Properties

Label 546.2.e.d.545.2
Level $546$
Weight $2$
Character 546.545
Analytic conductor $4.360$
Analytic rank $0$
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.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
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: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 545.2
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.545
Dual form 546.2.e.d.545.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.50000 + 0.866025i) q^{3} +1.00000 q^{4} +1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.50000 + 0.866025i) q^{3} +1.00000 q^{4} +1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +1.73205i q^{10} +(1.50000 + 0.866025i) q^{12} +(1.00000 + 3.46410i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{15} +1.00000 q^{16} +3.00000 q^{17} +(1.50000 + 2.59808i) q^{18} +2.00000 q^{19} +1.73205i q^{20} +(-3.00000 - 3.46410i) q^{21} -3.46410i q^{23} +(1.50000 + 0.866025i) q^{24} +2.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(-2.50000 - 0.866025i) q^{28} -6.92820i q^{29} +(-1.50000 + 2.59808i) q^{30} -8.00000 q^{31} +1.00000 q^{32} +3.00000 q^{34} +(1.50000 - 4.33013i) q^{35} +(1.50000 + 2.59808i) q^{36} -1.73205i q^{37} +2.00000 q^{38} +(-1.50000 + 6.06218i) q^{39} +1.73205i q^{40} +(-3.00000 - 3.46410i) q^{42} -11.0000 q^{43} +(-4.50000 + 2.59808i) q^{45} -3.46410i q^{46} -12.1244i q^{47} +(1.50000 + 0.866025i) q^{48} +(5.50000 + 4.33013i) q^{49} +2.00000 q^{50} +(4.50000 + 2.59808i) q^{51} +(1.00000 + 3.46410i) q^{52} -3.46410i q^{53} +5.19615i q^{54} +(-2.50000 - 0.866025i) q^{56} +(3.00000 + 1.73205i) q^{57} -6.92820i q^{58} -10.3923i q^{59} +(-1.50000 + 2.59808i) q^{60} -6.92820i q^{61} -8.00000 q^{62} +(-1.50000 - 7.79423i) q^{63} +1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} +13.8564i q^{67} +3.00000 q^{68} +(3.00000 - 5.19615i) q^{69} +(1.50000 - 4.33013i) q^{70} +9.00000 q^{71} +(1.50000 + 2.59808i) q^{72} -2.00000 q^{73} -1.73205i q^{74} +(3.00000 + 1.73205i) q^{75} +2.00000 q^{76} +(-1.50000 + 6.06218i) q^{78} +10.0000 q^{79} +1.73205i q^{80} +(-4.50000 + 7.79423i) q^{81} +3.46410i q^{83} +(-3.00000 - 3.46410i) q^{84} +5.19615i q^{85} -11.0000 q^{86} +(6.00000 - 10.3923i) q^{87} +3.46410i q^{89} +(-4.50000 + 2.59808i) q^{90} +(0.500000 - 9.52628i) q^{91} -3.46410i q^{92} +(-12.0000 - 6.92820i) q^{93} -12.1244i q^{94} +3.46410i q^{95} +(1.50000 + 0.866025i) q^{96} +8.00000 q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 3q^{3} + 2q^{4} + 3q^{6} - 5q^{7} + 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q + 2q^{2} + 3q^{3} + 2q^{4} + 3q^{6} - 5q^{7} + 2q^{8} + 3q^{9} + 3q^{12} + 2q^{13} - 5q^{14} - 3q^{15} + 2q^{16} + 6q^{17} + 3q^{18} + 4q^{19} - 6q^{21} + 3q^{24} + 4q^{25} + 2q^{26} - 5q^{28} - 3q^{30} - 16q^{31} + 2q^{32} + 6q^{34} + 3q^{35} + 3q^{36} + 4q^{38} - 3q^{39} - 6q^{42} - 22q^{43} - 9q^{45} + 3q^{48} + 11q^{49} + 4q^{50} + 9q^{51} + 2q^{52} - 5q^{56} + 6q^{57} - 3q^{60} - 16q^{62} - 3q^{63} + 2q^{64} - 12q^{65} + 6q^{68} + 6q^{69} + 3q^{70} + 18q^{71} + 3q^{72} - 4q^{73} + 6q^{75} + 4q^{76} - 3q^{78} + 20q^{79} - 9q^{81} - 6q^{84} - 22q^{86} + 12q^{87} - 9q^{90} + q^{91} - 24q^{93} + 3q^{96} + 16q^{97} + 11q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 1.00000 0.500000
\(5\) 1.73205i 0.774597i 0.921954 + 0.387298i \(0.126592\pi\)
−0.921954 + 0.387298i \(0.873408\pi\)
\(6\) 1.50000 + 0.866025i 0.612372 + 0.353553i
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 1.00000 0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 1.73205i 0.547723i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.50000 + 0.866025i 0.433013 + 0.250000i
\(13\) 1.00000 + 3.46410i 0.277350 + 0.960769i
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) −1.50000 + 2.59808i −0.387298 + 0.670820i
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 1.73205i 0.387298i
\(21\) −3.00000 3.46410i −0.654654 0.755929i
\(22\) 0 0
\(23\) 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
\(25\) 2.00000 0.400000
\(26\) 1.00000 + 3.46410i 0.196116 + 0.679366i
\(27\) 5.19615i 1.00000i
\(28\) −2.50000 0.866025i −0.472456 0.163663i
\(29\) 6.92820i 1.28654i −0.765641 0.643268i \(-0.777578\pi\)
0.765641 0.643268i \(-0.222422\pi\)
\(30\) −1.50000 + 2.59808i −0.273861 + 0.474342i
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 1.50000 4.33013i 0.253546 0.731925i
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) 1.73205i 0.284747i −0.989813 0.142374i \(-0.954527\pi\)
0.989813 0.142374i \(-0.0454735\pi\)
\(38\) 2.00000 0.324443
\(39\) −1.50000 + 6.06218i −0.240192 + 0.970725i
\(40\) 1.73205i 0.273861i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −3.00000 3.46410i −0.462910 0.534522i
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 0 0
\(45\) −4.50000 + 2.59808i −0.670820 + 0.387298i
\(46\) 3.46410i 0.510754i
\(47\) 12.1244i 1.76852i −0.466996 0.884260i \(-0.654664\pi\)
0.466996 0.884260i \(-0.345336\pi\)
\(48\) 1.50000 + 0.866025i 0.216506 + 0.125000i
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 2.00000 0.282843
\(51\) 4.50000 + 2.59808i 0.630126 + 0.363803i
\(52\) 1.00000 + 3.46410i 0.138675 + 0.480384i
\(53\) 3.46410i 0.475831i −0.971286 0.237915i \(-0.923536\pi\)
0.971286 0.237915i \(-0.0764641\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 0 0
\(56\) −2.50000 0.866025i −0.334077 0.115728i
\(57\) 3.00000 + 1.73205i 0.397360 + 0.229416i
\(58\) 6.92820i 0.909718i
\(59\) 10.3923i 1.35296i −0.736460 0.676481i \(-0.763504\pi\)
0.736460 0.676481i \(-0.236496\pi\)
\(60\) −1.50000 + 2.59808i −0.193649 + 0.335410i
\(61\) 6.92820i 0.887066i −0.896258 0.443533i \(-0.853725\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) −8.00000 −1.01600
\(63\) −1.50000 7.79423i −0.188982 0.981981i
\(64\) 1.00000 0.125000
\(65\) −6.00000 + 1.73205i −0.744208 + 0.214834i
\(66\) 0 0
\(67\) 13.8564i 1.69283i 0.532524 + 0.846415i \(0.321244\pi\)
−0.532524 + 0.846415i \(0.678756\pi\)
\(68\) 3.00000 0.363803
\(69\) 3.00000 5.19615i 0.361158 0.625543i
\(70\) 1.50000 4.33013i 0.179284 0.517549i
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 1.73205i 0.201347i
\(75\) 3.00000 + 1.73205i 0.346410 + 0.200000i
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) −1.50000 + 6.06218i −0.169842 + 0.686406i
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 1.73205i 0.193649i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 3.46410i 0.380235i 0.981761 + 0.190117i \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) −3.00000 3.46410i −0.327327 0.377964i
\(85\) 5.19615i 0.563602i
\(86\) −11.0000 −1.18616
\(87\) 6.00000 10.3923i 0.643268 1.11417i
\(88\) 0 0
\(89\) 3.46410i 0.367194i 0.983002 + 0.183597i \(0.0587741\pi\)
−0.983002 + 0.183597i \(0.941226\pi\)
\(90\) −4.50000 + 2.59808i −0.474342 + 0.273861i
\(91\) 0.500000 9.52628i 0.0524142 0.998625i
\(92\) 3.46410i 0.361158i
\(93\) −12.0000 6.92820i −1.24434 0.718421i
\(94\) 12.1244i 1.25053i
\(95\) 3.46410i 0.355409i
\(96\) 1.50000 + 0.866025i 0.153093 + 0.0883883i
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) 0 0
\(100\) 2.00000 0.200000
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 4.50000 + 2.59808i 0.445566 + 0.257248i
\(103\) 3.46410i 0.341328i −0.985329 0.170664i \(-0.945409\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 1.00000 + 3.46410i 0.0980581 + 0.339683i
\(105\) 6.00000 5.19615i 0.585540 0.507093i
\(106\) 3.46410i 0.336463i
\(107\) 10.3923i 1.00466i 0.864675 + 0.502331i \(0.167524\pi\)
−0.864675 + 0.502331i \(0.832476\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 5.19615i 0.497701i 0.968542 + 0.248851i \(0.0800528\pi\)
−0.968542 + 0.248851i \(0.919947\pi\)
\(110\) 0 0
\(111\) 1.50000 2.59808i 0.142374 0.246598i
\(112\) −2.50000 0.866025i −0.236228 0.0818317i
\(113\) 6.92820i 0.651751i −0.945413 0.325875i \(-0.894341\pi\)
0.945413 0.325875i \(-0.105659\pi\)
\(114\) 3.00000 + 1.73205i 0.280976 + 0.162221i
\(115\) 6.00000 0.559503
\(116\) 6.92820i 0.643268i
\(117\) −7.50000 + 7.79423i −0.693375 + 0.720577i
\(118\) 10.3923i 0.956689i
\(119\) −7.50000 2.59808i −0.687524 0.238165i
\(120\) −1.50000 + 2.59808i −0.136931 + 0.237171i
\(121\) −11.0000 −1.00000
\(122\) 6.92820i 0.627250i
\(123\) 0 0
\(124\) −8.00000 −0.718421
\(125\) 12.1244i 1.08444i
\(126\) −1.50000 7.79423i −0.133631 0.694365i
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 1.00000 0.0883883
\(129\) −16.5000 9.52628i −1.45274 0.838742i
\(130\) −6.00000 + 1.73205i −0.526235 + 0.151911i
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 0 0
\(133\) −5.00000 1.73205i −0.433555 0.150188i
\(134\) 13.8564i 1.19701i
\(135\) −9.00000 −0.774597
\(136\) 3.00000 0.257248
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 3.00000 5.19615i 0.255377 0.442326i
\(139\) 19.0526i 1.61602i −0.589171 0.808008i \(-0.700546\pi\)
0.589171 0.808008i \(-0.299454\pi\)
\(140\) 1.50000 4.33013i 0.126773 0.365963i
\(141\) 10.5000 18.1865i 0.884260 1.53158i
\(142\) 9.00000 0.755263
\(143\) 0 0
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 12.0000 0.996546
\(146\) −2.00000 −0.165521
\(147\) 4.50000 + 11.2583i 0.371154 + 0.928571i
\(148\) 1.73205i 0.142374i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 3.00000 + 1.73205i 0.244949 + 0.141421i
\(151\) 19.0526i 1.55048i 0.631670 + 0.775238i \(0.282370\pi\)
−0.631670 + 0.775238i \(0.717630\pi\)
\(152\) 2.00000 0.162221
\(153\) 4.50000 + 7.79423i 0.363803 + 0.630126i
\(154\) 0 0
\(155\) 13.8564i 1.11297i
\(156\) −1.50000 + 6.06218i −0.120096 + 0.485363i
\(157\) 10.3923i 0.829396i 0.909959 + 0.414698i \(0.136113\pi\)
−0.909959 + 0.414698i \(0.863887\pi\)
\(158\) 10.0000 0.795557
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 1.73205i 0.136931i
\(161\) −3.00000 + 8.66025i −0.236433 + 0.682524i
\(162\) −4.50000 + 7.79423i −0.353553 + 0.612372i
\(163\) 17.3205i 1.35665i −0.734763 0.678323i \(-0.762707\pi\)
0.734763 0.678323i \(-0.237293\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 3.46410i 0.268866i
\(167\) 3.46410i 0.268060i −0.990977 0.134030i \(-0.957208\pi\)
0.990977 0.134030i \(-0.0427919\pi\)
\(168\) −3.00000 3.46410i −0.231455 0.267261i
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 5.19615i 0.398527i
\(171\) 3.00000 + 5.19615i 0.229416 + 0.397360i
\(172\) −11.0000 −0.838742
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 6.00000 10.3923i 0.454859 0.787839i
\(175\) −5.00000 1.73205i −0.377964 0.130931i
\(176\) 0 0
\(177\) 9.00000 15.5885i 0.676481 1.17170i
\(178\) 3.46410i 0.259645i
\(179\) 12.1244i 0.906217i 0.891455 + 0.453108i \(0.149685\pi\)
−0.891455 + 0.453108i \(0.850315\pi\)
\(180\) −4.50000 + 2.59808i −0.335410 + 0.193649i
\(181\) 3.46410i 0.257485i 0.991678 + 0.128742i \(0.0410940\pi\)
−0.991678 + 0.128742i \(0.958906\pi\)
\(182\) 0.500000 9.52628i 0.0370625 0.706135i
\(183\) 6.00000 10.3923i 0.443533 0.768221i
\(184\) 3.46410i 0.255377i
\(185\) 3.00000 0.220564
\(186\) −12.0000 6.92820i −0.879883 0.508001i
\(187\) 0 0
\(188\) 12.1244i 0.884260i
\(189\) 4.50000 12.9904i 0.327327 0.944911i
\(190\) 3.46410i 0.251312i
\(191\) 20.7846i 1.50392i −0.659208 0.751961i \(-0.729108\pi\)
0.659208 0.751961i \(-0.270892\pi\)
\(192\) 1.50000 + 0.866025i 0.108253 + 0.0625000i
\(193\) 17.3205i 1.24676i 0.781920 + 0.623379i \(0.214240\pi\)
−0.781920 + 0.623379i \(0.785760\pi\)
\(194\) 8.00000 0.574367
\(195\) −10.5000 2.59808i −0.751921 0.186052i
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) −15.0000 −1.06871 −0.534353 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) 0 0
\(199\) 6.92820i 0.491127i 0.969380 + 0.245564i \(0.0789730\pi\)
−0.969380 + 0.245564i \(0.921027\pi\)
\(200\) 2.00000 0.141421
\(201\) −12.0000 + 20.7846i −0.846415 + 1.46603i
\(202\) −12.0000 −0.844317
\(203\) −6.00000 + 17.3205i −0.421117 + 1.21566i
\(204\) 4.50000 + 2.59808i 0.315063 + 0.181902i
\(205\) 0 0
\(206\) 3.46410i 0.241355i
\(207\) 9.00000 5.19615i 0.625543 0.361158i
\(208\) 1.00000 + 3.46410i 0.0693375 + 0.240192i
\(209\) 0 0
\(210\) 6.00000 5.19615i 0.414039 0.358569i
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 3.46410i 0.237915i
\(213\) 13.5000 + 7.79423i 0.925005 + 0.534052i
\(214\) 10.3923i 0.710403i
\(215\) 19.0526i 1.29937i
\(216\) 5.19615i 0.353553i
\(217\) 20.0000 + 6.92820i 1.35769 + 0.470317i
\(218\) 5.19615i 0.351928i
\(219\) −3.00000 1.73205i −0.202721 0.117041i
\(220\) 0 0
\(221\) 3.00000 + 10.3923i 0.201802 + 0.699062i
\(222\) 1.50000 2.59808i 0.100673 0.174371i
\(223\) −7.00000 −0.468755 −0.234377 0.972146i \(-0.575305\pi\)
−0.234377 + 0.972146i \(0.575305\pi\)
\(224\) −2.50000 0.866025i −0.167038 0.0578638i
\(225\) 3.00000 + 5.19615i 0.200000 + 0.346410i
\(226\) 6.92820i 0.460857i
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 3.00000 + 1.73205i 0.198680 + 0.114708i
\(229\) −5.00000 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 6.92820i 0.454859i
\(233\) 8.66025i 0.567352i 0.958920 + 0.283676i \(0.0915540\pi\)
−0.958920 + 0.283676i \(0.908446\pi\)
\(234\) −7.50000 + 7.79423i −0.490290 + 0.509525i
\(235\) 21.0000 1.36989
\(236\) 10.3923i 0.676481i
\(237\) 15.0000 + 8.66025i 0.974355 + 0.562544i
\(238\) −7.50000 2.59808i −0.486153 0.168408i
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) −1.50000 + 2.59808i −0.0968246 + 0.167705i
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) −11.0000 −0.707107
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 6.92820i 0.443533i
\(245\) −7.50000 + 9.52628i −0.479157 + 0.608612i
\(246\) 0 0
\(247\) 2.00000 + 6.92820i 0.127257 + 0.440831i
\(248\) −8.00000 −0.508001
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 12.1244i 0.766812i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −1.50000 7.79423i −0.0944911 0.490990i
\(253\) 0 0
\(254\) −2.00000 −0.125491
\(255\) −4.50000 + 7.79423i −0.281801 + 0.488094i
\(256\) 1.00000 0.0625000
\(257\) 21.0000 1.30994 0.654972 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) −16.5000 9.52628i −1.02725 0.593080i
\(259\) −1.50000 + 4.33013i −0.0932055 + 0.269061i
\(260\) −6.00000 + 1.73205i −0.372104 + 0.107417i
\(261\) 18.0000 10.3923i 1.11417 0.643268i
\(262\) −15.0000 −0.926703
\(263\) 13.8564i 0.854423i 0.904152 + 0.427211i \(0.140504\pi\)
−0.904152 + 0.427211i \(0.859496\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) −5.00000 1.73205i −0.306570 0.106199i
\(267\) −3.00000 + 5.19615i −0.183597 + 0.317999i
\(268\) 13.8564i 0.846415i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) −9.00000 −0.547723
\(271\) −1.00000 −0.0607457 −0.0303728 0.999539i \(-0.509669\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) 3.00000 0.181902
\(273\) 9.00000 13.8564i 0.544705 0.838628i
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) −16.0000 −0.961347 −0.480673 0.876900i \(-0.659608\pi\)
−0.480673 + 0.876900i \(0.659608\pi\)
\(278\) 19.0526i 1.14270i
\(279\) −12.0000 20.7846i −0.718421 1.24434i
\(280\) 1.50000 4.33013i 0.0896421 0.258775i
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 10.5000 18.1865i 0.625266 1.08299i
\(283\) 10.3923i 0.617758i 0.951101 + 0.308879i \(0.0999539\pi\)
−0.951101 + 0.308879i \(0.900046\pi\)
\(284\) 9.00000 0.534052
\(285\) −3.00000 + 5.19615i −0.177705 + 0.307794i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.50000 + 2.59808i 0.0883883 + 0.153093i
\(289\) −8.00000 −0.470588
\(290\) 12.0000 0.704664
\(291\) 12.0000 + 6.92820i 0.703452 + 0.406138i
\(292\) −2.00000 −0.117041
\(293\) 19.0526i 1.11306i 0.830827 + 0.556531i \(0.187868\pi\)
−0.830827 + 0.556531i \(0.812132\pi\)
\(294\) 4.50000 + 11.2583i 0.262445 + 0.656599i
\(295\) 18.0000 1.04800
\(296\) 1.73205i 0.100673i
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 12.0000 3.46410i 0.693978 0.200334i
\(300\) 3.00000 + 1.73205i 0.173205 + 0.100000i
\(301\) 27.5000 + 9.52628i 1.58507 + 0.549086i
\(302\) 19.0526i 1.09635i
\(303\) −18.0000 10.3923i −1.03407 0.597022i
\(304\) 2.00000 0.114708
\(305\) 12.0000 0.687118
\(306\) 4.50000 + 7.79423i 0.257248 + 0.445566i
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) 0 0
\(309\) 3.00000 5.19615i 0.170664 0.295599i
\(310\) 13.8564i 0.786991i
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) −1.50000 + 6.06218i −0.0849208 + 0.343203i
\(313\) 8.66025i 0.489506i −0.969585 0.244753i \(-0.921293\pi\)
0.969585 0.244753i \(-0.0787070\pi\)
\(314\) 10.3923i 0.586472i
\(315\) 13.5000 2.59808i 0.760639 0.146385i
\(316\) 10.0000 0.562544
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 3.00000 5.19615i 0.168232 0.291386i
\(319\) 0 0
\(320\) 1.73205i 0.0968246i
\(321\) −9.00000 + 15.5885i −0.502331 + 0.870063i
\(322\) −3.00000 + 8.66025i −0.167183 + 0.482617i
\(323\) 6.00000 0.333849
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 2.00000 + 6.92820i 0.110940 + 0.384308i
\(326\) 17.3205i 0.959294i
\(327\) −4.50000 + 7.79423i −0.248851 + 0.431022i
\(328\) 0 0
\(329\) −10.5000 + 30.3109i −0.578884 + 1.67109i
\(330\) 0 0
\(331\) 17.3205i 0.952021i −0.879440 0.476011i \(-0.842082\pi\)
0.879440 0.476011i \(-0.157918\pi\)
\(332\) 3.46410i 0.190117i
\(333\) 4.50000 2.59808i 0.246598 0.142374i
\(334\) 3.46410i 0.189547i
\(335\) −24.0000 −1.31126
\(336\) −3.00000 3.46410i −0.163663 0.188982i
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) −11.0000 + 6.92820i −0.598321 + 0.376845i
\(339\) 6.00000 10.3923i 0.325875 0.564433i
\(340\) 5.19615i 0.281801i
\(341\) 0 0
\(342\) 3.00000 + 5.19615i 0.162221 + 0.280976i
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −11.0000 −0.593080
\(345\) 9.00000 + 5.19615i 0.484544 + 0.279751i
\(346\) −6.00000 −0.322562
\(347\) 15.5885i 0.836832i 0.908255 + 0.418416i \(0.137415\pi\)
−0.908255 + 0.418416i \(0.862585\pi\)
\(348\) 6.00000 10.3923i 0.321634 0.557086i
\(349\) 1.00000 0.0535288 0.0267644 0.999642i \(-0.491480\pi\)
0.0267644 + 0.999642i \(0.491480\pi\)
\(350\) −5.00000 1.73205i −0.267261 0.0925820i
\(351\) −18.0000 + 5.19615i −0.960769 + 0.277350i
\(352\) 0 0
\(353\) 10.3923i 0.553127i 0.960996 + 0.276563i \(0.0891955\pi\)
−0.960996 + 0.276563i \(0.910804\pi\)
\(354\) 9.00000 15.5885i 0.478345 0.828517i
\(355\) 15.5885i 0.827349i
\(356\) 3.46410i 0.183597i
\(357\) −9.00000 10.3923i −0.476331 0.550019i
\(358\) 12.1244i 0.640792i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −4.50000 + 2.59808i −0.237171 + 0.136931i
\(361\) −15.0000 −0.789474
\(362\) 3.46410i 0.182069i
\(363\) −16.5000 9.52628i −0.866025 0.500000i
\(364\) 0.500000 9.52628i 0.0262071 0.499313i
\(365\) 3.46410i 0.181319i
\(366\) 6.00000 10.3923i 0.313625 0.543214i
\(367\) 34.6410i 1.80825i 0.427272 + 0.904123i \(0.359475\pi\)
−0.427272 + 0.904123i \(0.640525\pi\)
\(368\) 3.46410i 0.180579i
\(369\) 0 0
\(370\) 3.00000 0.155963
\(371\) −3.00000 + 8.66025i −0.155752 + 0.449618i
\(372\) −12.0000 6.92820i −0.622171 0.359211i
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) 0 0
\(375\) −10.5000 + 18.1865i −0.542218 + 0.939149i
\(376\) 12.1244i 0.625266i
\(377\) 24.0000 6.92820i 1.23606 0.356821i
\(378\) 4.50000 12.9904i 0.231455 0.668153i
\(379\) 17.3205i 0.889695i −0.895606 0.444847i \(-0.853258\pi\)
0.895606 0.444847i \(-0.146742\pi\)
\(380\) 3.46410i 0.177705i
\(381\) −3.00000 1.73205i −0.153695 0.0887357i
\(382\) 20.7846i 1.06343i
\(383\) 5.19615i 0.265511i −0.991149 0.132755i \(-0.957617\pi\)
0.991149 0.132755i \(-0.0423825\pi\)
\(384\) 1.50000 + 0.866025i 0.0765466 + 0.0441942i
\(385\) 0 0
\(386\) 17.3205i 0.881591i
\(387\) −16.5000 28.5788i −0.838742 1.45274i
\(388\) 8.00000 0.406138
\(389\) 10.3923i 0.526911i −0.964672 0.263455i \(-0.915138\pi\)
0.964672 0.263455i \(-0.0848622\pi\)
\(390\) −10.5000 2.59808i −0.531688 0.131559i
\(391\) 10.3923i 0.525561i
\(392\) 5.50000 + 4.33013i 0.277792 + 0.218704i
\(393\) −22.5000 12.9904i −1.13497 0.655278i
\(394\) −15.0000 −0.755689
\(395\) 17.3205i 0.871489i
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 6.92820i 0.347279i
\(399\) −6.00000 6.92820i −0.300376 0.346844i
\(400\) 2.00000 0.100000
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) −12.0000 + 20.7846i −0.598506 + 1.03664i
\(403\) −8.00000 27.7128i −0.398508 1.38047i
\(404\) −12.0000 −0.597022
\(405\) −13.5000 7.79423i −0.670820 0.387298i
\(406\) −6.00000 + 17.3205i −0.297775 + 0.859602i
\(407\) 0 0
\(408\) 4.50000 + 2.59808i 0.222783 + 0.128624i
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) 27.0000 + 15.5885i 1.33181 + 0.768922i
\(412\) 3.46410i 0.170664i
\(413\) −9.00000 + 25.9808i −0.442861 + 1.27843i
\(414\) 9.00000 5.19615i 0.442326 0.255377i
\(415\) −6.00000 −0.294528
\(416\) 1.00000 + 3.46410i 0.0490290 + 0.169842i
\(417\) 16.5000 28.5788i 0.808008 1.39951i
\(418\) 0 0
\(419\) −27.0000 −1.31904 −0.659518 0.751689i \(-0.729240\pi\)
−0.659518 + 0.751689i \(0.729240\pi\)
\(420\) 6.00000 5.19615i 0.292770 0.253546i
\(421\) 32.9090i 1.60388i 0.597401 + 0.801942i \(0.296200\pi\)
−0.597401 + 0.801942i \(0.703800\pi\)
\(422\) −13.0000 −0.632830
\(423\) 31.5000 18.1865i 1.53158 0.884260i
\(424\) 3.46410i 0.168232i
\(425\) 6.00000 0.291043
\(426\) 13.5000 + 7.79423i 0.654077 + 0.377632i
\(427\) −6.00000 + 17.3205i −0.290360 + 0.838198i
\(428\) 10.3923i 0.502331i
\(429\) 0 0
\(430\) 19.0526i 0.918796i
\(431\) −33.0000 −1.58955 −0.794777 0.606902i \(-0.792412\pi\)
−0.794777 + 0.606902i \(0.792412\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 5.19615i 0.249711i 0.992175 + 0.124856i \(0.0398468\pi\)
−0.992175 + 0.124856i \(0.960153\pi\)
\(434\) 20.0000 + 6.92820i 0.960031 + 0.332564i
\(435\) 18.0000 + 10.3923i 0.863034 + 0.498273i
\(436\) 5.19615i 0.248851i
\(437\) 6.92820i 0.331421i
\(438\) −3.00000 1.73205i −0.143346 0.0827606i
\(439\) 31.1769i 1.48799i −0.668184 0.743996i \(-0.732928\pi\)
0.668184 0.743996i \(-0.267072\pi\)
\(440\) 0 0
\(441\) −3.00000 + 20.7846i −0.142857 + 0.989743i
\(442\) 3.00000 + 10.3923i 0.142695 + 0.494312i
\(443\) 22.5167i 1.06980i −0.844916 0.534899i \(-0.820349\pi\)
0.844916 0.534899i \(-0.179651\pi\)
\(444\) 1.50000 2.59808i 0.0711868 0.123299i
\(445\) −6.00000 −0.284427
\(446\) −7.00000 −0.331460
\(447\) 9.00000 + 5.19615i 0.425685 + 0.245770i
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 3.00000 + 5.19615i 0.141421 + 0.244949i
\(451\) 0 0
\(452\) 6.92820i 0.325875i
\(453\) −16.5000 + 28.5788i −0.775238 + 1.34275i
\(454\) 0 0
\(455\) 16.5000 + 0.866025i 0.773532 + 0.0405999i
\(456\) 3.00000 + 1.73205i 0.140488 + 0.0811107i
\(457\) 10.3923i 0.486132i 0.970010 + 0.243066i \(0.0781531\pi\)
−0.970010 + 0.243066i \(0.921847\pi\)
\(458\) −5.00000 −0.233635
\(459\) 15.5885i 0.727607i
\(460\) 6.00000 0.279751
\(461\) 5.19615i 0.242009i 0.992652 + 0.121004i \(0.0386115\pi\)
−0.992652 + 0.121004i \(0.961388\pi\)
\(462\) 0 0
\(463\) 24.2487i 1.12693i −0.826139 0.563467i \(-0.809467\pi\)
0.826139 0.563467i \(-0.190533\pi\)
\(464\) 6.92820i 0.321634i
\(465\) 12.0000 20.7846i 0.556487 0.963863i
\(466\) 8.66025i 0.401179i
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) −7.50000 + 7.79423i −0.346688 + 0.360288i
\(469\) 12.0000 34.6410i 0.554109 1.59957i
\(470\) 21.0000 0.968658
\(471\) −9.00000 + 15.5885i −0.414698 + 0.718278i
\(472\) 10.3923i 0.478345i
\(473\) 0 0
\(474\) 15.0000 + 8.66025i 0.688973 + 0.397779i
\(475\) 4.00000 0.183533
\(476\) −7.50000 2.59808i −0.343762 0.119083i
\(477\) 9.00000 5.19615i 0.412082 0.237915i
\(478\) −15.0000 −0.686084
\(479\) 32.9090i 1.50365i −0.659363 0.751825i \(-0.729174\pi\)
0.659363 0.751825i \(-0.270826\pi\)
\(480\) −1.50000 + 2.59808i −0.0684653 + 0.118585i
\(481\) 6.00000 1.73205i 0.273576 0.0789747i
\(482\) 10.0000 0.455488
\(483\) −12.0000 + 10.3923i −0.546019 + 0.472866i
\(484\) −11.0000 −0.500000
\(485\) 13.8564i 0.629187i
\(486\) −13.5000 + 7.79423i −0.612372 + 0.353553i
\(487\) 24.2487i 1.09881i −0.835555 0.549407i \(-0.814854\pi\)
0.835555 0.549407i \(-0.185146\pi\)
\(488\) 6.92820i 0.313625i
\(489\) 15.0000 25.9808i 0.678323 1.17489i
\(490\) −7.50000 + 9.52628i −0.338815 + 0.430353i
\(491\) 36.3731i 1.64149i 0.571292 + 0.820747i \(0.306442\pi\)
−0.571292 + 0.820747i \(0.693558\pi\)
\(492\) 0 0
\(493\) 20.7846i 0.936092i
\(494\) 2.00000 + 6.92820i 0.0899843 + 0.311715i
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) −22.5000 7.79423i −1.00926 0.349619i
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 20.7846i 0.930447i 0.885193 + 0.465223i \(0.154026\pi\)
−0.885193 + 0.465223i \(0.845974\pi\)
\(500\) 12.1244i 0.542218i
\(501\) 3.00000 5.19615i 0.134030 0.232147i
\(502\) 12.0000 0.535586
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) −1.50000 7.79423i −0.0668153 0.347183i
\(505\) 20.7846i 0.924903i
\(506\) 0 0
\(507\) −22.5000 + 0.866025i −0.999260 + 0.0384615i
\(508\) −2.00000 −0.0887357
\(509\) 27.7128i 1.22835i −0.789170 0.614174i \(-0.789489\pi\)
0.789170 0.614174i \(-0.210511\pi\)
\(510\) −4.50000 + 7.79423i −0.199263 + 0.345134i
\(511\) 5.00000 + 1.73205i 0.221187 + 0.0766214i
\(512\) 1.00000 0.0441942
\(513\) 10.3923i 0.458831i
\(514\) 21.0000 0.926270
\(515\) 6.00000 0.264392
\(516\) −16.5000 9.52628i −0.726372 0.419371i
\(517\) 0 0
\(518\) −1.50000 + 4.33013i −0.0659062 + 0.190255i
\(519\) −9.00000 5.19615i −0.395056 0.228086i
\(520\) −6.00000 + 1.73205i −0.263117 + 0.0759555i
\(521\) −27.0000 −1.18289 −0.591446 0.806345i \(-0.701443\pi\)
−0.591446 + 0.806345i \(0.701443\pi\)
\(522\) 18.0000 10.3923i 0.787839 0.454859i
\(523\) 17.3205i 0.757373i −0.925525 0.378686i \(-0.876376\pi\)
0.925525 0.378686i \(-0.123624\pi\)
\(524\) −15.0000 −0.655278
\(525\) −6.00000 6.92820i −0.261861 0.302372i
\(526\) 13.8564i 0.604168i
\(527\) −24.0000 −1.04546
\(528\) 0 0
\(529\) 11.0000 0.478261
\(530\) 6.00000 0.260623
\(531\) 27.0000 15.5885i 1.17170 0.676481i
\(532\) −5.00000 1.73205i −0.216777 0.0750939i
\(533\) 0 0
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) −18.0000 −0.778208
\(536\) 13.8564i 0.598506i
\(537\) −10.5000 + 18.1865i −0.453108 + 0.784807i
\(538\) 0 0
\(539\) 0 0
\(540\) −9.00000 −0.387298
\(541\) 19.0526i 0.819133i −0.912280 0.409567i \(-0.865680\pi\)
0.912280 0.409567i \(-0.134320\pi\)
\(542\) −1.00000 −0.0429537
\(543\) −3.00000 + 5.19615i −0.128742 + 0.222988i
\(544\) 3.00000 0.128624
\(545\) −9.00000 −0.385518
\(546\) 9.00000 13.8564i 0.385164 0.592999i
\(547\) 17.0000 0.726868 0.363434 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) 18.0000 0.768922
\(549\) 18.0000 10.3923i 0.768221 0.443533i
\(550\) 0 0
\(551\) 13.8564i 0.590303i
\(552\) 3.00000 5.19615i 0.127688 0.221163i
\(553\) −25.0000 8.66025i −1.06311 0.368271i
\(554\) −16.0000 −0.679775
\(555\) 4.50000 + 2.59808i 0.191014 + 0.110282i
\(556\) 19.0526i 0.808008i
\(557\) −33.0000 −1.39825 −0.699127 0.714997i \(-0.746428\pi\)
−0.699127 + 0.714997i \(0.746428\pi\)
\(558\) −12.0000 20.7846i −0.508001 0.879883i
\(559\) −11.0000 38.1051i −0.465250 1.61167i
\(560\) 1.50000 4.33013i 0.0633866 0.182981i
\(561\) 0 0
\(562\) 30.0000 1.26547
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 10.5000 18.1865i 0.442130 0.765791i
\(565\) 12.0000 0.504844
\(566\) 10.3923i 0.436821i
\(567\) 18.0000 15.5885i 0.755929 0.654654i
\(568\) 9.00000 0.377632
\(569\) 32.9090i 1.37962i −0.723993 0.689808i \(-0.757695\pi\)
0.723993 0.689808i \(-0.242305\pi\)
\(570\) −3.00000 + 5.19615i −0.125656 + 0.217643i
\(571\) 13.0000 0.544033 0.272017 0.962293i \(-0.412309\pi\)
0.272017 + 0.962293i \(0.412309\pi\)
\(572\) 0 0
\(573\) 18.0000 31.1769i 0.751961 1.30243i
\(574\) 0 0
\(575\) 6.92820i 0.288926i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −46.0000 −1.91501 −0.957503 0.288425i \(-0.906868\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) −8.00000 −0.332756
\(579\) −15.0000 + 25.9808i −0.623379 + 1.07972i
\(580\) 12.0000 0.498273
\(581\) 3.00000 8.66025i 0.124461 0.359288i
\(582\) 12.0000 + 6.92820i 0.497416 + 0.287183i
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) −13.5000 12.9904i −0.558156 0.537086i
\(586\) 19.0526i 0.787054i
\(587\) 38.1051i 1.57277i 0.617739 + 0.786383i \(0.288049\pi\)
−0.617739 + 0.786383i \(0.711951\pi\)
\(588\) 4.50000 + 11.2583i 0.185577 + 0.464286i
\(589\) −16.0000 −0.659269
\(590\) 18.0000 0.741048
\(591\) −22.5000 12.9904i −0.925526 0.534353i
\(592\) 1.73205i 0.0711868i
\(593\) 48.4974i 1.99155i −0.0918243 0.995775i \(-0.529270\pi\)
0.0918243 0.995775i \(-0.470730\pi\)
\(594\) 0 0
\(595\) 4.50000 12.9904i 0.184482 0.532554i
\(596\) 6.00000 0.245770
\(597\) −6.00000 + 10.3923i −0.245564 + 0.425329i
\(598\) 12.0000 3.46410i 0.490716 0.141658i
\(599\) 24.2487i 0.990775i 0.868672 + 0.495388i \(0.164974\pi\)
−0.868672 + 0.495388i \(0.835026\pi\)
\(600\) 3.00000 + 1.73205i 0.122474 + 0.0707107i
\(601\) 5.19615i 0.211955i −0.994369 0.105978i \(-0.966203\pi\)
0.994369 0.105978i \(-0.0337972\pi\)
\(602\) 27.5000 + 9.52628i 1.12082 + 0.388262i
\(603\) −36.0000 + 20.7846i −1.46603 + 0.846415i
\(604\) 19.0526i 0.775238i
\(605\) 19.0526i 0.774597i
\(606\) −18.0000 10.3923i −0.731200 0.422159i
\(607\) 24.2487i 0.984225i 0.870532 + 0.492112i \(0.163775\pi\)
−0.870532 + 0.492112i \(0.836225\pi\)
\(608\) 2.00000 0.0811107
\(609\) −24.0000 + 20.7846i −0.972529 + 0.842235i
\(610\) 12.0000 0.485866
\(611\) 42.0000 12.1244i 1.69914 0.490499i
\(612\) 4.50000 + 7.79423i 0.181902 + 0.315063i
\(613\) 6.92820i 0.279827i −0.990164 0.139914i \(-0.955317\pi\)
0.990164 0.139914i \(-0.0446825\pi\)
\(614\) −14.0000 −0.564994
\(615\) 0 0
\(616\) 0 0
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 3.00000 5.19615i 0.120678 0.209020i
\(619\) −40.0000 −1.60774 −0.803868 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(620\) 13.8564i 0.556487i
\(621\) 18.0000 0.722315
\(622\) 30.0000 1.20289
\(623\) 3.00000 8.66025i 0.120192 0.346966i
\(624\) −1.50000 + 6.06218i −0.0600481 + 0.242681i
\(625\) −11.0000 −0.440000
\(626\) 8.66025i 0.346133i
\(627\) 0 0
\(628\) 10.3923i 0.414698i
\(629\) 5.19615i 0.207184i
\(630\) 13.5000 2.59808i 0.537853 0.103510i
\(631\) 22.5167i 0.896374i 0.893940 + 0.448187i \(0.147930\pi\)
−0.893940 + 0.448187i \(0.852070\pi\)
\(632\) 10.0000 0.397779
\(633\) −19.5000 11.2583i −0.775055 0.447478i
\(634\) −6.00000 −0.238290
\(635\) 3.46410i 0.137469i
\(636\) 3.00000 5.19615i 0.118958 0.206041i
\(637\) −9.50000 + 23.3827i −0.376404 + 0.926456i
\(638\) 0 0
\(639\) 13.5000 + 23.3827i 0.534052 + 0.925005i
\(640\) 1.73205i 0.0684653i
\(641\) 34.6410i 1.36824i −0.729370 0.684119i \(-0.760187\pi\)
0.729370 0.684119i \(-0.239813\pi\)
\(642\) −9.00000 + 15.5885i −0.355202 + 0.615227i
\(643\) 40.0000 1.57745 0.788723 0.614749i \(-0.210743\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) −3.00000 + 8.66025i −0.118217 + 0.341262i
\(645\) 16.5000 28.5788i 0.649687 1.12529i
\(646\) 6.00000 0.236067
\(647\) 30.0000 1.17942 0.589711 0.807614i \(-0.299242\pi\)
0.589711 + 0.807614i \(0.299242\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 0 0
\(650\) 2.00000 + 6.92820i 0.0784465 + 0.271746i
\(651\) 24.0000 + 27.7128i 0.940634 + 1.08615i
\(652\) 17.3205i 0.678323i
\(653\) 41.5692i 1.62673i 0.581754 + 0.813365i \(0.302367\pi\)
−0.581754 + 0.813365i \(0.697633\pi\)
\(654\) −4.50000 + 7.79423i −0.175964 + 0.304778i
\(655\) 25.9808i 1.01515i
\(656\) 0 0
\(657\) −3.00000 5.19615i −0.117041 0.202721i
\(658\) −10.5000 + 30.3109i −0.409333 + 1.18164i
\(659\) 24.2487i 0.944596i −0.881439 0.472298i \(-0.843425\pi\)
0.881439 0.472298i \(-0.156575\pi\)
\(660\) 0 0
\(661\) 22.0000 0.855701 0.427850 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) 17.3205i 0.673181i
\(663\) −4.50000 + 18.1865i −0.174766 + 0.706306i
\(664\) 3.46410i 0.134433i
\(665\) 3.00000 8.66025i 0.116335 0.335830i
\(666\) 4.50000 2.59808i 0.174371 0.100673i
\(667\) −24.0000 −0.929284
\(668\) 3.46410i 0.134030i
\(669\) −10.5000 6.06218i −0.405953 0.234377i
\(670\) −24.0000 −0.927201
\(671\) 0 0
\(672\) −3.00000 3.46410i −0.115728 0.133631i
\(673\) −17.0000 −0.655302 −0.327651 0.944799i \(-0.606257\pi\)
−0.327651 + 0.944799i \(0.606257\pi\)
\(674\) 5.00000 0.192593
\(675\) 10.3923i 0.400000i
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 6.00000 10.3923i 0.230429 0.399114i
\(679\) −20.0000 6.92820i −0.767530 0.265880i
\(680\) 5.19615i 0.199263i
\(681\) 0 0
\(682\) 0 0
\(683\) −30.0000 −1.14792 −0.573959 0.818884i \(-0.694593\pi\)
−0.573959 + 0.818884i \(0.694593\pi\)
\(684\) 3.00000 + 5.19615i 0.114708 + 0.198680i
\(685\) 31.1769i 1.19121i
\(686\) −10.0000 15.5885i −0.381802 0.595170i
\(687\) −7.50000 4.33013i −0.286143 0.165205i
\(688\) −11.0000 −0.419371
\(689\) 12.0000 3.46410i 0.457164 0.131972i
\(690\) 9.00000 + 5.19615i 0.342624 + 0.197814i
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 15.5885i 0.591730i
\(695\) 33.0000 1.25176
\(696\) 6.00000 10.3923i 0.227429 0.393919i
\(697\) 0 0
\(698\) 1.00000 0.0378506
\(699\) −7.50000 + 12.9904i −0.283676 + 0.491341i
\(700\) −5.00000 1.73205i −0.188982 0.0654654i
\(701\) 38.1051i 1.43921i −0.694383 0.719605i \(-0.744323\pi\)
0.694383 0.719605i \(-0.255677\pi\)
\(702\) −18.0000 + 5.19615i −0.679366 + 0.196116i
\(703\) 3.46410i 0.130651i
\(704\) 0 0
\(705\) 31.5000 + 18.1865i 1.18636 + 0.684944i
\(706\) 10.3923i 0.391120i
\(707\) 30.0000 + 10.3923i 1.12827 + 0.390843i
\(708\) 9.00000 15.5885i 0.338241 0.585850i
\(709\) 34.6410i 1.30097i 0.759519 + 0.650485i \(0.225434\pi\)
−0.759519 + 0.650485i \(0.774566\pi\)
\(710\) 15.5885i 0.585024i
\(711\) 15.0000 + 25.9808i 0.562544 + 0.974355i
\(712\) 3.46410i 0.129823i
\(713\) 27.7128i 1.03785i
\(714\) −9.00000 10.3923i −0.336817 0.388922i
\(715\) 0 0
\(716\) 12.1244i 0.453108i
\(717\) −22.5000 12.9904i −0.840278 0.485135i
\(718\) 0 0
\(719\) 12.0000 0.447524 0.223762 0.974644i \(-0.428166\pi\)
0.223762 + 0.974644i \(0.428166\pi\)
\(720\) −4.50000 + 2.59808i −0.167705 + 0.0968246i
\(721\) −3.00000 + 8.66025i −0.111726 + 0.322525i
\(722\) −15.0000 −0.558242
\(723\) 15.0000 + 8.66025i 0.557856 + 0.322078i
\(724\) 3.46410i 0.128742i
\(725\) 13.8564i 0.514614i
\(726\) −16.5000 9.52628i −0.612372 0.353553i
\(727\) 41.5692i 1.54172i 0.637006 + 0.770859i \(0.280172\pi\)
−0.637006 + 0.770859i \(0.719828\pi\)
\(728\) 0.500000 9.52628i 0.0185312 0.353067i
\(729\) −27.0000 −1.00000
\(730\) 3.46410i 0.128212i
\(731\) −33.0000 −1.22055
\(732\) 6.00000 10.3923i 0.221766 0.384111i
\(733\) 19.0000 0.701781 0.350891 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) 34.6410i 1.27862i
\(735\) −19.5000 + 7.79423i −0.719268 + 0.287494i
\(736\) 3.46410i 0.127688i
\(737\) 0 0
\(738\) 0 0
\(739\) 20.7846i 0.764574i −0.924044 0.382287i \(-0.875137\pi\)
0.924044 0.382287i \(-0.124863\pi\)
\(740\) 3.00000 0.110282
\(741\) −3.00000 + 12.1244i −0.110208 + 0.445399i
\(742\) −3.00000 + 8.66025i −0.110133 + 0.317928i
\(743\) 33.0000 1.21065 0.605326 0.795977i \(-0.293043\pi\)
0.605326 + 0.795977i \(0.293043\pi\)
\(744\) −12.0000 6.92820i −0.439941 0.254000i
\(745\) 10.3923i 0.380745i
\(746\) 16.0000 0.585802
\(747\) −9.00000 + 5.19615i −0.329293 + 0.190117i
\(748\) 0 0
\(749\) 9.00000 25.9808i 0.328853 0.949316i
\(750\) −10.5000 + 18.1865i −0.383406 + 0.664078i
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 12.1244i 0.442130i
\(753\) 18.0000 + 10.3923i 0.655956 + 0.378717i
\(754\) 24.0000 6.92820i 0.874028 0.252310i
\(755\) −33.0000 −1.20099
\(756\) 4.50000 12.9904i 0.163663 0.472456i
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 17.3205i 0.629109i
\(759\) 0 0
\(760\) 3.46410i 0.125656i
\(761\) 38.1051i 1.38131i 0.723185 + 0.690655i \(0.242678\pi\)
−0.723185 + 0.690655i \(0.757322\pi\)
\(762\) −3.00000 1.73205i −0.108679 0.0627456i
\(763\) 4.50000 12.9904i 0.162911 0.470283i
\(764\) 20.7846i 0.751961i
\(765\) −13.5000 + 7.79423i −0.488094 + 0.281801i
\(766\) 5.19615i 0.187745i
\(767\) 36.0000 10.3923i 1.29988 0.375244i
\(768\) 1.50000 + 0.866025i 0.0541266 + 0.0312500i
\(769\) 4.00000 0.144244 0.0721218 0.997396i \(-0.477023\pi\)
0.0721218 + 0.997396i \(0.477023\pi\)
\(770\) 0 0
\(771\) 31.5000 + 18.1865i 1.13444 + 0.654972i
\(772\) 17.3205i 0.623379i
\(773\) 15.5885i 0.560678i 0.959901 + 0.280339i \(0.0904469\pi\)
−0.959901 + 0.280339i \(0.909553\pi\)
\(774\) −16.5000 28.5788i −0.593080 1.02725i
\(775\) −16.0000 −0.574737
\(776\) 8.00000 0.287183
\(777\) −6.00000 + 5.19615i −0.215249 + 0.186411i
\(778\) 10.3923i 0.372582i
\(779\) 0 0
\(780\) −10.5000 2.59808i −0.375960 0.0930261i
\(781\) 0 0
\(782\) 10.3923i 0.371628i
\(783\) 36.0000 1.28654
\(784\) 5.50000 + 4.33013i 0.196429 + 0.154647i
\(785\) −18.0000 −0.642448