030i \(0.558724\pi\)
\(62\) −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 −0.671932 0.740613i \(-0.734535\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) 1.50000 2.59808i 0.176777 0.306186i
\(73\) 3.50000 6.06218i 0.409644 0.709524i −0.585206 0.810885i \(-0.698986\pi\)
0.994850 + 0.101361i \(0.0323196\pi\)
\(74\) 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 0.998388 0.0567635i \(-0.0180781\pi\)
−0.548352 + 0.836247i \(0.684745\pi\)
\(80\) −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 \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) −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 \(0.0587741\pi\)
−0.983002 + 0.183597i \(0.941226\pi\)
\(90\) 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 0.631810 0.775123i \(-0.282312\pi\)
−0.987181 + 0.159602i \(0.948979\pi\)
\(98\) −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 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) 4.50000 2.59808i 0.443398 0.255996i −0.261640 0.965166i \(-0.584263\pi\)
0.705038 + 0.709170i \(0.250930\pi\)
\(104\) −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 −0.0957826 0.995402i \(-0.530535\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 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 −0.190490 0.981689i \(-0.561008\pi\)
0.754923 + 0.655814i \(0.227674\pi\)
\(114\) 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 −0.887357 0.461084i \(-0.847461\pi\)
0.842989 + 0.537931i \(0.180794\pi\)
\(128\) 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 0.928199 + 0.372084i \(0.121357\pi\)
−0.141865 + 0.989886i \(0.545310\pi\)
\(132\) 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 −0.621803 0.783174i \(-0.713600\pi\)
0.367347 + 0.930084i \(0.380266\pi\)
\(140\) −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 0.216394 + 0.976306i \(0.430570\pi\)
−0.953703 + 0.300750i \(0.902763\pi\)
\(150\) 12.1244i 0.989949i
\(151\) 3.00000 + 1.73205i 0.244137 + 0.140952i 0.617076 0.786903i \(-0.288317\pi\)
−0.372940 + 0.927855i \(0.621650\pi\)
\(152\) 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 −0.333624 0.942706i \(-0.608272\pi\)
−0.983220 + 0.182426i \(0.941605\pi\)
\(158\) 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 0.557593 0.830115i \(-0.311725\pi\)
−0.440104 + 0.897947i \(0.645058\pi\)
\(164\) −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 0.611562 0.791196i \(-0.290541\pi\)
−0.379415 + 0.925227i \(0.623875\pi\)
\(168\) −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 −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 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 0.573400 0.819275i \(-0.305624\pi\)
0.996213 0.0869415i \(-0.0277093\pi\)
\(180\) 10.3923i 0.774597i
\(181\) 15.5885i 1.15868i −0.815086 0.579340i \(-0.803310\pi\)
0.815086 0.579340i \(-0.196690\pi\)
\(182\) 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 0.980821 0.194910i \(-0.0624416\pi\)
0.321613 + 0.946871i \(0.395775\pi\)
\(192\) −1.50000 + 0.866025i −0.108253 + 0.0625000i
\(193\) −4.50000 + 2.59808i −0.323917 + 0.187014i −0.653137 0.757240i \(-0.726548\pi\)
0.329220 + 0.944253i \(0.393214\pi\)
\(194\) −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 −0.996649 0.0818013i \(-0.973933\pi\)
0.569166 + 0.822222i \(0.307266\pi\)
\(198\) −18.0000 −1.27920
\(199\) 15.5885i 1.10504i −0.833501 0.552518i \(-0.813667\pi\)
0.833501 0.552518i \(-0.186333\pi\)
\(200\) 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 −0.939156 0.343490i \(-0.888391\pi\)
0.767049 + 0.641588i \(0.221724\pi\)
\(212\) −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 0.463409 + 0.886145i \(0.346626\pi\)
−0.999128 + 0.0417488i \(0.986707\pi\)
\(224\) −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 \(0.112081\pi\)
−0.938647 + 0.344881i \(0.887919\pi\)
\(228\) 8.66025i 0.573539i
\(229\) −14.5000 25.1147i −0.958187 1.65963i −0.726900 0.686743i \(-0.759040\pi\)
−0.231287 0.972886i \(-0.574293\pi\)
\(230\) −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 −0.290418 0.956900i \(-0.593794\pi\)
0.683491 + 0.729959i \(0.260461\pi\)
\(234\) −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 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) 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 −0.822052 0.569413i \(-0.807171\pi\)
0.0821001 + 0.996624i \(0.473837\pi\)
\(264\) 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 −0.543920 0.839137i \(-0.683060\pi\)
0.454754 + 0.890617i \(0.349727\pi\)
\(284\) 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 −0.664916 0.746918i \(-0.731533\pi\)
0.314392 + 0.949293i \(0.398199\pi\)
\(294\) 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 −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) 6.00000 + 1.73205i 0.339683 + 0.0980581i
\(313\) −28.5000 + 16.4545i −1.61092 + 0.930062i −0.621757 + 0.783210i \(0.713581\pi\)
−0.989158 + 0.146852i \(0.953086\pi\)
\(314\) −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 −0.999980 0.00635137i \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) 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 −0.0274825 0.999622i \(-0.508749\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) 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 −0.974847 0.222875i \(-0.928456\pi\)
0.680439 + 0.732805i \(0.261789\pi\)
\(350\) 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 −0.720009 0.693965i \(-0.755862\pi\)
0.240987 + 0.970528i \(0.422529\pi\)
\(354\) 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 −0.986865 0.161546i \(-0.948352\pi\)
0.353529 0.935423i \(-0.384981\pi\)
\(360\) 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 −0.460339 0.887743i \(-0.652272\pi\)
0.538639 + 0.842537i \(0.318939\pi\)
\(368\) 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 −0.838975 0.544170i \(-0.816844\pi\)
0.890753 + 0.454488i \(0.150178\pi\)
\(374\) 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 0.0625541 0.998042i \(-0.480075\pi\)
−0.833052 + 0.553194i \(0.813409\pi\)
\(380\) 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 −0.0361995 0.999345i \(-0.511525\pi\)
−0.883558 + 0.468323i \(0.844859\pi\)
\(384\) −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 0.710495 0.703702i \(-0.248471\pi\)
−0.254177 + 0.967158i \(0.581804\pi\)
\(390\) −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 −0.694359 0.719629i \(-0.744312\pi\)
0.970396 + 0.241518i \(0.0776454\pi\)
\(398\) 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 0.222885 + 0.974845i \(0.428453\pi\)
−0.955683 + 0.294398i \(0.904881\pi\)
\(420\) 12.0000 + 10.3923i 0.585540 + 0.507093i
\(421\) 27.7128i 1.35064i −0.737525 0.675320i \(-0.764006\pi\)
0.737525 0.675320i \(-0.235994\pi\)
\(422\) −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 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 18.0000 10.3923i 0.865025 0.499422i −0.000666943 1.00000i \(-0.500212\pi\)
0.865692 + 0.500577i \(0.166879\pi\)
\(434\) −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 \(-0.906567\pi\)
0.957229 0.289332i \(-0.0934331\pi\)
\(440\) 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 0.571461 0.820629i \(-0.306377\pi\)
0.996416 0.0845852i \(-0.0269565\pi\)
\(444\) −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 0.965637 + 0.259895i \(0.0836878\pi\)
−0.257743 + 0.966213i \(0.582979\pi\)
\(450\) −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 −0.0183573 0.999831i \(-0.505844\pi\)
0.856701 + 0.515814i \(0.172510\pi\)
\(462\) −18.0000 + 20.7846i −0.837436 + 0.966988i
\(463\) 19.0526i 0.885448i −0.896658 0.442724i \(-0.854012\pi\)
0.896658 0.442724i \(-0.145988\pi\)
\(464\) −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 0.579111 0.815249i \(-0.303400\pi\)
−0.995582 + 0.0939008i \(0.970066\pi\)
\(468\) −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 −0.630771 0.775969i \(-0.717261\pi\)
0.356624 + 0.934248i \(0.383928\pi\)
\(480\) 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 \(0.114903\pi\)
−0.935552 + 0.353190i \(0.885097\pi\)
\(488\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 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 −0.658389 0.752678i \(-0.728762\pi\)
0.322643 + 0.946521i \(0.395429\pi\)
\(500\) 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 −0.978235 0.207499i \(-0.933468\pi\)
0.309418 0.950926i \(-0.399866\pi\)
\(504\) 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 \(0.180594\pi\)
−0.843326 + 0.537403i \(0.819406\pi\)
\(510\) 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 −0.704137 0.710064i \(-0.748666\pi\)
0.967002 + 0.254769i \(0.0819994\pi\)
\(522\) −18.0000 + 10.3923i −0.787839 + 0.454859i
\(523\) 8.66025i 0.378686i −0.981911 0.189343i \(-0.939364\pi\)
0.981911 0.189343i \(-0.0606359\pi\)
\(524\) 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 −0.467408 0.884042i \(-0.654812\pi\)
0.531898 + 0.846808i \(0.321479\pi\)
\(542\) 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 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 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 \(0.197296\pi\)
−0.813982 + 0.580891i \(0.802704\pi\)
\(570\) −15.0000 25.9808i −0.628281 1.08821i
\(571\) −9.50000 + 16.4545i −0.397563 + 0.688599i −0.993425 0.114488i \(-0.963477\pi\)
0.595862 + 0.803087i \(0.296811\pi\)
\(572\) −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 0.167307 + 0.985905i \(0.446493\pi\)
−0.937472 + 0.348060i \(0.886840\pi\)
\(578\) −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 0.989436 + 0.144971i \(0.0463088\pi\)
0.620266 + 0.784391i \(0.287025\pi\)
\(588\) 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 −0.618110 0.786091i \(-0.712102\pi\)
0.371720 + 0.928345i \(0.378768\pi\)
\(594\) 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 −0.0781581 0.996941i \(-0.524904\pi\)
−0.902455 + 0.430784i \(0.858237\pi\)
\(600\) 12.1244i 0.494975i
\(601\) 1.50000 + 0.866025i 0.0611863 + 0.0353259i 0.530281 0.847822i \(-0.322086\pi\)
−0.469095 + 0.883148i \(0.655420\pi\)
\(602\) 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 0.200346 0.979725i \(-0.435793\pi\)
−0.748294 + 0.663367i \(0.769127\pi\)
\(608\) 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 0.0287324 0.999587i \(-0.490853\pi\)
0.880034 + 0.474911i \(0.157520\pi\)
\(614\) −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 −0.959117 0.283011i \(-0.908667\pi\)
0.234464 0.972125i \(-0.424666\pi\)
\(618\) −4.50000 + 7.79423i −0.181017 + 0.313530i
\(619\) 8.50000 14.7224i 0.341644 0.591744i −0.643094 0.765787i \(-0.722350\pi\)
0.984738 + 0.174042i \(0.0556830\pi\)
\(620\) 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 0.0199047 0.999802i \(-0.493664\pi\)
0.875806 + 0.482663i \(0.160330\pi\)
\(632\) 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 \(-0.728833\pi\)
0.658557 0.752531i \(-0.271167\pi\)
\(642\) 0 0
\(643\) −5.50000 9.52628i −0.216899 0.375680i 0.736959 0.675937i \(-0.236261\pi\)
−0.953858 + 0.300257i \(0.902928\pi\)
\(644\) −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 −0.965726 0.259565i \(-0.916421\pi\)
0.258073 0.966126i \(-0.416913\pi\)
\(648\) −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 −0.888360 0.459147i \(-0.848155\pi\)
−0.0465470 + 0.998916i \(0.514822\pi\)
\(660\) −36.0000 −1.40130
\(661\) −25.0000 43.3013i −0.972387 1.68422i −0.688301 0.725426i \(-0.741643\pi\)
−0.284087 0.958799i \(-0.591690\pi\)
\(662\) −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 −0.875501 0.483216i \(-0.839469\pi\)
0.856228 + 0.516599i \(0.172802\pi\)
\(674\) 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 0.639618 0.768693i \(-0.279092\pi\)
−0.985517 + 0.169580i \(0.945759\pi\)
\(678\) −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 \(-0.915725\pi\)
0.965156 0.261675i \(-0.0842747\pi\)
\(702\) 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 −0.316021 0.948752i \(-0.602347\pi\)
−0.979654 + 0.200694i \(0.935680\pi\)
\(710\) 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 −0.438141 0.898906i \(-0.644363\pi\)
0.997546 0.0700124i \(-0.0223039\pi\)
\(720\) 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 \(0.0617292\pi\)
−0.981255 + 0.192715i \(0.938271\pi\)
\(728\) 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 0.881633 + 0.471935i \(0.156444\pi\)
−0.0321090 + 0.999484i \(0.510222\pi\)
\(734\) 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 −0.922198 0.386718i \(-0.873609\pi\)
−0.126191 + 0.992006i \(0.540275\pi\)
\(740\) −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 0.447956 + 0.894055i \(0.352152\pi\)
−0.998253 + 0.0590862i \(0.981181\pi\)
\(744\) 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 0.281086 + 0.959683i \(0.409305\pi\)
−0.971652 + 0.236414i \(0.924028\pi\)
\(758\) −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 0.553388 0.832923i \(-0.313335\pi\)
−0.444639 + 0.895710i \(0.646668\pi\)
\(762\) 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 −0.856869 0.515534i \(-0.827594\pi\)
0.874900 + 0.484304i \(0.160927\pi\)
\(770\) −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 \(0.268780\pi\)
−0.664183 + 0.747570i \(0.731220\pi\)
\(774\) −3.00000 −0.107833
\(775\) 28.0000 + 48.4974i 1.00579 + 1.74208i
\(776\) −3.50000 6.06218i −0.125643 0.217620i
\(777\) 37.5000