Properties

Label 546.2.e.b.545.1
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 545.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.545
Dual form 546.2.e.b.545.2

$q$-expansion

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

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 \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 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 \(0.117618\pi\)
−0.932505 + 0.361158i \(0.882382\pi\)
\(24\) −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 \(0.222422\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(30\) −1.50000 2.59808i −0.273861 0.474342i
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −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
\(39\) −4.50000 4.33013i −0.720577 0.693375i
\(40\) 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 \(0.0764641\pi\)
−0.971286 + 0.237915i \(0.923536\pi\)
\(54\) 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 \(0.146275\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −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 \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 1.73205i 0.201347i
\(75\) 3.00000 1.73205i 0.346410 0.200000i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 4.50000 + 4.33013i 0.509525 + 0.490290i
\(79\) 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
\(91\) −5.50000 7.79423i −0.576557 0.817057i
\(92\) 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 \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) −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 \(0.0545913\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) 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 \(-0.832476\pi\)
0.864675 0.502331i \(-0.167524\pi\)
\(108\) 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 \(0.105659\pi\)
−0.945413 + 0.325875i \(0.894341\pi\)
\(114\) 3.00000 1.73205i 0.280976 0.162221i
\(115\) −6.00000 −0.559503
\(116\) 6.92820i 0.643268i
\(117\) −10.5000 2.59808i −0.970725 0.240192i
\(118\) 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 \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −3.00000 5.19615i −0.255377 0.442326i
\(139\) 19.0526i 1.61602i 0.589171 + 0.808008i \(0.299454\pi\)
−0.589171 + 0.808008i \(0.700546\pi\)
\(140\) 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 \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −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
\(156\) −4.50000 4.33013i −0.360288 0.346688i
\(157\) 10.3923i 0.829396i −0.909959 0.414698i \(-0.863887\pi\)
0.909959 0.414698i \(-0.136113\pi\)
\(158\) −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 \(-0.850315\pi\)
0.891455 0.453108i \(-0.149685\pi\)
\(180\) 4.50000 + 2.59808i 0.335410 + 0.193649i
\(181\) 3.46410i 0.257485i −0.991678 0.128742i \(-0.958906\pi\)
0.991678 0.128742i \(-0.0410940\pi\)
\(182\) 5.50000 + 7.79423i 0.407687 + 0.577747i
\(183\) 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 \(0.270892\pi\)
−0.659208 + 0.751961i \(0.729108\pi\)
\(192\) 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
\(195\) 7.50000 7.79423i 0.537086 0.558156i
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 0 0
\(199\) 6.92820i 0.491127i −0.969380 0.245564i \(-0.921027\pi\)
0.969380 0.245564i \(-0.0789730\pi\)
\(200\) −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 \(-0.424695\pi\)
0.234377 + 0.972146i \(0.424695\pi\)
\(224\) −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 \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 6.92820i 0.454859i
\(233\) 8.66025i 0.567352i −0.958920 0.283676i \(-0.908446\pi\)
0.958920 0.283676i \(-0.0915540\pi\)
\(234\) 10.5000 + 2.59808i 0.686406 + 0.169842i
\(235\) 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 \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 1.50000 + 2.59808i 0.0968246 + 0.167705i
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 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 \(-0.859496\pi\)
0.904152 0.427211i \(-0.140504\pi\)
\(264\) 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 \(-0.490331\pi\)
0.0303728 + 0.999539i \(0.490331\pi\)
\(272\) 3.00000 0.181902
\(273\) −15.0000 6.92820i −0.907841 0.419314i
\(274\) 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 \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 10.5000 + 18.1865i 0.625266 + 1.08299i
\(283\) 10.3923i 0.617758i −0.951101 0.308879i \(-0.900046\pi\)
0.951101 0.308879i \(-0.0999539\pi\)
\(284\) −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 \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(308\) 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 \(0.176256\pi\)
\(312\) 4.50000 + 4.33013i 0.254762 + 0.245145i
\(313\) 8.66025i 0.489506i 0.969585 + 0.244753i \(0.0787070\pi\)
−0.969585 + 0.244753i \(0.921293\pi\)
\(314\) 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 \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) −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 \(-0.862585\pi\)
0.908255 0.418416i \(-0.137415\pi\)
\(348\) 6.00000 + 10.3923i 0.321634 + 0.557086i
\(349\) −1.00000 −0.0535288 −0.0267644 0.999642i \(-0.508520\pi\)
−0.0267644 + 0.999642i \(0.508520\pi\)
\(350\) −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
\(364\) −5.50000 7.79423i −0.288278 0.408529i
\(365\) 3.46410i 0.181319i
\(366\) −6.00000 10.3923i −0.313625 0.543214i
\(367\) 34.6410i 1.80825i −0.427272 0.904123i \(-0.640525\pi\)
0.427272 0.904123i \(-0.359475\pi\)
\(368\) 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 \(0.0848622\pi\)
−0.964672 + 0.263455i \(0.915138\pi\)
\(390\) −7.50000 + 7.79423i −0.379777 + 0.394676i
\(391\) 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 \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 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 \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) −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 \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 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 \(-0.207588\pi\)
0.794777 + 0.606902i \(0.207588\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 5.19615i 0.249711i −0.992175 0.124856i \(-0.960153\pi\)
0.992175 0.124856i \(-0.0398468\pi\)
\(434\) −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 \(0.267072\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 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 \(0.179651\pi\)
−0.844916 + 0.534899i \(0.820349\pi\)
\(444\) −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
\(455\) 13.5000 9.52628i 0.632890 0.446599i
\(456\) 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 \(0.186655\pi\)
\(468\) −10.5000 2.59808i −0.485363 0.120096i
\(469\) 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 \(-0.693558\pi\)
0.571292 0.820747i \(-0.306442\pi\)
\(492\) 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
\(507\) −10.5000 + 19.9186i −0.466321 + 0.884615i
\(508\) −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 \(0.123624\pi\)
−0.925525 + 0.378686i \(0.876376\pi\)
\(524\) −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
\(546\) 15.0000 + 6.92820i 0.641941 + 0.296500i
\(547\) 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 \(-0.253572\pi\)
0.699127 + 0.714997i \(0.253572\pi\)
\(558\) −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 \(0.242305\pi\)
−0.723993 + 0.689808i \(0.757695\pi\)
\(570\) 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 \(-0.0931316\pi\)
0.957503 + 0.288425i \(0.0931316\pi\)
\(578\) 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
\(585\) 4.50000 18.1865i 0.186052 0.751921i
\(586\) 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 \(-0.835026\pi\)
0.868672 0.495388i \(-0.164974\pi\)
\(600\) −3.00000 + 1.73205i −0.122474 + 0.0707107i
\(601\) 5.19615i 0.211955i 0.994369 + 0.105978i \(0.0337972\pi\)
−0.994369 + 0.105978i \(0.966203\pi\)
\(602\) 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 \(-0.836225\pi\)
0.870532 0.492112i \(-0.163775\pi\)
\(608\) 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 \(-0.242000\pi\)
0.724653 + 0.689114i \(0.242000\pi\)
\(618\) −3.00000 5.19615i −0.120678 0.209020i
\(619\) 40.0000 1.60774 0.803868 0.594808i \(-0.202772\pi\)
0.803868 + 0.594808i \(0.202772\pi\)
\(620\) 13.8564i 0.556487i
\(621\) 18.0000 0.722315
\(622\) −30.0000 −1.20289
\(623\) 3.00000 + 8.66025i 0.120192 + 0.346966i
\(624\) −4.50000 4.33013i −0.180144 0.173344i
\(625\) −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
\(637\) −20.5000 14.7224i −0.812240 0.583324i
\(638\) 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 \(0.239813\pi\)
−0.729370 + 0.684119i \(0.760187\pi\)
\(642\) 9.00000 + 15.5885i 0.355202 + 0.615227i
\(643\) −40.0000 −1.57745 −0.788723 0.614749i \(-0.789257\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 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 \(-0.697633\pi\)
0.581754 0.813365i \(-0.302367\pi\)
\(654\) −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 \(0.156575\pi\)
−0.881439 + 0.472298i \(0.843425\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 17.3205i 0.673181i
\(663\) −13.5000 12.9904i −0.524297 0.504505i
\(664\) 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 \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(684\) −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 \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −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 \(0.255677\pi\)
−0.694383 + 0.719605i \(0.744323\pi\)
\(702\) 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 \(-0.719828\pi\)
0.637006 0.770859i \(-0.280172\pi\)
\(728\) 5.50000 + 7.79423i 0.203844 + 0.288873i
\(729\) −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 \(-0.614121\pi\)
−0.350891 + 0.936416i \(0.614121\pi\)
\(734\) 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
\(741\) 9.00000 + 8.66025i 0.330623 + 0.318142i
\(742\) −3.00000 8.66025i −0.110133 0.317928i
\(743\) −33.0000 −1.21065 −0.605326 0.795977i \(-0.706957\pi\)
−0.605326 + 0.795977i \(0.706957\pi\)
\(744\) −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 \(-0.522977\pi\)
−0.0721218 + 0.997396i \(0.522977\pi\)
\(770\) 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
\(780\) 7.50000 7.79423i 0.268543 0.279078i
\(781\) 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