Properties

Label 546.2.c.c.337.1
Level $546$
Weight $2$
Character 546.337
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.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 337.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 546.337
Dual form 546.2.c.c.337.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.00000i q^{11} -1.00000 q^{12} +(3.00000 + 2.00000i) q^{13} +1.00000 q^{14} +1.00000i q^{15} +1.00000 q^{16} +7.00000 q^{17} -1.00000i q^{18} -3.00000i q^{19} -1.00000i q^{20} +1.00000i q^{21} -3.00000 q^{22} +1.00000 q^{23} +1.00000i q^{24} +4.00000 q^{25} +(2.00000 - 3.00000i) q^{26} +1.00000 q^{27} -1.00000i q^{28} -1.00000 q^{29} +1.00000 q^{30} +8.00000i q^{31} -1.00000i q^{32} -3.00000i q^{33} -7.00000i q^{34} -1.00000 q^{35} -1.00000 q^{36} +1.00000i q^{37} -3.00000 q^{38} +(3.00000 + 2.00000i) q^{39} -1.00000 q^{40} -4.00000i q^{41} +1.00000 q^{42} -5.00000 q^{43} +3.00000i q^{44} +1.00000i q^{45} -1.00000i q^{46} +1.00000 q^{48} -1.00000 q^{49} -4.00000i q^{50} +7.00000 q^{51} +(-3.00000 - 2.00000i) q^{52} -6.00000 q^{53} -1.00000i q^{54} +3.00000 q^{55} -1.00000 q^{56} -3.00000i q^{57} +1.00000i q^{58} -10.0000i q^{59} -1.00000i q^{60} -13.0000 q^{61} +8.00000 q^{62} +1.00000i q^{63} -1.00000 q^{64} +(-2.00000 + 3.00000i) q^{65} -3.00000 q^{66} +8.00000i q^{67} -7.00000 q^{68} +1.00000 q^{69} +1.00000i q^{70} -6.00000i q^{71} +1.00000i q^{72} +13.0000i q^{73} +1.00000 q^{74} +4.00000 q^{75} +3.00000i q^{76} +3.00000 q^{77} +(2.00000 - 3.00000i) q^{78} -12.0000 q^{79} +1.00000i q^{80} +1.00000 q^{81} -4.00000 q^{82} -2.00000i q^{83} -1.00000i q^{84} +7.00000i q^{85} +5.00000i q^{86} -1.00000 q^{87} +3.00000 q^{88} -12.0000i q^{89} +1.00000 q^{90} +(-2.00000 + 3.00000i) q^{91} -1.00000 q^{92} +8.00000i q^{93} +3.00000 q^{95} -1.00000i q^{96} -6.00000i q^{97} +1.00000i q^{98} -3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - 2q^{4} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{4} + 2q^{9} + 2q^{10} - 2q^{12} + 6q^{13} + 2q^{14} + 2q^{16} + 14q^{17} - 6q^{22} + 2q^{23} + 8q^{25} + 4q^{26} + 2q^{27} - 2q^{29} + 2q^{30} - 2q^{35} - 2q^{36} - 6q^{38} + 6q^{39} - 2q^{40} + 2q^{42} - 10q^{43} + 2q^{48} - 2q^{49} + 14q^{51} - 6q^{52} - 12q^{53} + 6q^{55} - 2q^{56} - 26q^{61} + 16q^{62} - 2q^{64} - 4q^{65} - 6q^{66} - 14q^{68} + 2q^{69} + 2q^{74} + 8q^{75} + 6q^{77} + 4q^{78} - 24q^{79} + 2q^{81} - 8q^{82} - 2q^{87} + 6q^{88} + 2q^{90} - 4q^{91} - 2q^{92} + 6q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000 0.577350
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i 0.974679 + 0.223607i \(0.0717831\pi\)
−0.974679 + 0.223607i \(0.928217\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 3.00000i 0.904534i −0.891883 0.452267i \(-0.850615\pi\)
0.891883 0.452267i \(-0.149385\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.00000 + 2.00000i 0.832050 + 0.554700i
\(14\) 1.00000 0.267261
\(15\) 1.00000i 0.258199i
\(16\) 1.00000 0.250000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 3.00000i 0.688247i −0.938924 0.344124i \(-0.888176\pi\)
0.938924 0.344124i \(-0.111824\pi\)
\(20\) 1.00000i 0.223607i
\(21\) 1.00000i 0.218218i
\(22\) −3.00000 −0.639602
\(23\) 1.00000 0.208514 0.104257 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 4.00000 0.800000
\(26\) 2.00000 3.00000i 0.392232 0.588348i
\(27\) 1.00000 0.192450
\(28\) 1.00000i 0.188982i
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 1.00000 0.182574
\(31\) 8.00000i 1.43684i 0.695608 + 0.718421i \(0.255135\pi\)
−0.695608 + 0.718421i \(0.744865\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.00000i 0.522233i
\(34\) 7.00000i 1.20049i
\(35\) −1.00000 −0.169031
\(36\) −1.00000 −0.166667
\(37\) 1.00000i 0.164399i 0.996616 + 0.0821995i \(0.0261945\pi\)
−0.996616 + 0.0821995i \(0.973806\pi\)
\(38\) −3.00000 −0.486664
\(39\) 3.00000 + 2.00000i 0.480384 + 0.320256i
\(40\) −1.00000 −0.158114
\(41\) 4.00000i 0.624695i −0.949968 0.312348i \(-0.898885\pi\)
0.949968 0.312348i \(-0.101115\pi\)
\(42\) 1.00000 0.154303
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 3.00000i 0.452267i
\(45\) 1.00000i 0.149071i
\(46\) 1.00000i 0.147442i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.00000 −0.142857
\(50\) 4.00000i 0.565685i
\(51\) 7.00000 0.980196
\(52\) −3.00000 2.00000i −0.416025 0.277350i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 3.00000 0.404520
\(56\) −1.00000 −0.133631
\(57\) 3.00000i 0.397360i
\(58\) 1.00000i 0.131306i
\(59\) 10.0000i 1.30189i −0.759125 0.650945i \(-0.774373\pi\)
0.759125 0.650945i \(-0.225627\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −13.0000 −1.66448 −0.832240 0.554416i \(-0.812942\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 8.00000 1.01600
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) −2.00000 + 3.00000i −0.248069 + 0.372104i
\(66\) −3.00000 −0.369274
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) −7.00000 −0.848875
\(69\) 1.00000 0.120386
\(70\) 1.00000i 0.119523i
\(71\) 6.00000i 0.712069i −0.934473 0.356034i \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 13.0000i 1.52153i 0.649025 + 0.760767i \(0.275177\pi\)
−0.649025 + 0.760767i \(0.724823\pi\)
\(74\) 1.00000 0.116248
\(75\) 4.00000 0.461880
\(76\) 3.00000i 0.344124i
\(77\) 3.00000 0.341882
\(78\) 2.00000 3.00000i 0.226455 0.339683i
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 1.00000 0.111111
\(82\) −4.00000 −0.441726
\(83\) 2.00000i 0.219529i −0.993958 0.109764i \(-0.964990\pi\)
0.993958 0.109764i \(-0.0350096\pi\)
\(84\) 1.00000i 0.109109i
\(85\) 7.00000i 0.759257i
\(86\) 5.00000i 0.539164i
\(87\) −1.00000 −0.107211
\(88\) 3.00000 0.319801
\(89\) 12.0000i 1.27200i −0.771690 0.635999i \(-0.780588\pi\)
0.771690 0.635999i \(-0.219412\pi\)
\(90\) 1.00000 0.105409
\(91\) −2.00000 + 3.00000i −0.209657 + 0.314485i
\(92\) −1.00000 −0.104257
\(93\) 8.00000i 0.829561i
\(94\) 0 0
\(95\) 3.00000 0.307794
\(96\) 1.00000i 0.102062i
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 3.00000i 0.301511i
\(100\) −4.00000 −0.400000
\(101\) 14.0000 1.39305 0.696526 0.717532i \(-0.254728\pi\)
0.696526 + 0.717532i \(0.254728\pi\)
\(102\) 7.00000i 0.693103i
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) −2.00000 + 3.00000i −0.196116 + 0.294174i
\(105\) −1.00000 −0.0975900
\(106\) 6.00000i 0.582772i
\(107\) 2.00000 0.193347 0.0966736 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 7.00000i 0.670478i −0.942133 0.335239i \(-0.891183\pi\)
0.942133 0.335239i \(-0.108817\pi\)
\(110\) 3.00000i 0.286039i
\(111\) 1.00000i 0.0949158i
\(112\) 1.00000i 0.0944911i
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) −3.00000 −0.280976
\(115\) 1.00000i 0.0932505i
\(116\) 1.00000 0.0928477
\(117\) 3.00000 + 2.00000i 0.277350 + 0.184900i
\(118\) −10.0000 −0.920575
\(119\) 7.00000i 0.641689i
\(120\) −1.00000 −0.0912871
\(121\) 2.00000 0.181818
\(122\) 13.0000i 1.17696i
\(123\) 4.00000i 0.360668i
\(124\) 8.00000i 0.718421i
\(125\) 9.00000i 0.804984i
\(126\) 1.00000 0.0890871
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −5.00000 −0.440225
\(130\) 3.00000 + 2.00000i 0.263117 + 0.175412i
\(131\) −17.0000 −1.48530 −0.742648 0.669681i \(-0.766431\pi\)
−0.742648 + 0.669681i \(0.766431\pi\)
\(132\) 3.00000i 0.261116i
\(133\) 3.00000 0.260133
\(134\) 8.00000 0.691095
\(135\) 1.00000i 0.0860663i
\(136\) 7.00000i 0.600245i
\(137\) 17.0000i 1.45241i 0.687479 + 0.726204i \(0.258717\pi\)
−0.687479 + 0.726204i \(0.741283\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 1.00000 0.0845154
\(141\) 0 0
\(142\) −6.00000 −0.503509
\(143\) 6.00000 9.00000i 0.501745 0.752618i
\(144\) 1.00000 0.0833333
\(145\) 1.00000i 0.0830455i
\(146\) 13.0000 1.07589
\(147\) −1.00000 −0.0824786
\(148\) 1.00000i 0.0821995i
\(149\) 22.0000i 1.80231i 0.433497 + 0.901155i \(0.357280\pi\)
−0.433497 + 0.901155i \(0.642720\pi\)
\(150\) 4.00000i 0.326599i
\(151\) 11.0000i 0.895167i 0.894242 + 0.447584i \(0.147715\pi\)
−0.894242 + 0.447584i \(0.852285\pi\)
\(152\) 3.00000 0.243332
\(153\) 7.00000 0.565916
\(154\) 3.00000i 0.241747i
\(155\) −8.00000 −0.642575
\(156\) −3.00000 2.00000i −0.240192 0.160128i
\(157\) 19.0000 1.51637 0.758183 0.652042i \(-0.226088\pi\)
0.758183 + 0.652042i \(0.226088\pi\)
\(158\) 12.0000i 0.954669i
\(159\) −6.00000 −0.475831
\(160\) 1.00000 0.0790569
\(161\) 1.00000i 0.0788110i
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 3.00000 0.233550
\(166\) −2.00000 −0.155230
\(167\) 15.0000i 1.16073i −0.814355 0.580367i \(-0.802909\pi\)
0.814355 0.580367i \(-0.197091\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 5.00000 + 12.0000i 0.384615 + 0.923077i
\(170\) 7.00000 0.536875
\(171\) 3.00000i 0.229416i
\(172\) 5.00000 0.381246
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 1.00000i 0.0758098i
\(175\) 4.00000i 0.302372i
\(176\) 3.00000i 0.226134i
\(177\) 10.0000i 0.751646i
\(178\) −12.0000 −0.899438
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 1.00000i 0.0745356i
\(181\) −26.0000 −1.93256 −0.966282 0.257485i \(-0.917106\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 3.00000 + 2.00000i 0.222375 + 0.148250i
\(183\) −13.0000 −0.960988
\(184\) 1.00000i 0.0737210i
\(185\) −1.00000 −0.0735215
\(186\) 8.00000 0.586588
\(187\) 21.0000i 1.53567i
\(188\) 0 0
\(189\) 1.00000i 0.0727393i
\(190\) 3.00000i 0.217643i
\(191\) −9.00000 −0.651217 −0.325609 0.945505i \(-0.605569\pi\)
−0.325609 + 0.945505i \(0.605569\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 8.00000i 0.575853i 0.957653 + 0.287926i \(0.0929658\pi\)
−0.957653 + 0.287926i \(0.907034\pi\)
\(194\) −6.00000 −0.430775
\(195\) −2.00000 + 3.00000i −0.143223 + 0.214834i
\(196\) 1.00000 0.0714286
\(197\) 14.0000i 0.997459i −0.866758 0.498729i \(-0.833800\pi\)
0.866758 0.498729i \(-0.166200\pi\)
\(198\) −3.00000 −0.213201
\(199\) 9.00000 0.637993 0.318997 0.947756i \(-0.396654\pi\)
0.318997 + 0.947756i \(0.396654\pi\)
\(200\) 4.00000i 0.282843i
\(201\) 8.00000i 0.564276i
\(202\) 14.0000i 0.985037i
\(203\) 1.00000i 0.0701862i
\(204\) −7.00000 −0.490098
\(205\) 4.00000 0.279372
\(206\) 1.00000i 0.0696733i
\(207\) 1.00000 0.0695048
\(208\) 3.00000 + 2.00000i 0.208013 + 0.138675i
\(209\) −9.00000 −0.622543
\(210\) 1.00000i 0.0690066i
\(211\) 15.0000 1.03264 0.516321 0.856395i \(-0.327301\pi\)
0.516321 + 0.856395i \(0.327301\pi\)
\(212\) 6.00000 0.412082
\(213\) 6.00000i 0.411113i
\(214\) 2.00000i 0.136717i
\(215\) 5.00000i 0.340997i
\(216\) 1.00000i 0.0680414i
\(217\) −8.00000 −0.543075
\(218\) −7.00000 −0.474100
\(219\) 13.0000i 0.878459i
\(220\) −3.00000 −0.202260
\(221\) 21.0000 + 14.0000i 1.41261 + 0.941742i
\(222\) 1.00000 0.0671156
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) 1.00000 0.0668153
\(225\) 4.00000 0.266667
\(226\) 10.0000i 0.665190i
\(227\) 20.0000i 1.32745i −0.747978 0.663723i \(-0.768975\pi\)
0.747978 0.663723i \(-0.231025\pi\)
\(228\) 3.00000i 0.198680i
\(229\) 10.0000i 0.660819i −0.943838 0.330409i \(-0.892813\pi\)
0.943838 0.330409i \(-0.107187\pi\)
\(230\) 1.00000 0.0659380
\(231\) 3.00000 0.197386
\(232\) 1.00000i 0.0656532i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 2.00000 3.00000i 0.130744 0.196116i
\(235\) 0 0
\(236\) 10.0000i 0.650945i
\(237\) −12.0000 −0.779484
\(238\) 7.00000 0.453743
\(239\) 8.00000i 0.517477i −0.965947 0.258738i \(-0.916693\pi\)
0.965947 0.258738i \(-0.0833068\pi\)
\(240\) 1.00000i 0.0645497i
\(241\) 26.0000i 1.67481i −0.546585 0.837404i \(-0.684072\pi\)
0.546585 0.837404i \(-0.315928\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 1.00000 0.0641500
\(244\) 13.0000 0.832240
\(245\) 1.00000i 0.0638877i
\(246\) −4.00000 −0.255031
\(247\) 6.00000 9.00000i 0.381771 0.572656i
\(248\) −8.00000 −0.508001
\(249\) 2.00000i 0.126745i
\(250\) 9.00000 0.569210
\(251\) 17.0000 1.07303 0.536515 0.843891i \(-0.319740\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 3.00000i 0.188608i
\(254\) 4.00000i 0.250982i
\(255\) 7.00000i 0.438357i
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 5.00000i 0.311286i
\(259\) −1.00000 −0.0621370
\(260\) 2.00000 3.00000i 0.124035 0.186052i
\(261\) −1.00000 −0.0618984
\(262\) 17.0000i 1.05026i
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 3.00000 0.184637
\(265\) 6.00000i 0.368577i
\(266\) 3.00000i 0.183942i
\(267\) 12.0000i 0.734388i
\(268\) 8.00000i 0.488678i
\(269\) −4.00000 −0.243884 −0.121942 0.992537i \(-0.538912\pi\)
−0.121942 + 0.992537i \(0.538912\pi\)
\(270\) 1.00000 0.0608581
\(271\) 20.0000i 1.21491i −0.794353 0.607457i \(-0.792190\pi\)
0.794353 0.607457i \(-0.207810\pi\)
\(272\) 7.00000 0.424437
\(273\) −2.00000 + 3.00000i −0.121046 + 0.181568i
\(274\) 17.0000 1.02701
\(275\) 12.0000i 0.723627i
\(276\) −1.00000 −0.0601929
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 8.00000i 0.479808i
\(279\) 8.00000i 0.478947i
\(280\) 1.00000i 0.0597614i
\(281\) 10.0000i 0.596550i 0.954480 + 0.298275i \(0.0964112\pi\)
−0.954480 + 0.298275i \(0.903589\pi\)
\(282\) 0 0
\(283\) −14.0000 −0.832214 −0.416107 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) 6.00000i 0.356034i
\(285\) 3.00000 0.177705
\(286\) −9.00000 6.00000i −0.532181 0.354787i
\(287\) 4.00000 0.236113
\(288\) 1.00000i 0.0589256i
\(289\) 32.0000 1.88235
\(290\) −1.00000 −0.0587220
\(291\) 6.00000i 0.351726i
\(292\) 13.0000i 0.760767i
\(293\) 14.0000i 0.817889i 0.912559 + 0.408944i \(0.134103\pi\)
−0.912559 + 0.408944i \(0.865897\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 10.0000 0.582223
\(296\) −1.00000 −0.0581238
\(297\) 3.00000i 0.174078i
\(298\) 22.0000 1.27443
\(299\) 3.00000 + 2.00000i 0.173494 + 0.115663i
\(300\) −4.00000 −0.230940
\(301\) 5.00000i 0.288195i
\(302\) 11.0000 0.632979
\(303\) 14.0000 0.804279
\(304\) 3.00000i 0.172062i
\(305\) 13.0000i 0.744378i
\(306\) 7.00000i 0.400163i
\(307\) 16.0000i 0.913168i −0.889680 0.456584i \(-0.849073\pi\)
0.889680 0.456584i \(-0.150927\pi\)
\(308\) −3.00000 −0.170941
\(309\) −1.00000 −0.0568880
\(310\) 8.00000i 0.454369i
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) −2.00000 + 3.00000i −0.113228 + 0.169842i
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 19.0000i 1.07223i
\(315\) −1.00000 −0.0563436
\(316\) 12.0000 0.675053
\(317\) 24.0000i 1.34797i −0.738743 0.673987i \(-0.764580\pi\)
0.738743 0.673987i \(-0.235420\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 3.00000i 0.167968i
\(320\) 1.00000i 0.0559017i
\(321\) 2.00000 0.111629
\(322\) 1.00000 0.0557278
\(323\) 21.0000i 1.16847i
\(324\) −1.00000 −0.0555556
\(325\) 12.0000 + 8.00000i 0.665640 + 0.443760i
\(326\) −4.00000 −0.221540
\(327\) 7.00000i 0.387101i
\(328\) 4.00000 0.220863
\(329\) 0 0
\(330\) 3.00000i 0.165145i
\(331\) 8.00000i 0.439720i −0.975531 0.219860i \(-0.929440\pi\)
0.975531 0.219860i \(-0.0705600\pi\)
\(332\) 2.00000i 0.109764i
\(333\) 1.00000i 0.0547997i
\(334\) −15.0000 −0.820763
\(335\) −8.00000 −0.437087
\(336\) 1.00000i 0.0545545i
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) 12.0000 5.00000i 0.652714 0.271964i
\(339\) −10.0000 −0.543125
\(340\) 7.00000i 0.379628i
\(341\) 24.0000 1.29967
\(342\) −3.00000 −0.162221
\(343\) 1.00000i 0.0539949i
\(344\) 5.00000i 0.269582i
\(345\) 1.00000i 0.0538382i
\(346\) 6.00000i 0.322562i
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) 1.00000 0.0536056
\(349\) 16.0000i 0.856460i 0.903670 + 0.428230i \(0.140863\pi\)
−0.903670 + 0.428230i \(0.859137\pi\)
\(350\) 4.00000 0.213809
\(351\) 3.00000 + 2.00000i 0.160128 + 0.106752i
\(352\) −3.00000 −0.159901
\(353\) 16.0000i 0.851594i 0.904819 + 0.425797i \(0.140006\pi\)
−0.904819 + 0.425797i \(0.859994\pi\)
\(354\) −10.0000 −0.531494
\(355\) 6.00000 0.318447
\(356\) 12.0000i 0.635999i
\(357\) 7.00000i 0.370479i
\(358\) 6.00000i 0.317110i
\(359\) 26.0000i 1.37223i 0.727494 + 0.686114i \(0.240685\pi\)
−0.727494 + 0.686114i \(0.759315\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 10.0000 0.526316
\(362\) 26.0000i 1.36653i
\(363\) 2.00000 0.104973
\(364\) 2.00000 3.00000i 0.104828 0.157243i
\(365\) −13.0000 −0.680451
\(366\) 13.0000i 0.679521i
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 1.00000 0.0521286
\(369\) 4.00000i 0.208232i
\(370\) 1.00000i 0.0519875i
\(371\) 6.00000i 0.311504i
\(372\) 8.00000i 0.414781i
\(373\) 6.00000 0.310668 0.155334 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) −21.0000 −1.08588
\(375\) 9.00000i 0.464758i
\(376\) 0 0
\(377\) −3.00000 2.00000i −0.154508 0.103005i
\(378\) 1.00000 0.0514344
\(379\) 4.00000i 0.205466i −0.994709 0.102733i \(-0.967241\pi\)
0.994709 0.102733i \(-0.0327588\pi\)
\(380\) −3.00000 −0.153897
\(381\) −4.00000 −0.204926
\(382\) 9.00000i 0.460480i
\(383\) 17.0000i 0.868659i −0.900754 0.434330i \(-0.856985\pi\)
0.900754 0.434330i \(-0.143015\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 3.00000i 0.152894i
\(386\) 8.00000 0.407189
\(387\) −5.00000 −0.254164
\(388\) 6.00000i 0.304604i
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 3.00000 + 2.00000i 0.151911 + 0.101274i
\(391\) 7.00000 0.354005
\(392\) 1.00000i 0.0505076i
\(393\) −17.0000 −0.857537
\(394\) −14.0000 −0.705310
\(395\) 12.0000i 0.603786i
\(396\) 3.00000i 0.150756i
\(397\) 8.00000i 0.401508i −0.979642 0.200754i \(-0.935661\pi\)
0.979642 0.200754i \(-0.0643393\pi\)
\(398\) 9.00000i 0.451129i
\(399\) 3.00000 0.150188
\(400\) 4.00000 0.200000
\(401\) 6.00000i 0.299626i 0.988714 + 0.149813i \(0.0478671\pi\)
−0.988714 + 0.149813i \(0.952133\pi\)
\(402\) 8.00000 0.399004
\(403\) −16.0000 + 24.0000i −0.797017 + 1.19553i
\(404\) −14.0000 −0.696526
\(405\) 1.00000i 0.0496904i
\(406\) −1.00000 −0.0496292
\(407\) 3.00000 0.148704
\(408\) 7.00000i 0.346552i
\(409\) 29.0000i 1.43396i 0.697095 + 0.716979i \(0.254476\pi\)
−0.697095 + 0.716979i \(0.745524\pi\)
\(410\) 4.00000i 0.197546i
\(411\) 17.0000i 0.838548i
\(412\) 1.00000 0.0492665
\(413\) 10.0000 0.492068
\(414\) 1.00000i 0.0491473i
\(415\) 2.00000 0.0981761
\(416\) 2.00000 3.00000i 0.0980581 0.147087i
\(417\) −8.00000 −0.391762
\(418\) 9.00000i 0.440204i
\(419\) −11.0000 −0.537385 −0.268693 0.963226i \(-0.586592\pi\)
−0.268693 + 0.963226i \(0.586592\pi\)
\(420\) 1.00000 0.0487950
\(421\) 34.0000i 1.65706i 0.559946 + 0.828529i \(0.310822\pi\)
−0.559946 + 0.828529i \(0.689178\pi\)
\(422\) 15.0000i 0.730189i
\(423\) 0 0
\(424\) 6.00000i 0.291386i
\(425\) 28.0000 1.35820
\(426\) −6.00000 −0.290701
\(427\) 13.0000i 0.629114i
\(428\) −2.00000 −0.0966736
\(429\) 6.00000 9.00000i 0.289683 0.434524i
\(430\) −5.00000 −0.241121
\(431\) 14.0000i 0.674356i 0.941441 + 0.337178i \(0.109472\pi\)
−0.941441 + 0.337178i \(0.890528\pi\)
\(432\) 1.00000 0.0481125
\(433\) −8.00000 −0.384455 −0.192228 0.981350i \(-0.561571\pi\)
−0.192228 + 0.981350i \(0.561571\pi\)
\(434\) 8.00000i 0.384012i
\(435\) 1.00000i 0.0479463i
\(436\) 7.00000i 0.335239i
\(437\) 3.00000i 0.143509i
\(438\) 13.0000 0.621164
\(439\) 27.0000 1.28864 0.644320 0.764756i \(-0.277141\pi\)
0.644320 + 0.764756i \(0.277141\pi\)
\(440\) 3.00000i 0.143019i
\(441\) −1.00000 −0.0476190
\(442\) 14.0000 21.0000i 0.665912 0.998868i
\(443\) −34.0000 −1.61539 −0.807694 0.589601i \(-0.799285\pi\)
−0.807694 + 0.589601i \(0.799285\pi\)
\(444\) 1.00000i 0.0474579i
\(445\) 12.0000 0.568855
\(446\) −4.00000 −0.189405
\(447\) 22.0000i 1.04056i
\(448\) 1.00000i 0.0472456i
\(449\) 9.00000i 0.424736i 0.977190 + 0.212368i \(0.0681176\pi\)
−0.977190 + 0.212368i \(0.931882\pi\)
\(450\) 4.00000i 0.188562i
\(451\) −12.0000 −0.565058
\(452\) 10.0000 0.470360
\(453\) 11.0000i 0.516825i
\(454\) −20.0000 −0.938647
\(455\) −3.00000 2.00000i −0.140642 0.0937614i
\(456\) 3.00000 0.140488
\(457\) 28.0000i 1.30978i −0.755722 0.654892i \(-0.772714\pi\)
0.755722 0.654892i \(-0.227286\pi\)
\(458\) −10.0000 −0.467269
\(459\) 7.00000 0.326732
\(460\) 1.00000i 0.0466252i
\(461\) 27.0000i 1.25752i 0.777601 + 0.628758i \(0.216436\pi\)
−0.777601 + 0.628758i \(0.783564\pi\)
\(462\) 3.00000i 0.139573i
\(463\) 15.0000i 0.697109i 0.937288 + 0.348555i \(0.113327\pi\)
−0.937288 + 0.348555i \(0.886673\pi\)
\(464\) −1.00000 −0.0464238
\(465\) −8.00000 −0.370991
\(466\) 18.0000i 0.833834i
\(467\) 9.00000 0.416470 0.208235 0.978079i \(-0.433228\pi\)
0.208235 + 0.978079i \(0.433228\pi\)
\(468\) −3.00000 2.00000i −0.138675 0.0924500i
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 19.0000 0.875474
\(472\) 10.0000 0.460287
\(473\) 15.0000i 0.689701i
\(474\) 12.0000i 0.551178i
\(475\) 12.0000i 0.550598i
\(476\) 7.00000i 0.320844i
\(477\) −6.00000 −0.274721
\(478\) −8.00000 −0.365911
\(479\) 3.00000i 0.137073i 0.997649 + 0.0685367i \(0.0218330\pi\)
−0.997649 + 0.0685367i \(0.978167\pi\)
\(480\) 1.00000 0.0456435
\(481\) −2.00000 + 3.00000i −0.0911922 + 0.136788i
\(482\) −26.0000 −1.18427
\(483\) 1.00000i 0.0455016i
\(484\) −2.00000 −0.0909091
\(485\) 6.00000 0.272446
\(486\) 1.00000i 0.0453609i
\(487\) 24.0000i 1.08754i 0.839233 + 0.543772i \(0.183004\pi\)
−0.839233 + 0.543772i \(0.816996\pi\)
\(488\) 13.0000i 0.588482i
\(489\) 4.00000i 0.180886i
\(490\) −1.00000 −0.0451754
\(491\) −40.0000 −1.80517 −0.902587 0.430507i \(-0.858335\pi\)
−0.902587 + 0.430507i \(0.858335\pi\)
\(492\) 4.00000i 0.180334i
\(493\) −7.00000 −0.315264
\(494\) −9.00000 6.00000i −0.404929 0.269953i
\(495\) 3.00000 0.134840
\(496\) 8.00000i 0.359211i
\(497\) 6.00000 0.269137
\(498\) −2.00000 −0.0896221
\(499\) 14.0000i 0.626726i −0.949633 0.313363i \(-0.898544\pi\)
0.949633 0.313363i \(-0.101456\pi\)
\(500\) 9.00000i 0.402492i
\(501\) 15.0000i 0.670151i
\(502\) 17.0000i 0.758747i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 14.0000i 0.622992i
\(506\) −3.00000 −0.133366
\(507\) 5.00000 + 12.0000i 0.222058 + 0.532939i
\(508\) 4.00000 0.177471
\(509\) 27.0000i 1.19675i 0.801215 + 0.598377i \(0.204187\pi\)
−0.801215 + 0.598377i \(0.795813\pi\)
\(510\) 7.00000 0.309965
\(511\) −13.0000 −0.575086
\(512\) 1.00000i 0.0441942i
\(513\) 3.00000i 0.132453i
\(514\) 6.00000i 0.264649i
\(515\) 1.00000i 0.0440653i
\(516\) 5.00000 0.220113
\(517\) 0 0
\(518\) 1.00000i 0.0439375i
\(519\) −6.00000 −0.263371
\(520\) −3.00000 2.00000i −0.131559 0.0877058i
\(521\) 15.0000 0.657162 0.328581 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) 1.00000i 0.0437688i
\(523\) 16.0000 0.699631 0.349816 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) 17.0000 0.742648
\(525\) 4.00000i 0.174574i
\(526\) 24.0000i 1.04645i
\(527\) 56.0000i 2.43940i
\(528\) 3.00000i 0.130558i
\(529\) −22.0000 −0.956522
\(530\) −6.00000 −0.260623
\(531\) 10.0000i 0.433963i
\(532\) −3.00000 −0.130066
\(533\) 8.00000 12.0000i 0.346518 0.519778i
\(534\) −12.0000 −0.519291
\(535\) 2.00000i 0.0864675i
\(536\) −8.00000 −0.345547
\(537\) −6.00000 −0.258919
\(538\) 4.00000i 0.172452i
\(539\) 3.00000i 0.129219i
\(540\) 1.00000i 0.0430331i
\(541\) 25.0000i 1.07483i −0.843317 0.537417i \(-0.819400\pi\)
0.843317 0.537417i \(-0.180600\pi\)
\(542\) −20.0000 −0.859074
\(543\) −26.0000 −1.11577
\(544\) 7.00000i 0.300123i
\(545\) 7.00000 0.299847
\(546\) 3.00000 + 2.00000i 0.128388 + 0.0855921i
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 17.0000i 0.726204i
\(549\) −13.0000 −0.554826
\(550\) −12.0000 −0.511682
\(551\) 3.00000i 0.127804i
\(552\) 1.00000i 0.0425628i
\(553\) 12.0000i 0.510292i
\(554\) 28.0000i 1.18961i
\(555\) −1.00000 −0.0424476
\(556\) 8.00000 0.339276
\(557\) 30.0000i 1.27114i −0.772043 0.635570i \(-0.780765\pi\)
0.772043 0.635570i \(-0.219235\pi\)
\(558\) 8.00000 0.338667
\(559\) −15.0000 10.0000i −0.634432 0.422955i
\(560\) −1.00000 −0.0422577
\(561\) 21.0000i 0.886621i
\(562\) 10.0000 0.421825
\(563\) 41.0000 1.72794 0.863972 0.503540i \(-0.167969\pi\)
0.863972 + 0.503540i \(0.167969\pi\)
\(564\) 0 0
\(565\) 10.0000i 0.420703i
\(566\) 14.0000i 0.588464i
\(567\) 1.00000i 0.0419961i
\(568\) 6.00000 0.251754
\(569\) −2.00000 −0.0838444 −0.0419222 0.999121i \(-0.513348\pi\)
−0.0419222 + 0.999121i \(0.513348\pi\)
\(570\) 3.00000i 0.125656i
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) −6.00000 + 9.00000i −0.250873 + 0.376309i
\(573\) −9.00000 −0.375980
\(574\) 4.00000i 0.166957i
\(575\) 4.00000 0.166812
\(576\) −1.00000 −0.0416667
\(577\) 38.0000i 1.58196i −0.611842 0.790980i \(-0.709571\pi\)
0.611842 0.790980i \(-0.290429\pi\)
\(578\) 32.0000i 1.33102i
\(579\) 8.00000i 0.332469i
\(580\) 1.00000i 0.0415227i
\(581\) 2.00000 0.0829740
\(582\) −6.00000 −0.248708
\(583\) 18.0000i 0.745484i
\(584\) −13.0000 −0.537944
\(585\) −2.00000 + 3.00000i −0.0826898 + 0.124035i
\(586\) 14.0000 0.578335
\(587\) 16.0000i 0.660391i −0.943913 0.330195i \(-0.892885\pi\)
0.943913 0.330195i \(-0.107115\pi\)
\(588\) 1.00000 0.0412393
\(589\) 24.0000 0.988903
\(590\) 10.0000i 0.411693i
\(591\) 14.0000i 0.575883i
\(592\) 1.00000i 0.0410997i
\(593\) 16.0000i 0.657041i 0.944497 + 0.328521i \(0.106550\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(594\) −3.00000 −0.123091
\(595\) −7.00000 −0.286972
\(596\) 22.0000i 0.901155i
\(597\) 9.00000 0.368345
\(598\) 2.00000 3.00000i 0.0817861 0.122679i
\(599\) −3.00000 −0.122577 −0.0612883 0.998120i \(-0.519521\pi\)
−0.0612883 + 0.998120i \(0.519521\pi\)
\(600\) 4.00000i 0.163299i
\(601\) 4.00000 0.163163 0.0815817 0.996667i \(-0.474003\pi\)
0.0815817 + 0.996667i \(0.474003\pi\)
\(602\) −5.00000 −0.203785
\(603\) 8.00000i 0.325785i
\(604\) 11.0000i 0.447584i
\(605\) 2.00000i 0.0813116i
\(606\) 14.0000i 0.568711i
\(607\) −11.0000 −0.446476 −0.223238 0.974764i \(-0.571663\pi\)
−0.223238 + 0.974764i \(0.571663\pi\)
\(608\) −3.00000 −0.121666
\(609\) 1.00000i 0.0405220i
\(610\) −13.0000 −0.526355
\(611\) 0 0
\(612\) −7.00000 −0.282958
\(613\) 31.0000i 1.25208i −0.779792 0.626039i \(-0.784675\pi\)
0.779792 0.626039i \(-0.215325\pi\)
\(614\) −16.0000 −0.645707
\(615\) 4.00000 0.161296
\(616\) 3.00000i 0.120873i
\(617\) 37.0000i 1.48956i 0.667308 + 0.744782i \(0.267447\pi\)
−0.667308 + 0.744782i \(0.732553\pi\)
\(618\) 1.00000i 0.0402259i
\(619\) 23.0000i 0.924448i 0.886763 + 0.462224i \(0.152948\pi\)
−0.886763 + 0.462224i \(0.847052\pi\)
\(620\) 8.00000 0.321288
\(621\) 1.00000 0.0401286
\(622\) 4.00000i 0.160385i
\(623\) 12.0000 0.480770
\(624\) 3.00000 + 2.00000i 0.120096 + 0.0800641i
\(625\) 11.0000 0.440000
\(626\) 26.0000i 1.03917i
\(627\) −9.00000 −0.359425
\(628\) −19.0000 −0.758183
\(629\) 7.00000i 0.279108i
\(630\) 1.00000i 0.0398410i
\(631\) 47.0000i 1.87104i 0.353273 + 0.935520i \(0.385069\pi\)
−0.353273 + 0.935520i \(0.614931\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 15.0000 0.596196
\(634\) −24.0000 −0.953162
\(635\) 4.00000i 0.158735i
\(636\) 6.00000 0.237915
\(637\) −3.00000 2.00000i −0.118864 0.0792429i
\(638\) 3.00000 0.118771
\(639\) 6.00000i 0.237356i
\(640\) −1.00000 −0.0395285
\(641\) 12.0000 0.473972 0.236986 0.971513i \(-0.423841\pi\)
0.236986 + 0.971513i \(0.423841\pi\)
\(642\) 2.00000i 0.0789337i
\(643\) 39.0000i 1.53801i 0.639243 + 0.769005i \(0.279248\pi\)
−0.639243 + 0.769005i \(0.720752\pi\)
\(644\) 1.00000i 0.0394055i
\(645\) 5.00000i 0.196875i
\(646\) −21.0000 −0.826234
\(647\) 22.0000 0.864909 0.432455 0.901656i \(-0.357648\pi\)
0.432455 + 0.901656i \(0.357648\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −30.0000 −1.17760
\(650\) 8.00000 12.0000i 0.313786 0.470679i
\(651\) −8.00000 −0.313545
\(652\) 4.00000i 0.156652i
\(653\) −35.0000 −1.36966 −0.684828 0.728705i \(-0.740123\pi\)
−0.684828 + 0.728705i \(0.740123\pi\)
\(654\) −7.00000 −0.273722
\(655\) 17.0000i 0.664245i
\(656\) 4.00000i 0.156174i
\(657\) 13.0000i 0.507178i
\(658\) 0 0
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) −3.00000 −0.116775
\(661\) 10.0000i 0.388955i 0.980907 + 0.194477i \(0.0623011\pi\)
−0.980907 + 0.194477i \(0.937699\pi\)
\(662\) −8.00000 −0.310929
\(663\) 21.0000 + 14.0000i 0.815572 + 0.543715i
\(664\) 2.00000 0.0776151
\(665\) 3.00000i 0.116335i
\(666\) 1.00000 0.0387492
\(667\) −1.00000 −0.0387202
\(668\) 15.0000i 0.580367i
\(669\) 4.00000i 0.154649i
\(670\) 8.00000i 0.309067i
\(671\) 39.0000i 1.50558i
\(672\) 1.00000 0.0385758
\(673\) −3.00000 −0.115642 −0.0578208 0.998327i \(-0.518415\pi\)
−0.0578208 + 0.998327i \(0.518415\pi\)
\(674\) 23.0000i 0.885927i
\(675\) 4.00000 0.153960
\(676\) −5.00000 12.0000i −0.192308 0.461538i
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 10.0000i 0.384048i
\(679\) 6.00000 0.230259
\(680\) −7.00000 −0.268438
\(681\) 20.0000i 0.766402i
\(682\) 24.0000i 0.919007i
\(683\) 9.00000i 0.344375i −0.985064 0.172188i \(-0.944916\pi\)
0.985064 0.172188i \(-0.0550836\pi\)
\(684\) 3.00000i 0.114708i
\(685\) −17.0000 −0.649537
\(686\) −1.00000 −0.0381802
\(687\) 10.0000i 0.381524i
\(688\) −5.00000 −0.190623
\(689\) −18.0000 12.0000i −0.685745 0.457164i
\(690\) 1.00000 0.0380693
\(691\) 16.0000i 0.608669i 0.952565 + 0.304334i \(0.0984340\pi\)
−0.952565 + 0.304334i \(0.901566\pi\)
\(692\) 6.00000 0.228086
\(693\) 3.00000 0.113961
\(694\) 24.0000i 0.911028i
\(695\) 8.00000i 0.303457i
\(696\) 1.00000i 0.0379049i
\(697\) 28.0000i 1.06058i
\(698\) 16.0000 0.605609
\(699\) 18.0000 0.680823
\(700\) 4.00000i 0.151186i
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 2.00000 3.00000i 0.0754851 0.113228i
\(703\) 3.00000 0.113147
\(704\) 3.00000i 0.113067i
\(705\) 0 0
\(706\) 16.0000 0.602168
\(707\) 14.0000i 0.526524i
\(708\) 10.0000i 0.375823i
\(709\) 30.0000i 1.12667i 0.826227 + 0.563337i \(0.190483\pi\)
−0.826227 + 0.563337i \(0.809517\pi\)
\(710\) 6.00000i 0.225176i
\(711\) −12.0000 −0.450035
\(712\) 12.0000 0.449719
\(713\) 8.00000i 0.299602i
\(714\) 7.00000 0.261968
\(715\) 9.00000 + 6.00000i 0.336581 + 0.224387i
\(716\) 6.00000 0.224231
\(717\) 8.00000i 0.298765i
\(718\) 26.0000 0.970311
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 1.00000i 0.0372419i
\(722\) 10.0000i 0.372161i
\(723\) 26.0000i 0.966950i
\(724\) 26.0000 0.966282
\(725\) −4.00000 −0.148556
\(726\) 2.00000i 0.0742270i
\(727\) 35.0000 1.29808 0.649039 0.760755i \(-0.275171\pi\)
0.649039 + 0.760755i \(0.275171\pi\)
\(728\) −3.00000 2.00000i −0.111187 0.0741249i
\(729\) 1.00000 0.0370370
\(730\) 13.0000i 0.481152i
\(731\) −35.0000 −1.29452
\(732\) 13.0000 0.480494
\(733\) 8.00000i 0.295487i 0.989026 + 0.147743i \(0.0472010\pi\)
−0.989026 + 0.147743i \(0.952799\pi\)
\(734\) 32.0000i 1.18114i
\(735\) 1.00000i 0.0368856i
\(736\) 1.00000i 0.0368605i
\(737\) 24.0000 0.884051
\(738\) −4.00000 −0.147242
\(739\) 16.0000i 0.588570i −0.955718 0.294285i \(-0.904919\pi\)
0.955718 0.294285i \(-0.0950814\pi\)
\(740\) 1.00000 0.0367607
\(741\) 6.00000 9.00000i 0.220416 0.330623i
\(742\) −6.00000 −0.220267
\(743\) 40.0000i 1.46746i −0.679442 0.733729i \(-0.737778\pi\)
0.679442 0.733729i \(-0.262222\pi\)
\(744\) −8.00000 −0.293294
\(745\) −22.0000 −0.806018
\(746\) 6.00000i 0.219676i
\(747\) 2.00000i 0.0731762i
\(748\) 21.0000i 0.767836i
\(749\) 2.00000i 0.0730784i
\(750\) 9.00000 0.328634
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 0 0
\(753\) 17.0000 0.619514
\(754\) −2.00000 + 3.00000i −0.0728357 + 0.109254i
\(755\) −11.0000 −0.400331
\(756\) 1.00000i 0.0363696i
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −4.00000 −0.145287
\(759\) 3.00000i 0.108893i
\(760\) 3.00000i 0.108821i
\(761\) 30.0000i 1.08750i 0.839248 + 0.543750i \(0.182996\pi\)
−0.839248 + 0.543750i \(0.817004\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 7.00000 0.253417
\(764\) 9.00000 0.325609
\(765\) 7.00000i 0.253086i
\(766\) −17.0000 −0.614235
\(767\) 20.0000 30.0000i 0.722158 1.08324i
\(768\) 1.00000 0.0360844
\(769\) 39.0000i 1.40638i −0.711004 0.703188i \(-0.751759\pi\)
0.711004 0.703188i \(-0.248241\pi\)
\(770\) 3.00000 0.108112
\(771\) −6.00000 −0.216085
\(772\) 8.00000i 0.287926i
\(773\) 21.0000i 0.755318i −0.925945 0.377659i \(-0.876729\pi\)
0.925945 0.377659i \(-0.123271\pi\)
\(774\) 5.00000i 0.179721i
\(775\) 32.0000i 1.14947i
\(776\) 6.00000 0.215387
\(777\) −1.00000 −0.0358748
\(778\) 18.0000i 0.645331i
\(779\) −12.0000 −0.429945
\(780\) 2.00000 3.00000i 0.0716115 0.107417i
\(781\) −18.0000 −0.644091
\(782\) 7.00000i 0.250319i
\(783\) −1.00000 −0.0357371
\(784\) −1.00000 −0.0357143
\(785\) 19.0000i 0.678139i
\(786\) 17.0000i 0.606370i
\(787\) 17.0000i 0.605985i −0.952993 0.302992i \(-0.902014\pi\)
0.952993 0.302992i \(-0.0979856\pi\)
\(788\) 14.0000i 0.498729i
\(789\) −24.0000 −0.854423
\(790\) −12.0000 −0.426941
\(791\) 10.0000i 0.355559i
\(792\)