Properties

Label 546.2.e.c.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.c.545.2

$q$-expansion

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

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 \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) −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 \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 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
\(21\) −4.50000 0.866025i −0.981981 0.188982i
\(22\) 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 \(-0.244865\pi\)
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
\(39\) −1.50000 + 6.06218i −0.240192 + 0.970725i
\(40\) 1.73205i 0.273861i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −4.50000 0.866025i −0.694365 0.133631i
\(43\) −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 \(0.345336\pi\)
−0.466996 + 0.884260i \(0.654664\pi\)
\(48\) −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 \(0.236496\pi\)
−0.736460 + 0.676481i \(0.763504\pi\)
\(60\) −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
\(63\) 6.00000 + 5.19615i 0.755929 + 0.654654i
\(64\) 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 \(-0.462659\pi\)
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
\(78\) −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 \(-0.939113\pi\)
0.981761 0.190117i \(-0.0608868\pi\)
\(84\) −4.50000 0.866025i −0.490990 0.0944911i
\(85\) 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 \(-0.941226\pi\)
0.983002 0.183597i \(-0.0587741\pi\)
\(90\) 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 \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 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
\(105\) −1.50000 + 7.79423i −0.146385 + 0.760639i
\(106\) 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
\(126\) 6.00000 + 5.19615i 0.534522 + 0.462910i
\(127\) −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 \(-0.272551\pi\)
0.655278 + 0.755388i \(0.272551\pi\)
\(132\) 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 \(0.299454\pi\)
−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
\(147\) −12.0000 + 1.73205i −0.989743 + 0.142857i
\(148\) 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 \(-0.863887\pi\)
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 \(0.0427919\pi\)
−0.990977 + 0.134030i \(0.957208\pi\)
\(168\) −4.50000 0.866025i −0.347183 0.0668153i
\(169\) −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 \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −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 \(-0.958906\pi\)
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 \(-0.729108\pi\)
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 \(-0.921027\pi\)
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
\(210\) −1.50000 + 7.79423i −0.103510 + 0.537853i
\(211\) −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 \(0.0915540\pi\)
−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 \(-0.604381\pi\)
−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 \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 6.00000 + 5.19615i 0.377964 + 0.327327i
\(253\) 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 \(-0.727320\pi\)
−0.654972 + 0.755653i \(0.727320\pi\)
\(258\) 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 \(-0.490331\pi\)
0.0303728 + 0.999539i \(0.490331\pi\)
\(272\) −3.00000 −0.181902
\(273\) 1.50000 + 16.4545i 0.0907841 + 0.995871i
\(274\) 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 \(-0.900046\pi\)
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 \(-0.812132\pi\)
0.830827 0.556531i \(-0.187868\pi\)
\(294\) −12.0000 + 1.73205i −0.699854 + 0.101015i
\(295\) 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 \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) −1.50000 + 6.06218i −0.0849208 + 0.343203i
\(313\) 8.66025i 0.489506i 0.969585 + 0.244753i \(0.0787070\pi\)
−0.969585 + 0.244753i \(0.921293\pi\)
\(314\) 10.3923i 0.586472i
\(315\) 9.00000 10.3923i 0.507093 0.585540i
\(316\) 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
\(336\) −4.50000 0.866025i −0.245495 0.0472456i
\(337\) 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 \(-0.508520\pi\)
−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 \(-0.910804\pi\)
0.960996 0.276563i \(-0.0891955\pi\)
\(354\) 9.00000 15.5885i 0.478345 0.828517i
\(355\) 15.5885i 0.827349i
\(356\) 3.46410i 0.183597i
\(357\) 13.5000 + 2.59808i 0.714496 + 0.137505i
\(358\) 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 \(0.0423825\pi\)
−0.991149 + 0.132755i \(0.957617\pi\)
\(384\) −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 \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 6.92820i 0.347279i
\(399\) 9.00000 + 1.73205i 0.450564 + 0.0867110i
\(400\) 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 \(-0.612504\pi\)
−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 \(-0.270760\pi\)
0.659518 + 0.751689i \(0.270760\pi\)
\(420\) −1.50000 + 7.79423i −0.0731925 + 0.380319i
\(421\) 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 \(-0.960153\pi\)
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
\(441\) 19.5000 + 7.79423i 0.928571 + 0.371154i
\(442\) 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
\(455\) −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 \(-0.961388\pi\)
0.992652 0.121004i \(-0.0386115\pi\)
\(462\) 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 \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) 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 \(0.270826\pi\)
−0.659363 + 0.751825i \(0.729174\pi\)
\(480\) −1.50000 + 2.59808i −0.0684653 + 0.118585i
\(481\) −6.00000 + 1.73205i −0.273576 + 0.0789747i
\(482\) −10.0000 −0.455488
\(483\) −3.00000 + 15.5885i −0.136505 + 0.709299i
\(484\) −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 \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 6.00000 + 5.19615i 0.267261 + 0.231455i
\(505\) 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 \(0.210511\pi\)
−0.789170 + 0.614174i \(0.789489\pi\)
\(510\) 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 \(-0.298557\pi\)
0.591446 + 0.806345i \(0.298557\pi\)
\(522\) 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
\(525\) −9.00000 1.73205i −0.392792 0.0755929i
\(526\) 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
\(546\) 1.50000 + 16.4545i 0.0641941 + 0.704187i
\(547\) 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 \(-0.354084\pi\)
0.442522 + 0.896758i \(0.354084\pi\)
\(564\) 10.5000 18.1865i 0.442130 0.765791i
\(565\) −12.0000 −0.504844
\(566\) 10.3923i 0.436821i
\(567\) −4.50000 + 23.3827i −0.188982 + 0.981981i
\(568\) 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 \(-0.0931316\pi\)
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
\(585\) −13.5000 12.9904i −0.558156 0.537086i
\(586\) 19.0526i 0.787054i
\(587\) 38.1051i 1.57277i −0.617739 0.786383i \(-0.711951\pi\)
0.617739 0.786383i \(-0.288049\pi\)
\(588\) −12.0000 + 1.73205i −0.494872 + 0.0714286i
\(589\) −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 \(0.470730\pi\)
−0.0918243 + 0.995775i \(0.529270\pi\)
\(594\) 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 \(0.0337972\pi\)
−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
\(609\) −6.00000 + 31.1769i −0.243132 + 1.26335i
\(610\) 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 \(-0.202772\pi\)
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
\(624\) −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
\(630\) 9.00000 10.3923i 0.358569 0.414039i
\(631\) 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 \(-0.760187\pi\)
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 \(-0.789257\pi\)
−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 \(-0.700758\pi\)
−0.589711 + 0.807614i \(0.700758\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 0 0
\(650\) −2.00000 6.92820i −0.0784465 0.271746i
\(651\) −36.0000 6.92820i −1.41095 0.271538i
\(652\) 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 \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 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
\(672\) −4.50000 0.866025i −0.173591 0.0334077i
\(673\) −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 \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −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 \(-0.624220\pi\)
−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 \(-0.744323\pi\)
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
\(714\) 13.5000 + 2.59808i 0.505225 + 0.0972306i
\(715\) 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 \(-0.571834\pi\)
−0.223762 + 0.974644i \(0.571834\pi\)
\(720\) 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
\(735\) 3.00000 + 20.7846i 0.110657 + 0.766652i
\(736\) 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 \(-0.757322\pi\)
0.723185 0.690655i \(-0.242678\pi\)
\(762\) 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 \(-0.909553\pi\)
0.959901 0.280339i \(-0.0904469\pi\)
\(774\) −16.5000 28.5788i −0.593080 1.02725i
\(775\) 16.0000 0.574737
\(776\) −8.00000 −0.287183
\(777\) −1.50000 + 7.79423i −0.0538122 + 0.279616i
\(778\) 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