Properties

Label 108.2.b.a.107.2
Level 108
Weight 2
Character 108.107
Analytic conductor 0.862
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.862384341830\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{3}, \sqrt{-5})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.2
Root \(-0.866025 + 1.11803i\)
Character \(\chi\) = 108.107
Dual form 108.2.b.a.107.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 1.11803i) q^{2} +(-0.500000 - 1.93649i) q^{4} +2.23607i q^{5} +3.87298i q^{7} +(2.59808 + 1.11803i) q^{8} +O(q^{10})\) \(q+(-0.866025 + 1.11803i) q^{2} +(-0.500000 - 1.93649i) q^{4} +2.23607i q^{5} +3.87298i q^{7} +(2.59808 + 1.11803i) q^{8} +(-2.50000 - 1.93649i) q^{10} -1.73205 q^{11} +2.00000 q^{13} +(-4.33013 - 3.35410i) q^{14} +(-3.50000 + 1.93649i) q^{16} -4.47214i q^{17} +(4.33013 - 1.11803i) q^{20} +(1.50000 - 1.93649i) q^{22} +6.92820 q^{23} +(-1.73205 + 2.23607i) q^{26} +(7.50000 - 1.93649i) q^{28} -4.47214i q^{29} -3.87298i q^{31} +(0.866025 - 5.59017i) q^{32} +(5.00000 + 3.87298i) q^{34} -8.66025 q^{35} -4.00000 q^{37} +(-2.50000 + 5.80948i) q^{40} +8.94427i q^{41} -7.74597i q^{43} +(0.866025 + 3.35410i) q^{44} +(-6.00000 + 7.74597i) q^{46} +3.46410 q^{47} -8.00000 q^{49} +(-1.00000 - 3.87298i) q^{52} +2.23607i q^{53} -3.87298i q^{55} +(-4.33013 + 10.0623i) q^{56} +(5.00000 + 3.87298i) q^{58} -3.46410 q^{59} -4.00000 q^{61} +(4.33013 + 3.35410i) q^{62} +(5.50000 + 5.80948i) q^{64} +4.47214i q^{65} +7.74597i q^{67} +(-8.66025 + 2.23607i) q^{68} +(7.50000 - 9.68246i) q^{70} +10.3923 q^{71} +5.00000 q^{73} +(3.46410 - 4.47214i) q^{74} -6.70820i q^{77} -7.74597i q^{79} +(-4.33013 - 7.82624i) q^{80} +(-10.0000 - 7.74597i) q^{82} -12.1244 q^{83} +10.0000 q^{85} +(8.66025 + 6.70820i) q^{86} +(-4.50000 - 1.93649i) q^{88} -4.47214i q^{89} +7.74597i q^{91} +(-3.46410 - 13.4164i) q^{92} +(-3.00000 + 3.87298i) q^{94} +11.0000 q^{97} +(6.92820 - 8.94427i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{4} + O(q^{10}) \) \( 4q - 2q^{4} - 10q^{10} + 8q^{13} - 14q^{16} + 6q^{22} + 30q^{28} + 20q^{34} - 16q^{37} - 10q^{40} - 24q^{46} - 32q^{49} - 4q^{52} + 20q^{58} - 16q^{61} + 22q^{64} + 30q^{70} + 20q^{73} - 40q^{82} + 40q^{85} - 18q^{88} - 12q^{94} + 44q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 1.11803i −0.612372 + 0.790569i
\(3\) 0 0
\(4\) −0.500000 1.93649i −0.250000 0.968246i
\(5\) 2.23607i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) 3.87298i 1.46385i 0.681385 + 0.731925i \(0.261378\pi\)
−0.681385 + 0.731925i \(0.738622\pi\)
\(8\) 2.59808 + 1.11803i 0.918559 + 0.395285i
\(9\) 0 0
\(10\) −2.50000 1.93649i −0.790569 0.612372i
\(11\) −1.73205 −0.522233 −0.261116 0.965307i \(-0.584091\pi\)
−0.261116 + 0.965307i \(0.584091\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −4.33013 3.35410i −1.15728 0.896421i
\(15\) 0 0
\(16\) −3.50000 + 1.93649i −0.875000 + 0.484123i
\(17\) 4.47214i 1.08465i −0.840168 0.542326i \(-0.817544\pi\)
0.840168 0.542326i \(-0.182456\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 4.33013 1.11803i 0.968246 0.250000i
\(21\) 0 0
\(22\) 1.50000 1.93649i 0.319801 0.412861i
\(23\) 6.92820 1.44463 0.722315 0.691564i \(-0.243078\pi\)
0.722315 + 0.691564i \(0.243078\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.73205 + 2.23607i −0.339683 + 0.438529i
\(27\) 0 0
\(28\) 7.50000 1.93649i 1.41737 0.365963i
\(29\) 4.47214i 0.830455i −0.909718 0.415227i \(-0.863702\pi\)
0.909718 0.415227i \(-0.136298\pi\)
\(30\) 0 0
\(31\) 3.87298i 0.695608i −0.937567 0.347804i \(-0.886927\pi\)
0.937567 0.347804i \(-0.113073\pi\)
\(32\) 0.866025 5.59017i 0.153093 0.988212i
\(33\) 0 0
\(34\) 5.00000 + 3.87298i 0.857493 + 0.664211i
\(35\) −8.66025 −1.46385
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −2.50000 + 5.80948i −0.395285 + 0.918559i
\(41\) 8.94427i 1.39686i 0.715678 + 0.698430i \(0.246118\pi\)
−0.715678 + 0.698430i \(0.753882\pi\)
\(42\) 0 0
\(43\) 7.74597i 1.18125i −0.806947 0.590624i \(-0.798881\pi\)
0.806947 0.590624i \(-0.201119\pi\)
\(44\) 0.866025 + 3.35410i 0.130558 + 0.505650i
\(45\) 0 0
\(46\) −6.00000 + 7.74597i −0.884652 + 1.14208i
\(47\) 3.46410 0.505291 0.252646 0.967559i \(-0.418699\pi\)
0.252646 + 0.967559i \(0.418699\pi\)
\(48\) 0 0
\(49\) −8.00000 −1.14286
\(50\) 0 0
\(51\) 0 0
\(52\) −1.00000 3.87298i −0.138675 0.537086i
\(53\) 2.23607i 0.307148i 0.988137 + 0.153574i \(0.0490783\pi\)
−0.988137 + 0.153574i \(0.950922\pi\)
\(54\) 0 0
\(55\) 3.87298i 0.522233i
\(56\) −4.33013 + 10.0623i −0.578638 + 1.34463i
\(57\) 0 0
\(58\) 5.00000 + 3.87298i 0.656532 + 0.508548i
\(59\) −3.46410 −0.450988 −0.225494 0.974245i \(-0.572400\pi\)
−0.225494 + 0.974245i \(0.572400\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) 4.33013 + 3.35410i 0.549927 + 0.425971i
\(63\) 0 0
\(64\) 5.50000 + 5.80948i 0.687500 + 0.726184i
\(65\) 4.47214i 0.554700i
\(66\) 0 0
\(67\) 7.74597i 0.946320i 0.880976 + 0.473160i \(0.156887\pi\)
−0.880976 + 0.473160i \(0.843113\pi\)
\(68\) −8.66025 + 2.23607i −1.05021 + 0.271163i
\(69\) 0 0
\(70\) 7.50000 9.68246i 0.896421 1.15728i
\(71\) 10.3923 1.23334 0.616670 0.787222i \(-0.288481\pi\)
0.616670 + 0.787222i \(0.288481\pi\)
\(72\) 0 0
\(73\) 5.00000 0.585206 0.292603 0.956234i \(-0.405479\pi\)
0.292603 + 0.956234i \(0.405479\pi\)
\(74\) 3.46410 4.47214i 0.402694 0.519875i
\(75\) 0 0
\(76\) 0 0
\(77\) 6.70820i 0.764471i
\(78\) 0 0
\(79\) 7.74597i 0.871489i −0.900070 0.435745i \(-0.856485\pi\)
0.900070 0.435745i \(-0.143515\pi\)
\(80\) −4.33013 7.82624i −0.484123 0.875000i
\(81\) 0 0
\(82\) −10.0000 7.74597i −1.10432 0.855399i
\(83\) −12.1244 −1.33082 −0.665410 0.746478i \(-0.731743\pi\)
−0.665410 + 0.746478i \(0.731743\pi\)
\(84\) 0 0
\(85\) 10.0000 1.08465
\(86\) 8.66025 + 6.70820i 0.933859 + 0.723364i
\(87\) 0 0
\(88\) −4.50000 1.93649i −0.479702 0.206431i
\(89\) 4.47214i 0.474045i −0.971504 0.237023i \(-0.923828\pi\)
0.971504 0.237023i \(-0.0761716\pi\)
\(90\) 0 0
\(91\) 7.74597i 0.811998i
\(92\) −3.46410 13.4164i −0.361158 1.39876i
\(93\) 0 0
\(94\) −3.00000 + 3.87298i −0.309426 + 0.399468i
\(95\) 0 0
\(96\) 0 0
\(97\) 11.0000 1.11688 0.558440 0.829545i \(-0.311400\pi\)
0.558440 + 0.829545i \(0.311400\pi\)
\(98\) 6.92820 8.94427i 0.699854 0.903508i
\(99\) 0 0
\(100\) 0 0
\(101\) 2.23607i 0.222497i 0.993793 + 0.111249i \(0.0354850\pi\)
−0.993793 + 0.111249i \(0.964515\pi\)
\(102\) 0 0
\(103\) 7.74597i 0.763233i 0.924321 + 0.381616i \(0.124632\pi\)
−0.924321 + 0.381616i \(0.875368\pi\)
\(104\) 5.19615 + 2.23607i 0.509525 + 0.219265i
\(105\) 0 0
\(106\) −2.50000 1.93649i −0.242821 0.188089i
\(107\) 5.19615 0.502331 0.251166 0.967944i \(-0.419186\pi\)
0.251166 + 0.967944i \(0.419186\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 4.33013 + 3.35410i 0.412861 + 0.319801i
\(111\) 0 0
\(112\) −7.50000 13.5554i −0.708683 1.28087i
\(113\) 17.8885i 1.68281i −0.540403 0.841406i \(-0.681728\pi\)
0.540403 0.841406i \(-0.318272\pi\)
\(114\) 0 0
\(115\) 15.4919i 1.44463i
\(116\) −8.66025 + 2.23607i −0.804084 + 0.207614i
\(117\) 0 0
\(118\) 3.00000 3.87298i 0.276172 0.356537i
\(119\) 17.3205 1.58777
\(120\) 0 0
\(121\) −8.00000 −0.727273
\(122\) 3.46410 4.47214i 0.313625 0.404888i
\(123\) 0 0
\(124\) −7.50000 + 1.93649i −0.673520 + 0.173902i
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) 11.6190i 1.03102i 0.856885 + 0.515508i \(0.172397\pi\)
−0.856885 + 0.515508i \(0.827603\pi\)
\(128\) −11.2583 + 1.11803i −0.995105 + 0.0988212i
\(129\) 0 0
\(130\) −5.00000 3.87298i −0.438529 0.339683i
\(131\) −19.0526 −1.66463 −0.832315 0.554303i \(-0.812985\pi\)
−0.832315 + 0.554303i \(0.812985\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.66025 6.70820i −0.748132 0.579501i
\(135\) 0 0
\(136\) 5.00000 11.6190i 0.428746 0.996317i
\(137\) 4.47214i 0.382080i −0.981582 0.191040i \(-0.938814\pi\)
0.981582 0.191040i \(-0.0611861\pi\)
\(138\) 0 0
\(139\) 15.4919i 1.31401i −0.753887 0.657004i \(-0.771823\pi\)
0.753887 0.657004i \(-0.228177\pi\)
\(140\) 4.33013 + 16.7705i 0.365963 + 1.41737i
\(141\) 0 0
\(142\) −9.00000 + 11.6190i −0.755263 + 0.975041i
\(143\) −3.46410 −0.289683
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) −4.33013 + 5.59017i −0.358364 + 0.462646i
\(147\) 0 0
\(148\) 2.00000 + 7.74597i 0.164399 + 0.636715i
\(149\) 2.23607i 0.183186i 0.995797 + 0.0915929i \(0.0291958\pi\)
−0.995797 + 0.0915929i \(0.970804\pi\)
\(150\) 0 0
\(151\) 3.87298i 0.315179i 0.987505 + 0.157589i \(0.0503723\pi\)
−0.987505 + 0.157589i \(0.949628\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 7.50000 + 5.80948i 0.604367 + 0.468141i
\(155\) 8.66025 0.695608
\(156\) 0 0
\(157\) 20.0000 1.59617 0.798087 0.602542i \(-0.205846\pi\)
0.798087 + 0.602542i \(0.205846\pi\)
\(158\) 8.66025 + 6.70820i 0.688973 + 0.533676i
\(159\) 0 0
\(160\) 12.5000 + 1.93649i 0.988212 + 0.153093i
\(161\) 26.8328i 2.11472i
\(162\) 0 0
\(163\) 23.2379i 1.82013i −0.414462 0.910066i \(-0.636030\pi\)
0.414462 0.910066i \(-0.363970\pi\)
\(164\) 17.3205 4.47214i 1.35250 0.349215i
\(165\) 0 0
\(166\) 10.5000 13.5554i 0.814958 1.05211i
\(167\) −3.46410 −0.268060 −0.134030 0.990977i \(-0.542792\pi\)
−0.134030 + 0.990977i \(0.542792\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −8.66025 + 11.1803i −0.664211 + 0.857493i
\(171\) 0 0
\(172\) −15.0000 + 3.87298i −1.14374 + 0.295312i
\(173\) 15.6525i 1.19004i 0.803712 + 0.595018i \(0.202855\pi\)
−0.803712 + 0.595018i \(0.797145\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.06218 3.35410i 0.456954 0.252825i
\(177\) 0 0
\(178\) 5.00000 + 3.87298i 0.374766 + 0.290292i
\(179\) −5.19615 −0.388379 −0.194189 0.980964i \(-0.562208\pi\)
−0.194189 + 0.980964i \(0.562208\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −8.66025 6.70820i −0.641941 0.497245i
\(183\) 0 0
\(184\) 18.0000 + 7.74597i 1.32698 + 0.571040i
\(185\) 8.94427i 0.657596i
\(186\) 0 0
\(187\) 7.74597i 0.566441i
\(188\) −1.73205 6.70820i −0.126323 0.489246i
\(189\) 0 0
\(190\) 0 0
\(191\) −17.3205 −1.25327 −0.626634 0.779314i \(-0.715568\pi\)
−0.626634 + 0.779314i \(0.715568\pi\)
\(192\) 0 0
\(193\) −25.0000 −1.79954 −0.899770 0.436365i \(-0.856266\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) −9.52628 + 12.2984i −0.683947 + 0.882972i
\(195\) 0 0
\(196\) 4.00000 + 15.4919i 0.285714 + 1.10657i
\(197\) 24.5967i 1.75245i −0.481906 0.876223i \(-0.660055\pi\)
0.481906 0.876223i \(-0.339945\pi\)
\(198\) 0 0
\(199\) 11.6190i 0.823646i −0.911264 0.411823i \(-0.864892\pi\)
0.911264 0.411823i \(-0.135108\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −2.50000 1.93649i −0.175899 0.136251i
\(203\) 17.3205 1.21566
\(204\) 0 0
\(205\) −20.0000 −1.39686
\(206\) −8.66025 6.70820i −0.603388 0.467383i
\(207\) 0 0
\(208\) −7.00000 + 3.87298i −0.485363 + 0.268543i
\(209\) 0 0
\(210\) 0 0
\(211\) 15.4919i 1.06651i −0.845955 0.533254i \(-0.820969\pi\)
0.845955 0.533254i \(-0.179031\pi\)
\(212\) 4.33013 1.11803i 0.297394 0.0767869i
\(213\) 0 0
\(214\) −4.50000 + 5.80948i −0.307614 + 0.397128i
\(215\) 17.3205 1.18125
\(216\) 0 0
\(217\) 15.0000 1.01827
\(218\) 3.46410 4.47214i 0.234619 0.302891i
\(219\) 0 0
\(220\) −7.50000 + 1.93649i −0.505650 + 0.130558i
\(221\) 8.94427i 0.601657i
\(222\) 0 0
\(223\) 7.74597i 0.518708i −0.965782 0.259354i \(-0.916490\pi\)
0.965782 0.259354i \(-0.0835097\pi\)
\(224\) 21.6506 + 3.35410i 1.44659 + 0.224105i
\(225\) 0 0
\(226\) 20.0000 + 15.4919i 1.33038 + 1.03051i
\(227\) 3.46410 0.229920 0.114960 0.993370i \(-0.463326\pi\)
0.114960 + 0.993370i \(0.463326\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) −17.3205 13.4164i −1.14208 0.884652i
\(231\) 0 0
\(232\) 5.00000 11.6190i 0.328266 0.762821i
\(233\) 4.47214i 0.292979i −0.989212 0.146490i \(-0.953202\pi\)
0.989212 0.146490i \(-0.0467975\pi\)
\(234\) 0 0
\(235\) 7.74597i 0.505291i
\(236\) 1.73205 + 6.70820i 0.112747 + 0.436667i
\(237\) 0 0
\(238\) −15.0000 + 19.3649i −0.972306 + 1.25524i
\(239\) −13.8564 −0.896296 −0.448148 0.893959i \(-0.647916\pi\)
−0.448148 + 0.893959i \(0.647916\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 6.92820 8.94427i 0.445362 0.574960i
\(243\) 0 0
\(244\) 2.00000 + 7.74597i 0.128037 + 0.495885i
\(245\) 17.8885i 1.14286i
\(246\) 0 0
\(247\) 0 0
\(248\) 4.33013 10.0623i 0.274963 0.638957i
\(249\) 0 0
\(250\) −12.5000 9.68246i −0.790569 0.612372i
\(251\) 10.3923 0.655956 0.327978 0.944685i \(-0.393633\pi\)
0.327978 + 0.944685i \(0.393633\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) −12.9904 10.0623i −0.815089 0.631365i
\(255\) 0 0
\(256\) 8.50000 13.5554i 0.531250 0.847215i
\(257\) 22.3607i 1.39482i 0.716672 + 0.697410i \(0.245665\pi\)
−0.716672 + 0.697410i \(0.754335\pi\)
\(258\) 0 0
\(259\) 15.4919i 0.962622i
\(260\) 8.66025 2.23607i 0.537086 0.138675i
\(261\) 0 0
\(262\) 16.5000 21.3014i 1.01937 1.31601i
\(263\) −6.92820 −0.427211 −0.213606 0.976920i \(-0.568521\pi\)
−0.213606 + 0.976920i \(0.568521\pi\)
\(264\) 0 0
\(265\) −5.00000 −0.307148
\(266\) 0 0
\(267\) 0 0
\(268\) 15.0000 3.87298i 0.916271 0.236580i
\(269\) 4.47214i 0.272671i −0.990663 0.136335i \(-0.956467\pi\)
0.990663 0.136335i \(-0.0435325\pi\)
\(270\) 0 0
\(271\) 11.6190i 0.705801i 0.935661 + 0.352900i \(0.114805\pi\)
−0.935661 + 0.352900i \(0.885195\pi\)
\(272\) 8.66025 + 15.6525i 0.525105 + 0.949071i
\(273\) 0 0
\(274\) 5.00000 + 3.87298i 0.302061 + 0.233975i
\(275\) 0 0
\(276\) 0 0
\(277\) 20.0000 1.20168 0.600842 0.799368i \(-0.294832\pi\)
0.600842 + 0.799368i \(0.294832\pi\)
\(278\) 17.3205 + 13.4164i 1.03882 + 0.804663i
\(279\) 0 0
\(280\) −22.5000 9.68246i −1.34463 0.578638i
\(281\) 4.47214i 0.266785i −0.991063 0.133393i \(-0.957413\pi\)
0.991063 0.133393i \(-0.0425871\pi\)
\(282\) 0 0
\(283\) 30.9839i 1.84180i 0.389799 + 0.920900i \(0.372544\pi\)
−0.389799 + 0.920900i \(0.627456\pi\)
\(284\) −5.19615 20.1246i −0.308335 1.19418i
\(285\) 0 0
\(286\) 3.00000 3.87298i 0.177394 0.229014i
\(287\) −34.6410 −2.04479
\(288\) 0 0
\(289\) −3.00000 −0.176471
\(290\) −8.66025 + 11.1803i −0.508548 + 0.656532i
\(291\) 0 0
\(292\) −2.50000 9.68246i −0.146301 0.566623i
\(293\) 22.3607i 1.30632i 0.757218 + 0.653162i \(0.226558\pi\)
−0.757218 + 0.653162i \(0.773442\pi\)
\(294\) 0 0
\(295\) 7.74597i 0.450988i
\(296\) −10.3923 4.47214i −0.604040 0.259938i
\(297\) 0 0
\(298\) −2.50000 1.93649i −0.144821 0.112178i
\(299\) 13.8564 0.801337
\(300\) 0 0
\(301\) 30.0000 1.72917
\(302\) −4.33013 3.35410i −0.249171 0.193007i
\(303\) 0 0
\(304\) 0 0
\(305\) 8.94427i 0.512148i
\(306\) 0 0
\(307\) 23.2379i 1.32626i 0.748506 + 0.663129i \(0.230772\pi\)
−0.748506 + 0.663129i \(0.769228\pi\)
\(308\) −12.9904 + 3.35410i −0.740196 + 0.191118i
\(309\) 0 0
\(310\) −7.50000 + 9.68246i −0.425971 + 0.549927i
\(311\) 27.7128 1.57145 0.785725 0.618576i \(-0.212290\pi\)
0.785725 + 0.618576i \(0.212290\pi\)
\(312\) 0 0
\(313\) 5.00000 0.282617 0.141308 0.989966i \(-0.454869\pi\)
0.141308 + 0.989966i \(0.454869\pi\)
\(314\) −17.3205 + 22.3607i −0.977453 + 1.26189i
\(315\) 0 0
\(316\) −15.0000 + 3.87298i −0.843816 + 0.217872i
\(317\) 15.6525i 0.879131i 0.898211 + 0.439565i \(0.144867\pi\)
−0.898211 + 0.439565i \(0.855133\pi\)
\(318\) 0 0
\(319\) 7.74597i 0.433691i
\(320\) −12.9904 + 12.2984i −0.726184 + 0.687500i
\(321\) 0 0
\(322\) −30.0000 23.2379i −1.67183 1.29500i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 25.9808 + 20.1246i 1.43894 + 1.11460i
\(327\) 0 0
\(328\) −10.0000 + 23.2379i −0.552158 + 1.28310i
\(329\) 13.4164i 0.739671i
\(330\) 0 0
\(331\) 7.74597i 0.425757i −0.977079 0.212878i \(-0.931716\pi\)
0.977079 0.212878i \(-0.0682838\pi\)
\(332\) 6.06218 + 23.4787i 0.332705 + 1.28856i
\(333\) 0 0
\(334\) 3.00000 3.87298i 0.164153 0.211920i
\(335\) −17.3205 −0.946320
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 7.79423 10.0623i 0.423950 0.547317i
\(339\) 0 0
\(340\) −5.00000 19.3649i −0.271163 1.05021i
\(341\) 6.70820i 0.363270i
\(342\) 0 0
\(343\) 3.87298i 0.209121i
\(344\) 8.66025 20.1246i 0.466930 1.08505i
\(345\) 0 0
\(346\) −17.5000 13.5554i −0.940806 0.728745i
\(347\) 32.9090 1.76665 0.883323 0.468765i \(-0.155301\pi\)
0.883323 + 0.468765i \(0.155301\pi\)
\(348\) 0 0
\(349\) −16.0000 −0.856460 −0.428230 0.903670i \(-0.640863\pi\)
−0.428230 + 0.903670i \(0.640863\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.50000 + 9.68246i −0.0799503 + 0.516077i
\(353\) 17.8885i 0.952111i −0.879415 0.476056i \(-0.842066\pi\)
0.879415 0.476056i \(-0.157934\pi\)
\(354\) 0 0
\(355\) 23.2379i 1.23334i
\(356\) −8.66025 + 2.23607i −0.458993 + 0.118511i
\(357\) 0 0
\(358\) 4.50000 5.80948i 0.237832 0.307040i
\(359\) −31.1769 −1.64545 −0.822727 0.568436i \(-0.807549\pi\)
−0.822727 + 0.568436i \(0.807549\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 13.8564 17.8885i 0.728277 0.940201i
\(363\) 0 0
\(364\) 15.0000 3.87298i 0.786214 0.202999i
\(365\) 11.1803i 0.585206i
\(366\) 0 0
\(367\) 27.1109i 1.41518i 0.706625 + 0.707588i \(0.250217\pi\)
−0.706625 + 0.707588i \(0.749783\pi\)
\(368\) −24.2487 + 13.4164i −1.26405 + 0.699379i
\(369\) 0 0
\(370\) 10.0000 + 7.74597i 0.519875 + 0.402694i
\(371\) −8.66025 −0.449618
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −8.66025 6.70820i −0.447811 0.346873i
\(375\) 0 0
\(376\) 9.00000 + 3.87298i 0.464140 + 0.199734i
\(377\) 8.94427i 0.460653i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 15.0000 19.3649i 0.767467 0.990795i
\(383\) −24.2487 −1.23905 −0.619526 0.784976i \(-0.712675\pi\)
−0.619526 + 0.784976i \(0.712675\pi\)
\(384\) 0 0
\(385\) 15.0000 0.764471
\(386\) 21.6506 27.9508i 1.10199 1.42266i
\(387\) 0 0
\(388\) −5.50000 21.3014i −0.279220 1.08142i
\(389\) 2.23607i 0.113373i 0.998392 + 0.0566866i \(0.0180536\pi\)
−0.998392 + 0.0566866i \(0.981946\pi\)
\(390\) 0 0
\(391\) 30.9839i 1.56692i
\(392\) −20.7846 8.94427i −1.04978 0.451754i
\(393\) 0 0
\(394\) 27.5000 + 21.3014i 1.38543 + 1.07315i
\(395\) 17.3205 0.871489
\(396\) 0 0
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 12.9904 + 10.0623i 0.651149 + 0.504378i
\(399\) 0 0
\(400\) 0 0
\(401\) 17.8885i 0.893311i −0.894706 0.446656i \(-0.852615\pi\)
0.894706 0.446656i \(-0.147385\pi\)
\(402\) 0 0
\(403\) 7.74597i 0.385854i
\(404\) 4.33013 1.11803i 0.215432 0.0556243i
\(405\) 0 0
\(406\) −15.0000 + 19.3649i −0.744438 + 0.961065i
\(407\) 6.92820 0.343418
\(408\) 0 0
\(409\) −7.00000 −0.346128 −0.173064 0.984911i \(-0.555367\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) 17.3205 22.3607i 0.855399 1.10432i
\(411\) 0 0
\(412\) 15.0000 3.87298i 0.738997 0.190808i
\(413\) 13.4164i 0.660178i
\(414\) 0 0
\(415\) 27.1109i 1.33082i
\(416\) 1.73205 11.1803i 0.0849208 0.548161i
\(417\) 0 0
\(418\) 0 0
\(419\) 17.3205 0.846162 0.423081 0.906092i \(-0.360949\pi\)
0.423081 + 0.906092i \(0.360949\pi\)
\(420\) 0 0
\(421\) −4.00000 −0.194948 −0.0974740 0.995238i \(-0.531076\pi\)
−0.0974740 + 0.995238i \(0.531076\pi\)
\(422\) 17.3205 + 13.4164i 0.843149 + 0.653101i
\(423\) 0 0
\(424\) −2.50000 + 5.80948i −0.121411 + 0.282133i
\(425\) 0 0
\(426\) 0 0
\(427\) 15.4919i 0.749707i
\(428\) −2.59808 10.0623i −0.125583 0.486380i
\(429\) 0 0
\(430\) −15.0000 + 19.3649i −0.723364 + 0.933859i
\(431\) 10.3923 0.500580 0.250290 0.968171i \(-0.419474\pi\)
0.250290 + 0.968171i \(0.419474\pi\)
\(432\) 0 0
\(433\) −13.0000 −0.624740 −0.312370 0.949960i \(-0.601123\pi\)
−0.312370 + 0.949960i \(0.601123\pi\)
\(434\) −12.9904 + 16.7705i −0.623558 + 0.805010i
\(435\) 0 0
\(436\) 2.00000 + 7.74597i 0.0957826 + 0.370965i
\(437\) 0 0
\(438\) 0 0
\(439\) 3.87298i 0.184847i 0.995720 + 0.0924237i \(0.0294614\pi\)
−0.995720 + 0.0924237i \(0.970539\pi\)
\(440\) 4.33013 10.0623i 0.206431 0.479702i
\(441\) 0 0
\(442\) 10.0000 + 7.74597i 0.475651 + 0.368438i
\(443\) 24.2487 1.15209 0.576046 0.817418i \(-0.304595\pi\)
0.576046 + 0.817418i \(0.304595\pi\)
\(444\) 0 0
\(445\) 10.0000 0.474045
\(446\) 8.66025 + 6.70820i 0.410075 + 0.317643i
\(447\) 0 0
\(448\) −22.5000 + 21.3014i −1.06303 + 1.00640i
\(449\) 17.8885i 0.844213i −0.906546 0.422106i \(-0.861291\pi\)
0.906546 0.422106i \(-0.138709\pi\)
\(450\) 0 0
\(451\) 15.4919i 0.729487i
\(452\) −34.6410 + 8.94427i −1.62938 + 0.420703i
\(453\) 0 0
\(454\) −3.00000 + 3.87298i −0.140797 + 0.181768i
\(455\) −17.3205 −0.811998
\(456\) 0 0
\(457\) −31.0000 −1.45012 −0.725059 0.688686i \(-0.758188\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) −1.73205 + 2.23607i −0.0809334 + 0.104485i
\(459\) 0 0
\(460\) 30.0000 7.74597i 1.39876 0.361158i
\(461\) 38.0132i 1.77045i −0.465164 0.885225i \(-0.654005\pi\)
0.465164 0.885225i \(-0.345995\pi\)
\(462\) 0 0
\(463\) 3.87298i 0.179993i −0.995942 0.0899964i \(-0.971314\pi\)
0.995942 0.0899964i \(-0.0286856\pi\)
\(464\) 8.66025 + 15.6525i 0.402042 + 0.726648i
\(465\) 0 0
\(466\) 5.00000 + 3.87298i 0.231621 + 0.179412i
\(467\) −5.19615 −0.240449 −0.120225 0.992747i \(-0.538361\pi\)
−0.120225 + 0.992747i \(0.538361\pi\)
\(468\) 0 0
\(469\) −30.0000 −1.38527
\(470\) −8.66025 6.70820i −0.399468 0.309426i
\(471\) 0 0
\(472\) −9.00000 3.87298i −0.414259 0.178269i
\(473\) 13.4164i 0.616887i
\(474\) 0 0
\(475\) 0 0
\(476\) −8.66025 33.5410i −0.396942 1.53735i
\(477\) 0 0
\(478\) 12.0000 15.4919i 0.548867 0.708585i
\(479\) −17.3205 −0.791394 −0.395697 0.918381i \(-0.629497\pi\)
−0.395697 + 0.918381i \(0.629497\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) −12.1244 + 15.6525i −0.552249 + 0.712951i
\(483\) 0 0
\(484\) 4.00000 + 15.4919i 0.181818 + 0.704179i
\(485\) 24.5967i 1.11688i
\(486\) 0 0
\(487\) 23.2379i 1.05301i 0.850172 + 0.526505i \(0.176498\pi\)
−0.850172 + 0.526505i \(0.823502\pi\)
\(488\) −10.3923 4.47214i −0.470438 0.202444i
\(489\) 0 0
\(490\) 20.0000 + 15.4919i 0.903508 + 0.699854i
\(491\) −8.66025 −0.390832 −0.195416 0.980720i \(-0.562606\pi\)
−0.195416 + 0.980720i \(0.562606\pi\)
\(492\) 0 0
\(493\) −20.0000 −0.900755
\(494\) 0 0
\(495\) 0 0
\(496\) 7.50000 + 13.5554i 0.336760 + 0.608657i
\(497\) 40.2492i 1.80542i
\(498\) 0 0
\(499\) 38.7298i 1.73379i −0.498495 0.866893i \(-0.666114\pi\)
0.498495 0.866893i \(-0.333886\pi\)
\(500\) 21.6506 5.59017i 0.968246 0.250000i
\(501\) 0 0
\(502\) −9.00000 + 11.6190i −0.401690 + 0.518579i
\(503\) 20.7846 0.926740 0.463370 0.886165i \(-0.346640\pi\)
0.463370 + 0.886165i \(0.346640\pi\)
\(504\) 0 0
\(505\) −5.00000 −0.222497
\(506\) 10.3923 13.4164i 0.461994 0.596432i
\(507\) 0 0
\(508\) 22.5000 5.80948i 0.998276 0.257754i
\(509\) 11.1803i 0.495560i −0.968816 0.247780i \(-0.920299\pi\)
0.968816 0.247780i \(-0.0797010\pi\)
\(510\) 0 0
\(511\) 19.3649i 0.856653i
\(512\) 7.79423 + 21.2426i 0.344459 + 0.938801i
\(513\) 0 0
\(514\) −25.0000 19.3649i −1.10270 0.854150i
\(515\) −17.3205 −0.763233
\(516\) 0 0
\(517\) −6.00000 −0.263880
\(518\) 17.3205 + 13.4164i 0.761019 + 0.589483i
\(519\) 0 0
\(520\) −5.00000 + 11.6190i −0.219265 + 0.509525i
\(521\) 22.3607i 0.979639i 0.871824 + 0.489820i \(0.162937\pi\)
−0.871824 + 0.489820i \(0.837063\pi\)
\(522\) 0 0
\(523\) 23.2379i 1.01612i −0.861321 0.508061i \(-0.830362\pi\)
0.861321 0.508061i \(-0.169638\pi\)
\(524\) 9.52628 + 36.8951i 0.416157 + 1.61177i
\(525\) 0 0
\(526\) 6.00000 7.74597i 0.261612 0.337740i
\(527\) −17.3205 −0.754493
\(528\) 0 0
\(529\) 25.0000 1.08696
\(530\) 4.33013 5.59017i 0.188089 0.242821i
\(531\) 0 0
\(532\) 0 0
\(533\) 17.8885i 0.774839i
\(534\) 0 0
\(535\) 11.6190i 0.502331i
\(536\) −8.66025 + 20.1246i −0.374066 + 0.869251i
\(537\) 0 0
\(538\) 5.00000 + 3.87298i 0.215565 + 0.166976i
\(539\) 13.8564 0.596838
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) −12.9904 10.0623i −0.557985 0.432213i
\(543\) 0 0
\(544\) −25.0000 3.87298i −1.07187 0.166053i
\(545\) 8.94427i 0.383131i
\(546\) 0 0
\(547\) 7.74597i 0.331194i −0.986194 0.165597i \(-0.947045\pi\)
0.986194 0.165597i \(-0.0529550\pi\)
\(548\) −8.66025 + 2.23607i −0.369948 + 0.0955201i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 30.0000 1.27573
\(554\) −17.3205 + 22.3607i −0.735878 + 0.950014i
\(555\) 0 0
\(556\) −30.0000 + 7.74597i −1.27228 + 0.328502i
\(557\) 15.6525i 0.663217i 0.943417 + 0.331608i \(0.107591\pi\)
−0.943417 + 0.331608i \(0.892409\pi\)
\(558\) 0 0
\(559\) 15.4919i 0.655239i
\(560\) 30.3109 16.7705i 1.28087 0.708683i
\(561\) 0 0
\(562\) 5.00000 + 3.87298i 0.210912 + 0.163372i
\(563\) −19.0526 −0.802970 −0.401485 0.915866i \(-0.631506\pi\)
−0.401485 + 0.915866i \(0.631506\pi\)
\(564\) 0 0
\(565\) 40.0000 1.68281
\(566\) −34.6410 26.8328i −1.45607 1.12787i
\(567\) 0 0
\(568\) 27.0000 + 11.6190i 1.13289 + 0.487520i
\(569\) 35.7771i 1.49985i 0.661521 + 0.749927i \(0.269911\pi\)
−0.661521 + 0.749927i \(0.730089\pi\)
\(570\) 0 0
\(571\) 7.74597i 0.324159i 0.986778 + 0.162079i \(0.0518200\pi\)
−0.986778 + 0.162079i \(0.948180\pi\)
\(572\) 1.73205 + 6.70820i 0.0724207 + 0.280484i
\(573\) 0 0
\(574\) 30.0000 38.7298i 1.25218 1.61655i
\(575\) 0 0
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 2.59808 3.35410i 0.108066 0.139512i
\(579\) 0 0
\(580\) −5.00000 19.3649i −0.207614 0.804084i
\(581\) 46.9574i 1.94812i
\(582\) 0 0
\(583\) 3.87298i 0.160403i
\(584\) 12.9904 + 5.59017i 0.537546 + 0.231323i
\(585\) 0 0
\(586\) −25.0000 19.3649i −1.03274 0.799957i
\(587\) 19.0526 0.786383 0.393192 0.919457i \(-0.371371\pi\)
0.393192 + 0.919457i \(0.371371\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 8.66025 + 6.70820i 0.356537 + 0.276172i
\(591\) 0 0
\(592\) 14.0000 7.74597i 0.575396 0.318357i
\(593\) 4.47214i 0.183649i −0.995775 0.0918243i \(-0.970730\pi\)
0.995775 0.0918243i \(-0.0292698\pi\)
\(594\) 0 0
\(595\) 38.7298i 1.58777i
\(596\) 4.33013 1.11803i 0.177369 0.0457965i
\(597\) 0 0
\(598\) −12.0000 + 15.4919i −0.490716 + 0.633512i
\(599\) 17.3205 0.707697 0.353848 0.935303i \(-0.384873\pi\)
0.353848 + 0.935303i \(0.384873\pi\)
\(600\) 0 0
\(601\) −31.0000 −1.26452 −0.632258 0.774758i \(-0.717872\pi\)
−0.632258 + 0.774758i \(0.717872\pi\)
\(602\) −25.9808 + 33.5410i −1.05890 + 1.36703i
\(603\) 0 0
\(604\) 7.50000 1.93649i 0.305171 0.0787947i
\(605\) 17.8885i 0.727273i
\(606\) 0 0
\(607\) 7.74597i 0.314399i 0.987567 + 0.157200i \(0.0502466\pi\)
−0.987567 + 0.157200i \(0.949753\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 10.0000 + 7.74597i 0.404888 + 0.313625i
\(611\) 6.92820 0.280285
\(612\) 0 0
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) −25.9808 20.1246i −1.04850 0.812163i
\(615\) 0 0
\(616\) 7.50000 17.4284i 0.302184 0.702211i
\(617\) 17.8885i 0.720166i −0.932920 0.360083i \(-0.882748\pi\)
0.932920 0.360083i \(-0.117252\pi\)
\(618\) 0 0
\(619\) 38.7298i 1.55668i 0.627841 + 0.778342i \(0.283939\pi\)
−0.627841 + 0.778342i \(0.716061\pi\)
\(620\) −4.33013 16.7705i −0.173902 0.673520i
\(621\) 0 0
\(622\) −24.0000 + 30.9839i −0.962312 + 1.24234i
\(623\) 17.3205 0.693932
\(624\) 0 0
\(625\) −25.0000 −1.00000
\(626\) −4.33013 + 5.59017i −0.173067 + 0.223428i
\(627\) 0 0
\(628\) −10.0000 38.7298i −0.399043 1.54549i
\(629\) 17.8885i 0.713263i
\(630\) 0 0
\(631\) 34.8569i 1.38763i 0.720154 + 0.693815i \(0.244071\pi\)
−0.720154 + 0.693815i \(0.755929\pi\)
\(632\) 8.66025 20.1246i 0.344486 0.800514i
\(633\) 0 0
\(634\) −17.5000 13.5554i −0.695014 0.538355i
\(635\) −25.9808 −1.03102
\(636\) 0 0
\(637\) −16.0000 −0.633943
\(638\) −8.66025 6.70820i −0.342863 0.265580i
\(639\) 0 0
\(640\) −2.50000 25.1744i −0.0988212 0.995105i
\(641\) 44.7214i 1.76639i −0.469008 0.883194i \(-0.655389\pi\)
0.469008 0.883194i \(-0.344611\pi\)
\(642\) 0 0
\(643\) 30.9839i 1.22188i 0.791675 + 0.610942i \(0.209209\pi\)
−0.791675 + 0.610942i \(0.790791\pi\)
\(644\) 51.9615 13.4164i 2.04757 0.528681i
\(645\) 0 0
\(646\) 0 0
\(647\) −20.7846 −0.817127 −0.408564 0.912730i \(-0.633970\pi\)
−0.408564 + 0.912730i \(0.633970\pi\)
\(648\) 0 0
\(649\) 6.00000 0.235521
\(650\) 0 0
\(651\) 0 0
\(652\) −45.0000 + 11.6190i −1.76234 + 0.455033i
\(653\) 11.1803i 0.437521i −0.975779 0.218760i \(-0.929799\pi\)
0.975779 0.218760i \(-0.0702013\pi\)
\(654\) 0 0
\(655\) 42.6028i 1.66463i
\(656\) −17.3205 31.3050i −0.676252 1.22225i
\(657\) 0 0
\(658\) −15.0000 11.6190i −0.584761 0.452954i
\(659\) 8.66025 0.337356 0.168678 0.985671i \(-0.446050\pi\)
0.168678 + 0.985671i \(0.446050\pi\)
\(660\) 0 0
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 8.66025 + 6.70820i 0.336590 + 0.260722i
\(663\) 0 0
\(664\) −31.5000 13.5554i −1.22244 0.526053i
\(665\) 0 0
\(666\) 0 0
\(667\) 30.9839i 1.19970i
\(668\) 1.73205 + 6.70820i 0.0670151 + 0.259548i
\(669\) 0 0
\(670\) 15.0000 19.3649i 0.579501 0.748132i
\(671\) 6.92820 0.267460
\(672\) 0 0
\(673\) 23.0000 0.886585 0.443292 0.896377i \(-0.353810\pi\)
0.443292 + 0.896377i \(0.353810\pi\)
\(674\) 8.66025 11.1803i 0.333581 0.430651i
\(675\) 0 0
\(676\) 4.50000 + 17.4284i 0.173077 + 0.670324i
\(677\) 22.3607i 0.859391i 0.902974 + 0.429695i \(0.141379\pi\)
−0.902974 + 0.429695i \(0.858621\pi\)
\(678\) 0 0
\(679\) 42.6028i 1.63495i
\(680\) 25.9808 + 11.1803i 0.996317 + 0.428746i
\(681\) 0 0
\(682\) −7.50000 5.80948i −0.287190 0.222456i
\(683\) −10.3923 −0.397650 −0.198825 0.980035i \(-0.563713\pi\)
−0.198825 + 0.980035i \(0.563713\pi\)
\(684\) 0 0
\(685\) 10.0000 0.382080
\(686\) 4.33013 + 3.35410i 0.165325 + 0.128060i
\(687\) 0 0
\(688\) 15.0000 + 27.1109i 0.571870 + 1.03359i
\(689\) 4.47214i 0.170375i
\(690\) 0 0
\(691\) 15.4919i 0.589341i 0.955599 + 0.294670i \(0.0952099\pi\)
−0.955599 + 0.294670i \(0.904790\pi\)
\(692\) 30.3109 7.82624i 1.15225 0.297509i
\(693\) 0 0
\(694\) −28.5000 + 36.7933i −1.08185 + 1.39666i
\(695\) 34.6410 1.31401
\(696\) 0 0
\(697\) 40.0000 1.51511
\(698\) 13.8564 17.8885i 0.524473 0.677091i
\(699\) 0 0
\(700\) 0 0
\(701\) 15.6525i 0.591186i 0.955314 + 0.295593i \(0.0955172\pi\)
−0.955314 + 0.295593i \(0.904483\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −9.52628 10.0623i −0.359035 0.379237i
\(705\) 0 0
\(706\) 20.0000 + 15.4919i 0.752710 + 0.583047i
\(707\) −8.66025 −0.325702
\(708\) 0 0
\(709\) 32.0000 1.20179 0.600893 0.799330i \(-0.294812\pi\)
0.600893 + 0.799330i \(0.294812\pi\)
\(710\) −25.9808 20.1246i −0.975041 0.755263i
\(711\) 0 0
\(712\) 5.00000 11.6190i 0.187383 0.435439i
\(713\) 26.8328i 1.00490i
\(714\) 0 0
\(715\) 7.74597i 0.289683i
\(716\) 2.59808 + 10.0623i 0.0970947 + 0.376046i
\(717\) 0 0
\(718\) 27.0000 34.8569i 1.00763 1.30085i
\(719\) 20.7846 0.775135 0.387568 0.921841i \(-0.373315\pi\)
0.387568 + 0.921841i \(0.373315\pi\)
\(720\) 0 0
\(721\) −30.0000 −1.11726
\(722\) −16.4545 + 21.2426i −0.612372 + 0.790569i
\(723\) 0 0
\(724\) 8.00000 + 30.9839i 0.297318 + 1.15151i
\(725\) 0 0
\(726\) 0 0
\(727\) 42.6028i 1.58005i −0.613074 0.790026i \(-0.710067\pi\)
0.613074 0.790026i \(-0.289933\pi\)
\(728\) −8.66025 + 20.1246i −0.320970 + 0.745868i
\(729\) 0 0
\(730\) −12.5000 9.68246i −0.462646 0.358364i
\(731\) −34.6410 −1.28124
\(732\) 0 0
\(733\) 8.00000 0.295487 0.147743 0.989026i \(-0.452799\pi\)
0.147743 + 0.989026i \(0.452799\pi\)
\(734\) −30.3109 23.4787i −1.11880 0.866615i
\(735\) 0 0
\(736\) 6.00000 38.7298i 0.221163 1.42760i
\(737\) 13.4164i 0.494200i
\(738\) 0 0
\(739\) 23.2379i 0.854820i 0.904058 + 0.427410i \(0.140574\pi\)
−0.904058 + 0.427410i \(0.859426\pi\)
\(740\) −17.3205 + 4.47214i −0.636715 + 0.164399i
\(741\) 0 0
\(742\) 7.50000 9.68246i 0.275334 0.355454i
\(743\) −24.2487 −0.889599 −0.444799 0.895630i \(-0.646725\pi\)
−0.444799 + 0.895630i \(0.646725\pi\)
\(744\) 0 0
\(745\) −5.00000 −0.183186
\(746\) 8.66025 11.1803i 0.317074 0.409341i
\(747\) 0 0
\(748\) 15.0000 3.87298i 0.548454 0.141610i
\(749\) 20.1246i 0.735337i
\(750\) 0 0
\(751\) 3.87298i 0.141327i −0.997500 0.0706636i \(-0.977488\pi\)
0.997500 0.0706636i \(-0.0225117\pi\)
\(752\) −12.1244 + 6.70820i −0.442130 + 0.244623i
\(753\) 0 0
\(754\) 10.0000 + 7.74597i 0.364179 + 0.282091i
\(755\) −8.66025 −0.315179
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17.8885i 0.648459i −0.945978 0.324230i \(-0.894895\pi\)
0.945978 0.324230i \(-0.105105\pi\)
\(762\) 0 0
\(763\) 15.4919i 0.560846i
\(764\) 8.66025 + 33.5410i 0.313317 + 1.21347i
\(765\) 0 0
\(766\) 21.0000 27.1109i 0.758761 0.979556i
\(767\) −6.92820 −0.250163
\(768\) 0 0
\(769\) 11.0000 0.396670 0.198335 0.980134i \(-0.436447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(770\) −12.9904 + 16.7705i −0.468141 + 0.604367i
\(771\) 0 0
\(772\) 12.5000 + 48.4123i 0.449885 + 1.74240i
\(773\) 4.47214i 0.160852i −0.996761 0.0804258i \(-0.974372\pi\)
0.996761 0.0804258i \(-0.0256280\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 28.5788 + 12.2984i 1.02592 + 0.441486i
\(777\) 0 0
\(778\) −2.50000 1.93649i −0.0896293 0.0694266i
\(779\) 0 0
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 34.6410 + 26.8328i 1.23876 + 0.959540i
\(783\) 0 0
\(784\) 28.0000 15.4919i 1.00000 0.553283i
\(785\) 44.7214i 1.59617i
\(786\) 0 0
\(787\) 15.4919i 0.552228i −0.961125 0.276114i \(-0.910953\pi\)
0.961125 0.276114i \(-0.0890467\pi\)
\(788\) −47.6314 + 12.2984i −1.69680 + 0.438111i
\(789\) 0 0
\(790\) −15.0000 + 19.3649i −0.533676 + 0.688973i
\(791\) 69.2820 2.46339
\(792\) 0 0
\(793\) −8.00000 −0.284088
\(794\) −12.1244 + 15.6525i −0.430277 + 0.555486i
\(795\) 0 0
\(796\) −22.5000 + 5.80948i −0.797491 + 0.205911i
\(797\) 42.4853i 1.50491i 0.658646 + 0.752453i \(0.271130\pi\)
−0.658646 + 0.752453i \(0.728870\pi\)
\(798\) 0 0
\(799\) 15.4919i 0.548065i
\(800\) 0 0
\(801\) 0 0
\(802\) 20.0000 + 15.4919i