Properties

Label 1386.2.k.v.793.2
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.21870000.1
Defining polynomial: \(x^{6} - 3 x^{5} + 24 x^{4} - 43 x^{3} + 138 x^{2} - 117 x + 73\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.2
Root \(0.500000 + 3.05087i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.v.991.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.806615 + 1.39710i) q^{5} +(-0.806615 + 2.51980i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.806615 + 1.39710i) q^{5} +(-0.806615 + 2.51980i) q^{7} -1.00000 q^{8} +(0.806615 + 1.39710i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.77890 + 1.95845i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.67103 - 6.35841i) q^{17} +(-0.585515 + 1.01414i) q^{19} +1.61323 q^{20} -1.00000 q^{22} +(1.77890 - 3.08115i) q^{23} +(1.19874 + 2.07629i) q^{25} +(2.58551 - 0.561349i) q^{28} -10.3975 q^{29} +(-3.17103 - 5.49238i) q^{31} +(0.500000 + 0.866025i) q^{32} -7.34206 q^{34} +(-2.86977 - 3.15943i) q^{35} +(-1.41449 + 2.44996i) q^{37} +(0.585515 + 1.01414i) q^{38} +(0.806615 - 1.39710i) q^{40} -4.94457 q^{41} -11.5131 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.77890 - 3.08115i) q^{46} +(3.39213 - 5.87534i) q^{47} +(-5.69874 - 4.06501i) q^{49} +2.39749 q^{50} +(4.00000 + 6.92820i) q^{53} +1.61323 q^{55} +(0.806615 - 2.51980i) q^{56} +(-5.19874 + 9.00449i) q^{58} +(2.19874 + 3.80834i) q^{59} +(5.97764 - 10.3536i) q^{61} -6.34206 q^{62} +1.00000 q^{64} +(-1.47229 - 2.55007i) q^{67} +(-3.67103 + 6.35841i) q^{68} +(-4.17103 + 0.905585i) q^{70} -15.5131 q^{71} +(2.55780 + 4.43024i) q^{73} +(1.41449 + 2.44996i) q^{74} +1.17103 q^{76} +(2.58551 - 0.561349i) q^{77} +(-2.80661 + 4.86120i) q^{79} +(-0.806615 - 1.39710i) q^{80} +(-2.47229 + 4.28212i) q^{82} -5.05543 q^{83} +11.8444 q^{85} +(-5.75654 + 9.97063i) q^{86} +(0.500000 + 0.866025i) q^{88} +(-0.386770 + 0.669906i) q^{89} -3.55780 q^{92} +(-3.39213 - 5.87534i) q^{94} +(-0.944570 - 1.63604i) q^{95} +7.00000 q^{97} +(-6.36977 + 2.90275i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} - 3q^{11} + 3q^{14} - 3q^{16} + 3q^{17} + 9q^{19} - 6q^{22} + 3q^{23} - 15q^{25} + 3q^{28} - 18q^{29} + 6q^{31} + 3q^{32} + 6q^{34} + 30q^{35} - 21q^{37} - 9q^{38} - 24q^{41} + 6q^{43} - 3q^{44} - 3q^{46} + 3q^{47} - 12q^{49} - 30q^{50} + 24q^{53} - 9q^{58} - 9q^{59} + 6q^{61} + 12q^{62} + 6q^{64} - 6q^{67} + 3q^{68} - 18q^{71} + 21q^{74} - 18q^{76} + 3q^{77} - 12q^{79} - 12q^{82} - 36q^{83} + 3q^{86} + 3q^{88} - 12q^{89} - 6q^{92} - 3q^{94} + 42q^{97} + 9q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.806615 + 1.39710i −0.360729 + 0.624801i −0.988081 0.153935i \(-0.950805\pi\)
0.627352 + 0.778736i \(0.284139\pi\)
\(6\) 0 0
\(7\) −0.806615 + 2.51980i −0.304872 + 0.952393i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.806615 + 1.39710i 0.255074 + 0.441801i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 1.77890 + 1.95845i 0.475431 + 0.523417i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.67103 6.35841i −0.890356 1.54214i −0.839450 0.543438i \(-0.817122\pi\)
−0.0509059 0.998703i \(-0.516211\pi\)
\(18\) 0 0
\(19\) −0.585515 + 1.01414i −0.134326 + 0.232660i −0.925340 0.379139i \(-0.876220\pi\)
0.791014 + 0.611799i \(0.209554\pi\)
\(20\) 1.61323 0.360729
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 1.77890 3.08115i 0.370926 0.642463i −0.618782 0.785563i \(-0.712374\pi\)
0.989708 + 0.143100i \(0.0457069\pi\)
\(24\) 0 0
\(25\) 1.19874 + 2.07629i 0.239749 + 0.415257i
\(26\) 0 0
\(27\) 0 0
\(28\) 2.58551 0.561349i 0.488616 0.106085i
\(29\) −10.3975 −1.93077 −0.965383 0.260838i \(-0.916001\pi\)
−0.965383 + 0.260838i \(0.916001\pi\)
\(30\) 0 0
\(31\) −3.17103 5.49238i −0.569534 0.986461i −0.996612 0.0822467i \(-0.973790\pi\)
0.427078 0.904215i \(-0.359543\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −7.34206 −1.25915
\(35\) −2.86977 3.15943i −0.485080 0.534040i
\(36\) 0 0
\(37\) −1.41449 + 2.44996i −0.232540 + 0.402771i −0.958555 0.284908i \(-0.908037\pi\)
0.726015 + 0.687679i \(0.241370\pi\)
\(38\) 0.585515 + 1.01414i 0.0949831 + 0.164515i
\(39\) 0 0
\(40\) 0.806615 1.39710i 0.127537 0.220901i
\(41\) −4.94457 −0.772212 −0.386106 0.922454i \(-0.626180\pi\)
−0.386106 + 0.922454i \(0.626180\pi\)
\(42\) 0 0
\(43\) −11.5131 −1.75573 −0.877865 0.478908i \(-0.841033\pi\)
−0.877865 + 0.478908i \(0.841033\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −1.77890 3.08115i −0.262284 0.454290i
\(47\) 3.39213 5.87534i 0.494793 0.857007i −0.505189 0.863009i \(-0.668577\pi\)
0.999982 + 0.00600214i \(0.00191055\pi\)
\(48\) 0 0
\(49\) −5.69874 4.06501i −0.814106 0.580716i
\(50\) 2.39749 0.339056
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 + 6.92820i 0.549442 + 0.951662i 0.998313 + 0.0580651i \(0.0184931\pi\)
−0.448871 + 0.893597i \(0.648174\pi\)
\(54\) 0 0
\(55\) 1.61323 0.217528
\(56\) 0.806615 2.51980i 0.107788 0.336722i
\(57\) 0 0
\(58\) −5.19874 + 9.00449i −0.682629 + 1.18235i
\(59\) 2.19874 + 3.80834i 0.286252 + 0.495803i 0.972912 0.231175i \(-0.0742572\pi\)
−0.686660 + 0.726979i \(0.740924\pi\)
\(60\) 0 0
\(61\) 5.97764 10.3536i 0.765359 1.32564i −0.174698 0.984622i \(-0.555895\pi\)
0.940057 0.341019i \(-0.110772\pi\)
\(62\) −6.34206 −0.805442
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.47229 2.55007i −0.179868 0.311541i 0.761967 0.647616i \(-0.224234\pi\)
−0.941835 + 0.336075i \(0.890900\pi\)
\(68\) −3.67103 + 6.35841i −0.445178 + 0.771070i
\(69\) 0 0
\(70\) −4.17103 + 0.905585i −0.498533 + 0.108238i
\(71\) −15.5131 −1.84106 −0.920532 0.390666i \(-0.872245\pi\)
−0.920532 + 0.390666i \(0.872245\pi\)
\(72\) 0 0
\(73\) 2.55780 + 4.43024i 0.299368 + 0.518520i 0.975991 0.217809i \(-0.0698909\pi\)
−0.676624 + 0.736329i \(0.736558\pi\)
\(74\) 1.41449 + 2.44996i 0.164431 + 0.284802i
\(75\) 0 0
\(76\) 1.17103 0.134326
\(77\) 2.58551 0.561349i 0.294647 0.0639717i
\(78\) 0 0
\(79\) −2.80661 + 4.86120i −0.315769 + 0.546928i −0.979601 0.200954i \(-0.935596\pi\)
0.663832 + 0.747882i \(0.268929\pi\)
\(80\) −0.806615 1.39710i −0.0901823 0.156200i
\(81\) 0 0
\(82\) −2.47229 + 4.28212i −0.273018 + 0.472881i
\(83\) −5.05543 −0.554906 −0.277453 0.960739i \(-0.589490\pi\)
−0.277453 + 0.960739i \(0.589490\pi\)
\(84\) 0 0
\(85\) 11.8444 1.28471
\(86\) −5.75654 + 9.97063i −0.620744 + 1.07516i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −0.386770 + 0.669906i −0.0409976 + 0.0710098i −0.885796 0.464075i \(-0.846387\pi\)
0.844799 + 0.535085i \(0.179720\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.55780 −0.370926
\(93\) 0 0
\(94\) −3.39213 5.87534i −0.349871 0.605995i
\(95\) −0.944570 1.63604i −0.0969108 0.167855i
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −6.36977 + 2.90275i −0.643444 + 0.293222i
\(99\) 0 0
\(100\) 1.19874 2.07629i 0.119874 0.207629i
\(101\) 6.81197 + 11.7987i 0.677817 + 1.17401i 0.975637 + 0.219391i \(0.0704071\pi\)
−0.297820 + 0.954622i \(0.596260\pi\)
\(102\) 0 0
\(103\) 6.17103 10.6885i 0.608050 1.05317i −0.383512 0.923536i \(-0.625285\pi\)
0.991562 0.129637i \(-0.0413812\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) −7.86977 + 13.6308i −0.760800 + 1.31774i 0.181639 + 0.983365i \(0.441860\pi\)
−0.942439 + 0.334379i \(0.891474\pi\)
\(108\) 0 0
\(109\) −1.97764 3.42538i −0.189424 0.328092i 0.755634 0.654994i \(-0.227329\pi\)
−0.945058 + 0.326902i \(0.893995\pi\)
\(110\) 0.806615 1.39710i 0.0769077 0.133208i
\(111\) 0 0
\(112\) −1.77890 1.95845i −0.168090 0.185056i
\(113\) 4.34206 0.408467 0.204233 0.978922i \(-0.434530\pi\)
0.204233 + 0.978922i \(0.434530\pi\)
\(114\) 0 0
\(115\) 2.86977 + 4.97060i 0.267608 + 0.463510i
\(116\) 5.19874 + 9.00449i 0.482691 + 0.836046i
\(117\) 0 0
\(118\) 4.39749 0.404822
\(119\) 18.9830 4.12146i 1.74017 0.377813i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −5.97764 10.3536i −0.541191 0.937369i
\(123\) 0 0
\(124\) −3.17103 + 5.49238i −0.284767 + 0.493231i
\(125\) −11.9339 −1.06740
\(126\) 0 0
\(127\) −0.442200 −0.0392389 −0.0196195 0.999808i \(-0.506245\pi\)
−0.0196195 + 0.999808i \(0.506245\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.17103 + 2.02828i −0.102313 + 0.177212i −0.912637 0.408770i \(-0.865958\pi\)
0.810324 + 0.585982i \(0.199291\pi\)
\(132\) 0 0
\(133\) −2.08314 2.29340i −0.180632 0.198863i
\(134\) −2.94457 −0.254372
\(135\) 0 0
\(136\) 3.67103 + 6.35841i 0.314788 + 0.545229i
\(137\) 1.61323 + 2.79420i 0.137828 + 0.238724i 0.926674 0.375866i \(-0.122655\pi\)
−0.788847 + 0.614590i \(0.789321\pi\)
\(138\) 0 0
\(139\) 18.3975 1.56045 0.780227 0.625496i \(-0.215103\pi\)
0.780227 + 0.625496i \(0.215103\pi\)
\(140\) −1.30126 + 4.06501i −0.109976 + 0.343556i
\(141\) 0 0
\(142\) −7.75654 + 13.4347i −0.650915 + 1.12742i
\(143\) 0 0
\(144\) 0 0
\(145\) 8.38677 14.5263i 0.696483 1.20634i
\(146\) 5.11560 0.423370
\(147\) 0 0
\(148\) 2.82897 0.232540
\(149\) 9.81197 16.9948i 0.803828 1.39227i −0.113251 0.993566i \(-0.536126\pi\)
0.917079 0.398705i \(-0.130540\pi\)
\(150\) 0 0
\(151\) 0.165670 + 0.286949i 0.0134820 + 0.0233516i 0.872688 0.488279i \(-0.162375\pi\)
−0.859206 + 0.511630i \(0.829042\pi\)
\(152\) 0.585515 1.01414i 0.0474915 0.0822577i
\(153\) 0 0
\(154\) 0.806615 2.51980i 0.0649989 0.203051i
\(155\) 10.2312 0.821790
\(156\) 0 0
\(157\) −9.98300 17.2911i −0.796730 1.37998i −0.921735 0.387821i \(-0.873228\pi\)
0.125004 0.992156i \(-0.460106\pi\)
\(158\) 2.80661 + 4.86120i 0.223282 + 0.386736i
\(159\) 0 0
\(160\) −1.61323 −0.127537
\(161\) 6.32897 + 6.96776i 0.498793 + 0.549137i
\(162\) 0 0
\(163\) −10.6433 + 18.4348i −0.833649 + 1.44392i 0.0614771 + 0.998108i \(0.480419\pi\)
−0.895126 + 0.445814i \(0.852914\pi\)
\(164\) 2.47229 + 4.28212i 0.193053 + 0.334378i
\(165\) 0 0
\(166\) −2.52771 + 4.37813i −0.196189 + 0.339809i
\(167\) −22.0214 −1.70407 −0.852035 0.523485i \(-0.824632\pi\)
−0.852035 + 0.523485i \(0.824632\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 5.92221 10.2576i 0.454213 0.786720i
\(171\) 0 0
\(172\) 5.75654 + 9.97063i 0.438932 + 0.760253i
\(173\) 0.828970 1.43582i 0.0630254 0.109163i −0.832791 0.553588i \(-0.813258\pi\)
0.895816 + 0.444424i \(0.146592\pi\)
\(174\) 0 0
\(175\) −6.19874 + 1.34583i −0.468581 + 0.101735i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) 0.386770 + 0.669906i 0.0289896 + 0.0502115i
\(179\) 7.53008 + 13.0425i 0.562825 + 0.974841i 0.997248 + 0.0741327i \(0.0236188\pi\)
−0.434423 + 0.900709i \(0.643048\pi\)
\(180\) 0 0
\(181\) 15.1156 1.12353 0.561767 0.827296i \(-0.310122\pi\)
0.561767 + 0.827296i \(0.310122\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.77890 + 3.08115i −0.131142 + 0.227145i
\(185\) −2.28189 3.95235i −0.167768 0.290582i
\(186\) 0 0
\(187\) −3.67103 + 6.35841i −0.268452 + 0.464973i
\(188\) −6.78426 −0.494793
\(189\) 0 0
\(190\) −1.88914 −0.137053
\(191\) −2.38677 + 4.13401i −0.172701 + 0.299126i −0.939363 0.342924i \(-0.888583\pi\)
0.766663 + 0.642050i \(0.221916\pi\)
\(192\) 0 0
\(193\) −1.55780 2.69819i −0.112133 0.194220i 0.804497 0.593957i \(-0.202435\pi\)
−0.916630 + 0.399737i \(0.869102\pi\)
\(194\) 3.50000 6.06218i 0.251285 0.435239i
\(195\) 0 0
\(196\) −0.671030 + 6.96776i −0.0479307 + 0.497697i
\(197\) 4.82897 0.344050 0.172025 0.985093i \(-0.444969\pi\)
0.172025 + 0.985093i \(0.444969\pi\)
\(198\) 0 0
\(199\) −2.94457 5.10015i −0.208735 0.361540i 0.742581 0.669756i \(-0.233601\pi\)
−0.951316 + 0.308216i \(0.900268\pi\)
\(200\) −1.19874 2.07629i −0.0847641 0.146816i
\(201\) 0 0
\(202\) 13.6239 0.958578
\(203\) 8.38677 26.1996i 0.588636 1.83885i
\(204\) 0 0
\(205\) 3.98836 6.90805i 0.278559 0.482479i
\(206\) −6.17103 10.6885i −0.429956 0.744706i
\(207\) 0 0
\(208\) 0 0
\(209\) 1.17103 0.0810018
\(210\) 0 0
\(211\) −13.6794 −0.941727 −0.470864 0.882206i \(-0.656058\pi\)
−0.470864 + 0.882206i \(0.656058\pi\)
\(212\) 4.00000 6.92820i 0.274721 0.475831i
\(213\) 0 0
\(214\) 7.86977 + 13.6308i 0.537967 + 0.931786i
\(215\) 9.28663 16.0849i 0.633343 1.09698i
\(216\) 0 0
\(217\) 16.3975 3.56011i 1.11313 0.241676i
\(218\) −3.95529 −0.267886
\(219\) 0 0
\(220\) −0.806615 1.39710i −0.0543820 0.0941923i
\(221\) 0 0
\(222\) 0 0
\(223\) −5.11560 −0.342566 −0.171283 0.985222i \(-0.554791\pi\)
−0.171283 + 0.985222i \(0.554791\pi\)
\(224\) −2.58551 + 0.561349i −0.172752 + 0.0375067i
\(225\) 0 0
\(226\) 2.17103 3.76033i 0.144415 0.250134i
\(227\) −2.64331 4.57836i −0.175443 0.303876i 0.764872 0.644183i \(-0.222802\pi\)
−0.940314 + 0.340307i \(0.889469\pi\)
\(228\) 0 0
\(229\) 2.44220 4.23001i 0.161385 0.279527i −0.773981 0.633209i \(-0.781737\pi\)
0.935366 + 0.353682i \(0.115071\pi\)
\(230\) 5.73955 0.378455
\(231\) 0 0
\(232\) 10.3975 0.682629
\(233\) 4.89749 8.48270i 0.320845 0.555720i −0.659817 0.751426i \(-0.729366\pi\)
0.980663 + 0.195706i \(0.0626997\pi\)
\(234\) 0 0
\(235\) 5.47229 + 9.47828i 0.356973 + 0.618295i
\(236\) 2.19874 3.80834i 0.143126 0.247902i
\(237\) 0 0
\(238\) 5.92221 18.5005i 0.383880 1.19921i
\(239\) 23.9106 1.54665 0.773323 0.634012i \(-0.218593\pi\)
0.773323 + 0.634012i \(0.218593\pi\)
\(240\) 0 0
\(241\) −0.944570 1.63604i −0.0608451 0.105387i 0.833998 0.551767i \(-0.186046\pi\)
−0.894843 + 0.446380i \(0.852713\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) −11.9553 −0.765359
\(245\) 10.2759 4.68281i 0.656504 0.299174i
\(246\) 0 0
\(247\) 0 0
\(248\) 3.17103 + 5.49238i 0.201361 + 0.348767i
\(249\) 0 0
\(250\) −5.96693 + 10.3350i −0.377381 + 0.653644i
\(251\) −0.939830 −0.0593215 −0.0296608 0.999560i \(-0.509443\pi\)
−0.0296608 + 0.999560i \(0.509443\pi\)
\(252\) 0 0
\(253\) −3.55780 −0.223677
\(254\) −0.221100 + 0.382956i −0.0138730 + 0.0240288i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −5.61323 + 9.72240i −0.350144 + 0.606467i −0.986274 0.165115i \(-0.947201\pi\)
0.636131 + 0.771581i \(0.280534\pi\)
\(258\) 0 0
\(259\) −5.03246 5.54039i −0.312702 0.344263i
\(260\) 0 0
\(261\) 0 0
\(262\) 1.17103 + 2.02828i 0.0723465 + 0.125308i
\(263\) −0.613230 1.06215i −0.0378134 0.0654947i 0.846499 0.532390i \(-0.178706\pi\)
−0.884313 + 0.466895i \(0.845373\pi\)
\(264\) 0 0
\(265\) −12.9058 −0.792799
\(266\) −3.02771 + 0.657356i −0.185641 + 0.0403051i
\(267\) 0 0
\(268\) −1.47229 + 2.55007i −0.0899341 + 0.155770i
\(269\) 4.75119 + 8.22929i 0.289685 + 0.501749i 0.973734 0.227687i \(-0.0731162\pi\)
−0.684050 + 0.729435i \(0.739783\pi\)
\(270\) 0 0
\(271\) −1.61323 + 2.79420i −0.0979967 + 0.169735i −0.910855 0.412726i \(-0.864577\pi\)
0.812859 + 0.582461i \(0.197910\pi\)
\(272\) 7.34206 0.445178
\(273\) 0 0
\(274\) 3.22646 0.194918
\(275\) 1.19874 2.07629i 0.0722870 0.125205i
\(276\) 0 0
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) 9.19874 15.9327i 0.551704 0.955579i
\(279\) 0 0
\(280\) 2.86977 + 3.15943i 0.171502 + 0.188812i
\(281\) 11.2312 0.669997 0.334999 0.942219i \(-0.391264\pi\)
0.334999 + 0.942219i \(0.391264\pi\)
\(282\) 0 0
\(283\) 12.7288 + 22.0470i 0.756650 + 1.31056i 0.944550 + 0.328369i \(0.106499\pi\)
−0.187899 + 0.982188i \(0.560168\pi\)
\(284\) 7.75654 + 13.4347i 0.460266 + 0.797205i
\(285\) 0 0
\(286\) 0 0
\(287\) 3.98836 12.4593i 0.235426 0.735450i
\(288\) 0 0
\(289\) −18.4529 + 31.9614i −1.08547 + 1.88008i
\(290\) −8.38677 14.5263i −0.492488 0.853014i
\(291\) 0 0
\(292\) 2.55780 4.43024i 0.149684 0.259260i
\(293\) −17.9446 −1.04833 −0.524166 0.851616i \(-0.675623\pi\)
−0.524166 + 0.851616i \(0.675623\pi\)
\(294\) 0 0
\(295\) −7.09416 −0.413038
\(296\) 1.41449 2.44996i 0.0822153 0.142401i
\(297\) 0 0
\(298\) −9.81197 16.9948i −0.568392 0.984485i
\(299\) 0 0
\(300\) 0 0
\(301\) 9.28663 29.0106i 0.535272 1.67215i
\(302\) 0.331340 0.0190665
\(303\) 0 0
\(304\) −0.585515 1.01414i −0.0335816 0.0581650i
\(305\) 9.64331 + 16.7027i 0.552175 + 0.956394i
\(306\) 0 0
\(307\) −33.0262 −1.88490 −0.942452 0.334342i \(-0.891486\pi\)
−0.942452 + 0.334342i \(0.891486\pi\)
\(308\) −1.77890 1.95845i −0.101362 0.111593i
\(309\) 0 0
\(310\) 5.11560 8.86048i 0.290547 0.503241i
\(311\) −0.165670 0.286949i −0.00939429 0.0162714i 0.861290 0.508114i \(-0.169657\pi\)
−0.870684 + 0.491842i \(0.836324\pi\)
\(312\) 0 0
\(313\) 7.19874 12.4686i 0.406897 0.704766i −0.587643 0.809120i \(-0.699944\pi\)
0.994540 + 0.104354i \(0.0332774\pi\)
\(314\) −19.9660 −1.12675
\(315\) 0 0
\(316\) 5.61323 0.315769
\(317\) 8.76190 15.1761i 0.492118 0.852373i −0.507841 0.861451i \(-0.669556\pi\)
0.999959 + 0.00907805i \(0.00288967\pi\)
\(318\) 0 0
\(319\) 5.19874 + 9.00449i 0.291074 + 0.504155i
\(320\) −0.806615 + 1.39710i −0.0450911 + 0.0781002i
\(321\) 0 0
\(322\) 9.19874 1.99717i 0.512626 0.111298i
\(323\) 8.59777 0.478393
\(324\) 0 0
\(325\) 0 0
\(326\) 10.6433 + 18.4348i 0.589479 + 1.02101i
\(327\) 0 0
\(328\) 4.94457 0.273018
\(329\) 12.0685 + 13.2866i 0.665359 + 0.732515i
\(330\) 0 0
\(331\) 4.47229 7.74622i 0.245819 0.425771i −0.716543 0.697543i \(-0.754276\pi\)
0.962362 + 0.271772i \(0.0876098\pi\)
\(332\) 2.52771 + 4.37813i 0.138726 + 0.240281i
\(333\) 0 0
\(334\) −11.0107 + 19.0711i −0.602480 + 1.04353i
\(335\) 4.75027 0.259535
\(336\) 0 0
\(337\) −3.33732 −0.181795 −0.0908977 0.995860i \(-0.528974\pi\)
−0.0908977 + 0.995860i \(0.528974\pi\)
\(338\) −6.50000 + 11.2583i −0.353553 + 0.612372i
\(339\) 0 0
\(340\) −5.92221 10.2576i −0.321177 0.556295i
\(341\) −3.17103 + 5.49238i −0.171721 + 0.297429i
\(342\) 0 0
\(343\) 14.8397 11.0808i 0.801268 0.598306i
\(344\) 11.5131 0.620744
\(345\) 0 0
\(346\) −0.828970 1.43582i −0.0445657 0.0771901i
\(347\) −15.2118 26.3477i −0.816614 1.41442i −0.908163 0.418616i \(-0.862515\pi\)
0.0915491 0.995801i \(-0.470818\pi\)
\(348\) 0 0
\(349\) 17.5238 0.938028 0.469014 0.883191i \(-0.344609\pi\)
0.469014 + 0.883191i \(0.344609\pi\)
\(350\) −1.93385 + 6.04118i −0.103369 + 0.322915i
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 2.55780 + 4.43024i 0.136138 + 0.235798i 0.926032 0.377446i \(-0.123198\pi\)
−0.789894 + 0.613244i \(0.789864\pi\)
\(354\) 0 0
\(355\) 12.5131 21.6733i 0.664126 1.15030i
\(356\) 0.773540 0.0409976
\(357\) 0 0
\(358\) 15.0602 0.795955
\(359\) −15.3421 + 26.5732i −0.809723 + 1.40248i 0.103333 + 0.994647i \(0.467049\pi\)
−0.913056 + 0.407834i \(0.866284\pi\)
\(360\) 0 0
\(361\) 8.81434 + 15.2669i 0.463913 + 0.803521i
\(362\) 7.55780 13.0905i 0.397229 0.688021i
\(363\) 0 0
\(364\) 0 0
\(365\) −8.25264 −0.431963
\(366\) 0 0
\(367\) −0.728830 1.26237i −0.0380446 0.0658952i 0.846376 0.532586i \(-0.178780\pi\)
−0.884421 + 0.466690i \(0.845446\pi\)
\(368\) 1.77890 + 3.08115i 0.0927316 + 0.160616i
\(369\) 0 0
\(370\) −4.56378 −0.237260
\(371\) −20.6841 + 4.49079i −1.07387 + 0.233150i
\(372\) 0 0
\(373\) 17.0932 29.6064i 0.885055 1.53296i 0.0394037 0.999223i \(-0.487454\pi\)
0.845651 0.533736i \(-0.179212\pi\)
\(374\) 3.67103 + 6.35841i 0.189824 + 0.328786i
\(375\) 0 0
\(376\) −3.39213 + 5.87534i −0.174936 + 0.302998i
\(377\) 0 0
\(378\) 0 0
\(379\) −9.28663 −0.477022 −0.238511 0.971140i \(-0.576659\pi\)
−0.238511 + 0.971140i \(0.576659\pi\)
\(380\) −0.944570 + 1.63604i −0.0484554 + 0.0839273i
\(381\) 0 0
\(382\) 2.38677 + 4.13401i 0.122118 + 0.211514i
\(383\) −1.81197 + 3.13843i −0.0925876 + 0.160366i −0.908599 0.417669i \(-0.862847\pi\)
0.816012 + 0.578035i \(0.196180\pi\)
\(384\) 0 0
\(385\) −1.30126 + 4.06501i −0.0663181 + 0.207172i
\(386\) −3.11560 −0.158580
\(387\) 0 0
\(388\) −3.50000 6.06218i −0.177686 0.307760i
\(389\) 3.58016 + 6.20101i 0.181521 + 0.314404i 0.942399 0.334492i \(-0.108565\pi\)
−0.760878 + 0.648895i \(0.775231\pi\)
\(390\) 0 0
\(391\) −26.1216 −1.32103
\(392\) 5.69874 + 4.06501i 0.287830 + 0.205314i
\(393\) 0 0
\(394\) 2.41449 4.18201i 0.121640 0.210687i
\(395\) −4.52771 7.84223i −0.227814 0.394586i
\(396\) 0 0
\(397\) 15.1987 26.3250i 0.762803 1.32121i −0.178597 0.983922i \(-0.557156\pi\)
0.941400 0.337291i \(-0.109511\pi\)
\(398\) −5.88914 −0.295196
\(399\) 0 0
\(400\) −2.39749 −0.119874
\(401\) −6.01072 + 10.4109i −0.300161 + 0.519894i −0.976172 0.216997i \(-0.930374\pi\)
0.676011 + 0.736891i \(0.263707\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 6.81197 11.7987i 0.338908 0.587007i
\(405\) 0 0
\(406\) −18.4961 20.3629i −0.917946 1.01060i
\(407\) 2.82897 0.140227
\(408\) 0 0
\(409\) −8.78426 15.2148i −0.434354 0.752323i 0.562889 0.826533i \(-0.309690\pi\)
−0.997243 + 0.0742099i \(0.976357\pi\)
\(410\) −3.98836 6.90805i −0.196971 0.341164i
\(411\) 0 0
\(412\) −12.3421 −0.608050
\(413\) −11.3698 + 2.46853i −0.559470 + 0.121468i
\(414\) 0 0
\(415\) 4.07779 7.06293i 0.200171 0.346706i
\(416\) 0 0
\(417\) 0 0
\(418\) 0.585515 1.01414i 0.0286385 0.0496033i
\(419\) 27.1710 1.32739 0.663696 0.748003i \(-0.268987\pi\)
0.663696 + 0.748003i \(0.268987\pi\)
\(420\) 0 0
\(421\) 23.1710 1.12929 0.564643 0.825335i \(-0.309014\pi\)
0.564643 + 0.825335i \(0.309014\pi\)
\(422\) −6.83969 + 11.8467i −0.332951 + 0.576688i
\(423\) 0 0
\(424\) −4.00000 6.92820i −0.194257 0.336463i
\(425\) 8.80126 15.2442i 0.426924 0.739453i
\(426\) 0 0
\(427\) 21.2673 + 23.4138i 1.02920 + 1.13307i
\(428\) 15.7395 0.760800
\(429\) 0 0
\(430\) −9.28663 16.0849i −0.447841 0.775683i
\(431\) −8.38677 14.5263i −0.403977 0.699708i 0.590225 0.807239i \(-0.299039\pi\)
−0.994202 + 0.107531i \(0.965706\pi\)
\(432\) 0 0
\(433\) 17.3421 0.833406 0.416703 0.909043i \(-0.363185\pi\)
0.416703 + 0.909043i \(0.363185\pi\)
\(434\) 5.11560 15.9807i 0.245557 0.767098i
\(435\) 0 0
\(436\) −1.97764 + 3.42538i −0.0947120 + 0.164046i
\(437\) 2.08314 + 3.60811i 0.0996503 + 0.172599i
\(438\) 0 0
\(439\) −16.5739 + 28.7068i −0.791028 + 1.37010i 0.134303 + 0.990940i \(0.457121\pi\)
−0.925331 + 0.379160i \(0.876213\pi\)
\(440\) −1.61323 −0.0769077
\(441\) 0 0
\(442\) 0 0
\(443\) −6.02771 + 10.4403i −0.286385 + 0.496034i −0.972944 0.231040i \(-0.925787\pi\)
0.686559 + 0.727074i \(0.259120\pi\)
\(444\) 0 0
\(445\) −0.623949 1.08071i −0.0295780 0.0512306i
\(446\) −2.55780 + 4.43024i −0.121115 + 0.209778i
\(447\) 0 0
\(448\) −0.806615 + 2.51980i −0.0381090 + 0.119049i
\(449\) 36.5947 1.72701 0.863505 0.504340i \(-0.168264\pi\)
0.863505 + 0.504340i \(0.168264\pi\)
\(450\) 0 0
\(451\) 2.47229 + 4.28212i 0.116415 + 0.201637i
\(452\) −2.17103 3.76033i −0.102117 0.176871i
\(453\) 0 0
\(454\) −5.28663 −0.248114
\(455\) 0 0
\(456\) 0 0
\(457\) −18.9106 + 32.7541i −0.884600 + 1.53217i −0.0384276 + 0.999261i \(0.512235\pi\)
−0.846172 + 0.532910i \(0.821098\pi\)
\(458\) −2.44220 4.23001i −0.114117 0.197656i
\(459\) 0 0
\(460\) 2.86977 4.97060i 0.133804 0.231755i
\(461\) −34.9707 −1.62875 −0.814375 0.580339i \(-0.802920\pi\)
−0.814375 + 0.580339i \(0.802920\pi\)
\(462\) 0 0
\(463\) 7.56852 0.351739 0.175869 0.984413i \(-0.443726\pi\)
0.175869 + 0.984413i \(0.443726\pi\)
\(464\) 5.19874 9.00449i 0.241346 0.418023i
\(465\) 0 0
\(466\) −4.89749 8.48270i −0.226872 0.392954i
\(467\) −7.31434 + 12.6688i −0.338468 + 0.586243i −0.984145 0.177368i \(-0.943242\pi\)
0.645677 + 0.763610i \(0.276575\pi\)
\(468\) 0 0
\(469\) 7.61323 1.65293i 0.351546 0.0763253i
\(470\) 10.9446 0.504835
\(471\) 0 0
\(472\) −2.19874 3.80834i −0.101205 0.175293i
\(473\) 5.75654 + 9.97063i 0.264686 + 0.458450i
\(474\) 0 0
\(475\) −2.80753 −0.128818
\(476\) −13.0608 14.3790i −0.598640 0.659062i
\(477\) 0 0
\(478\) 11.9553 20.7072i 0.546822 0.947124i
\(479\) −0.613230 1.06215i −0.0280192 0.0485307i 0.851676 0.524069i \(-0.175587\pi\)
−0.879695 + 0.475538i \(0.842253\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.88914 −0.0860480
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −5.64630 + 9.77969i −0.256385 + 0.444073i
\(486\) 0 0
\(487\) −15.3528 26.5918i −0.695701 1.20499i −0.969944 0.243329i \(-0.921761\pi\)
0.274243 0.961660i \(-0.411573\pi\)
\(488\) −5.97764 + 10.3536i −0.270595 + 0.468685i
\(489\) 0 0
\(490\) 1.08253 11.2406i 0.0489035 0.507799i
\(491\) −30.9446 −1.39651 −0.698254 0.715850i \(-0.746040\pi\)
−0.698254 + 0.715850i \(0.746040\pi\)
\(492\) 0 0
\(493\) 38.1695 + 66.1115i 1.71907 + 2.97751i
\(494\) 0 0
\(495\) 0 0
\(496\) 6.34206 0.284767
\(497\) 12.5131 39.0898i 0.561289 1.75342i
\(498\) 0 0
\(499\) 5.17103 8.95649i 0.231487 0.400947i −0.726759 0.686893i \(-0.758974\pi\)
0.958246 + 0.285945i \(0.0923076\pi\)
\(500\) 5.96693 + 10.3350i 0.266849 + 0.462196i
\(501\) 0 0
\(502\) −0.469915 + 0.813917i −0.0209733 + 0.0363269i
\(503\) −4.66268 −0.207899 −0.103949 0.994583i \(-0.533148\pi\)
−0.103949 + 0.994583i \(0.533148\pi\)
\(504\) 0 0
\(505\) −21.9786 −0.978033
\(506\) −1.77890 + 3.08115i −0.0790817 + 0.136974i
\(507\) 0 0
\(508\) 0.221100 + 0.382956i 0.00980973 + 0.0169909i
\(509\) 12.7950 22.1616i 0.567127 0.982294i −0.429721 0.902962i \(-0.641388\pi\)
0.996848 0.0793318i \(-0.0252787\pi\)
\(510\) 0 0
\(511\) −13.2265 + 2.87164i −0.585104 + 0.127034i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 5.61323 + 9.72240i 0.247589 + 0.428837i
\(515\) 9.95529 + 17.2431i 0.438682 + 0.759820i
\(516\) 0 0
\(517\) −6.78426 −0.298371
\(518\) −7.31434 + 1.58804i −0.321374 + 0.0697745i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) 0 0
\(523\) −15.1817 + 26.2956i −0.663852 + 1.14982i 0.315744 + 0.948844i \(0.397746\pi\)
−0.979595 + 0.200980i \(0.935587\pi\)
\(524\) 2.34206 0.102313
\(525\) 0 0
\(526\) −1.22646 −0.0534762
\(527\) −23.2819 + 40.3254i −1.01418 + 1.75660i
\(528\) 0 0
\(529\) 5.17103 + 8.95649i 0.224827 + 0.389412i
\(530\) −6.45292 + 11.1768i −0.280297 + 0.485488i
\(531\) 0 0
\(532\) −0.944570 + 2.95076i −0.0409523 + 0.127932i
\(533\) 0 0
\(534\) 0 0
\(535\) −12.6958 21.9897i −0.548885 0.950697i
\(536\) 1.47229 + 2.55007i 0.0635930 + 0.110146i
\(537\) 0 0
\(538\) 9.50237 0.409676
\(539\) −0.671030 + 6.96776i −0.0289033 + 0.300123i
\(540\) 0 0
\(541\) −0.806615 + 1.39710i −0.0346791 + 0.0600659i −0.882844 0.469666i \(-0.844374\pi\)
0.848165 + 0.529732i \(0.177708\pi\)
\(542\) 1.61323 + 2.79420i 0.0692942 + 0.120021i
\(543\) 0 0
\(544\) 3.67103 6.35841i 0.157394 0.272615i
\(545\) 6.38079 0.273323
\(546\) 0 0
\(547\) 15.7348 0.672772 0.336386 0.941724i \(-0.390795\pi\)
0.336386 + 0.941724i \(0.390795\pi\)
\(548\) 1.61323 2.79420i 0.0689138 0.119362i
\(549\) 0 0
\(550\) −1.19874 2.07629i −0.0511146 0.0885332i
\(551\) 6.08788 10.5445i 0.259353 0.449212i
\(552\) 0 0
\(553\) −9.98537 10.9932i −0.424621 0.467479i
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) −9.19874 15.9327i −0.390114 0.675697i
\(557\) 5.64094 + 9.77040i 0.239015 + 0.413985i 0.960432 0.278515i \(-0.0898423\pi\)
−0.721417 + 0.692501i \(0.756509\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 4.17103 0.905585i 0.176258 0.0382680i
\(561\) 0 0
\(562\) 5.61560 9.72650i 0.236880 0.410288i
\(563\) 10.4529 + 18.1050i 0.440538 + 0.763034i 0.997729 0.0673499i \(-0.0214544\pi\)
−0.557191 + 0.830384i \(0.688121\pi\)
\(564\) 0 0
\(565\) −3.50237 + 6.06628i −0.147346 + 0.255210i
\(566\) 25.4577 1.07007
\(567\) 0 0
\(568\) 15.5131 0.650915
\(569\) −3.91686 + 6.78419i −0.164203 + 0.284408i −0.936372 0.351009i \(-0.885839\pi\)
0.772169 + 0.635417i \(0.219172\pi\)
\(570\) 0 0
\(571\) −1.19874 2.07629i −0.0501659 0.0868899i 0.839852 0.542815i \(-0.182642\pi\)
−0.890018 + 0.455926i \(0.849308\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −8.79590 9.68368i −0.367134 0.404189i
\(575\) 8.52979 0.355717
\(576\) 0 0
\(577\) −12.8143 22.1951i −0.533468 0.923994i −0.999236 0.0390869i \(-0.987555\pi\)
0.465768 0.884907i \(-0.345778\pi\)
\(578\) 18.4529 + 31.9614i 0.767540 + 1.32942i
\(579\) 0 0
\(580\) −16.7735 −0.696483
\(581\) 4.07779 12.7387i 0.169175 0.528488i
\(582\) 0 0
\(583\) 4.00000 6.92820i 0.165663 0.286937i
\(584\) −2.55780 4.43024i −0.105843 0.183325i
\(585\) 0 0
\(586\) −8.97229 + 15.5405i −0.370642 + 0.641970i
\(587\) −5.79972 −0.239380 −0.119690 0.992811i \(-0.538190\pi\)
−0.119690 + 0.992811i \(0.538190\pi\)
\(588\) 0 0
\(589\) 7.42674 0.306014
\(590\) −3.54708 + 6.14372i −0.146031 + 0.252933i
\(591\) 0 0
\(592\) −1.41449 2.44996i −0.0581350 0.100693i
\(593\) 15.5962 27.0135i 0.640461 1.10931i −0.344869 0.938651i \(-0.612077\pi\)
0.985330 0.170660i \(-0.0545898\pi\)
\(594\) 0 0
\(595\) −9.55389 + 29.8455i −0.391671 + 1.22355i
\(596\) −19.6239 −0.803828
\(597\) 0 0
\(598\) 0 0
\(599\) −15.6463 27.1002i −0.639291 1.10728i −0.985589 0.169159i \(-0.945895\pi\)
0.346298 0.938125i \(-0.387439\pi\)
\(600\) 0 0
\(601\) −22.1203 −0.902307 −0.451154 0.892446i \(-0.648987\pi\)
−0.451154 + 0.892446i \(0.648987\pi\)
\(602\) −20.4806 22.5478i −0.834728 0.918979i
\(603\) 0 0
\(604\) 0.165670 0.286949i 0.00674102 0.0116758i
\(605\) −0.806615 1.39710i −0.0327936 0.0568001i
\(606\) 0 0
\(607\) 10.3090 17.8557i 0.418429 0.724740i −0.577353 0.816495i \(-0.695914\pi\)
0.995782 + 0.0917548i \(0.0292476\pi\)
\(608\) −1.17103 −0.0474915
\(609\) 0 0
\(610\) 19.2866 0.780893
\(611\) 0 0
\(612\) 0 0
\(613\) 7.87750 + 13.6442i 0.318169 + 0.551086i 0.980106 0.198474i \(-0.0635986\pi\)
−0.661937 + 0.749560i \(0.730265\pi\)
\(614\) −16.5131 + 28.6015i −0.666414 + 1.15426i
\(615\) 0 0
\(616\) −2.58551 + 0.561349i −0.104173 + 0.0226174i
\(617\) −34.2526 −1.37896 −0.689480 0.724305i \(-0.742161\pi\)
−0.689480 + 0.724305i \(0.742161\pi\)
\(618\) 0 0
\(619\) 10.9854 + 19.0272i 0.441539 + 0.764769i 0.997804 0.0662365i \(-0.0210992\pi\)
−0.556264 + 0.831005i \(0.687766\pi\)
\(620\) −5.11560 8.86048i −0.205447 0.355845i
\(621\) 0 0
\(622\) −0.331340 −0.0132855
\(623\) −1.37605 1.51494i −0.0551303 0.0606947i
\(624\) 0 0
\(625\) 3.63230 6.29133i 0.145292 0.251653i
\(626\) −7.19874 12.4686i −0.287720 0.498345i
\(627\) 0 0
\(628\) −9.98300 + 17.2911i −0.398365 + 0.689989i
\(629\) 20.7705 0.828173
\(630\) 0 0
\(631\) −27.5685 −1.09749 −0.548743 0.835991i \(-0.684893\pi\)
−0.548743 + 0.835991i \(0.684893\pi\)
\(632\) 2.80661 4.86120i 0.111641 0.193368i
\(633\) 0 0
\(634\) −8.76190 15.1761i −0.347980 0.602718i
\(635\) 0.356685 0.617797i 0.0141546 0.0245165i
\(636\) 0 0
\(637\) 0 0
\(638\) 10.3975 0.411641
\(639\) 0 0
\(640\) 0.806615 + 1.39710i 0.0318843 + 0.0552251i
\(641\) 2.82897 + 4.89992i 0.111738 + 0.193535i 0.916471 0.400101i \(-0.131025\pi\)
−0.804733 + 0.593636i \(0.797692\pi\)
\(642\) 0 0
\(643\) 17.4791 0.689308 0.344654 0.938730i \(-0.387996\pi\)
0.344654 + 0.938730i \(0.387996\pi\)
\(644\) 2.86977 8.96493i 0.113085 0.353268i
\(645\) 0 0
\(646\) 4.29889 7.44589i 0.169137 0.292955i
\(647\) −4.41984 7.65540i −0.173762 0.300965i 0.765970 0.642876i \(-0.222259\pi\)
−0.939732 + 0.341912i \(0.888926\pi\)
\(648\) 0 0
\(649\) 2.19874 3.80834i 0.0863083 0.149490i
\(650\) 0 0
\(651\) 0 0
\(652\) 21.2866 0.833649
\(653\) −12.3751 + 21.4344i −0.484276 + 0.838791i −0.999837 0.0180618i \(-0.994250\pi\)
0.515560 + 0.856853i \(0.327584\pi\)
\(654\) 0 0
\(655\) −1.88914 3.27209i −0.0738148 0.127851i
\(656\) 2.47229 4.28212i 0.0965265 0.167189i
\(657\) 0 0
\(658\) 17.5408 3.80834i 0.683812 0.148464i
\(659\) −5.62869 −0.219263 −0.109631 0.993972i \(-0.534967\pi\)
−0.109631 + 0.993972i \(0.534967\pi\)
\(660\) 0 0
\(661\) 6.70111 + 11.6067i 0.260643 + 0.451447i 0.966413 0.256994i \(-0.0827321\pi\)
−0.705770 + 0.708441i \(0.749399\pi\)
\(662\) −4.47229 7.74622i −0.173820 0.301066i
\(663\) 0 0
\(664\) 5.05543 0.196189
\(665\) 4.88440 1.06047i 0.189409 0.0411231i
\(666\) 0 0
\(667\) −18.4961 + 32.0362i −0.716172 + 1.24045i
\(668\) 11.0107 + 19.0711i 0.426018 + 0.737884i
\(669\) 0 0
\(670\) 2.37513 4.11385i 0.0917594 0.158932i
\(671\) −11.9553 −0.461529
\(672\) 0 0
\(673\) −29.0262 −1.11888 −0.559438 0.828872i \(-0.688983\pi\)
−0.559438 + 0.828872i \(0.688983\pi\)
\(674\) −1.66866 + 2.89020i −0.0642744 + 0.111326i
\(675\) 0 0
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) −10.1540 + 17.5873i −0.390251 + 0.675935i −0.992482 0.122387i \(-0.960945\pi\)
0.602231 + 0.798322i \(0.294279\pi\)
\(678\) 0 0
\(679\) −5.64630 + 17.6386i −0.216685 + 0.676906i
\(680\) −11.8444 −0.454213
\(681\) 0 0
\(682\) 3.17103 + 5.49238i 0.121425 + 0.210314i
\(683\) −5.36977 9.30072i −0.205469 0.355882i 0.744813 0.667273i \(-0.232539\pi\)
−0.950282 + 0.311391i \(0.899205\pi\)
\(684\) 0 0
\(685\) −5.20502 −0.198874
\(686\) −2.17639 18.3919i −0.0830949 0.702207i
\(687\) 0 0
\(688\) 5.75654 9.97063i 0.219466 0.380127i
\(689\) 0 0
\(690\) 0 0
\(691\) −2.98537 + 5.17082i −0.113569 + 0.196707i −0.917207 0.398411i \(-0.869562\pi\)
0.803638 + 0.595119i \(0.202895\pi\)
\(692\) −1.65794 −0.0630254
\(693\) 0 0
\(694\) −30.4237 −1.15487
\(695\) −14.8397 + 25.7031i −0.562902 + 0.974974i
\(696\) 0 0
\(697\) 18.1517 + 31.4396i 0.687543 + 1.19086i
\(698\) 8.76190 15.1761i 0.331643 0.574422i
\(699\) 0 0
\(700\) 4.26489 + 4.69536i 0.161198 + 0.177468i
\(701\) 5.28189 0.199494 0.0997471 0.995013i \(-0.468197\pi\)
0.0997471 + 0.995013i \(0.468197\pi\)
\(702\) 0 0
\(703\) −1.65640 2.86898i −0.0624725 0.108205i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) 5.11560 0.192528
\(707\) −35.2249 + 7.64779i −1.32477 + 0.287625i
\(708\) 0 0
\(709\) −19.6564 + 34.0459i −0.738212 + 1.27862i 0.215088 + 0.976595i \(0.430996\pi\)
−0.953300 + 0.302026i \(0.902337\pi\)
\(710\) −12.5131 21.6733i −0.469608 0.813385i
\(711\) 0 0
\(712\) 0.386770 0.669906i 0.0144948 0.0251058i
\(713\) −22.5638 −0.845020
\(714\) 0 0
\(715\) 0 0
\(716\) 7.53008 13.0425i 0.281412 0.487421i
\(717\) 0 0
\(718\) 15.3421 + 26.5732i 0.572561 + 0.991704i
\(719\) −17.6788 + 30.6205i −0.659306 + 1.14195i 0.321489 + 0.946913i \(0.395817\pi\)
−0.980795 + 0.195039i \(0.937517\pi\)
\(720\) 0 0
\(721\) 21.9553 + 24.1713i 0.817658 + 0.900185i
\(722\) 17.6287 0.656072
\(723\) 0 0
\(724\) −7.55780 13.0905i −0.280883 0.486504i
\(725\) −12.4639 21.5882i −0.462899 0.801765i
\(726\) 0 0
\(727\) −40.2312 −1.49209 −0.746046 0.665894i \(-0.768050\pi\)
−0.746046 + 0.665894i \(0.768050\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −4.12632 + 7.14699i −0.152722 + 0.264522i
\(731\) 42.2649 + 73.2049i 1.56322 + 2.70758i
\(732\) 0 0
\(733\) −14.3644 + 24.8799i −0.530562 + 0.918960i 0.468802 + 0.883303i \(0.344686\pi\)
−0.999364 + 0.0356568i \(0.988648\pi\)
\(734\) −1.45766 −0.0538032
\(735\) 0 0
\(736\) 3.55780 0.131142
\(737\) −1.47229 + 2.55007i −0.0542323 + 0.0939331i
\(738\) 0 0
\(739\) 8.17103 + 14.1526i 0.300576 + 0.520613i 0.976267 0.216572i \(-0.0694877\pi\)
−0.675690 + 0.737186i \(0.736154\pi\)
\(740\) −2.28189 + 3.95235i −0.0838839 + 0.145291i
\(741\) 0 0
\(742\) −6.45292 + 20.1584i −0.236894 + 0.740037i
\(743\) −45.3897 −1.66519 −0.832593 0.553885i \(-0.813145\pi\)
−0.832593 + 0.553885i \(0.813145\pi\)
\(744\) 0 0
\(745\) 15.8290 + 27.4166i 0.579929 + 1.00447i
\(746\) −17.0932 29.6064i −0.625828 1.08397i
\(747\) 0 0
\(748\) 7.34206 0.268452
\(749\) −27.9991 30.8251i −1.02306 1.12632i
\(750\) 0 0
\(751\) 13.8999 24.0753i 0.507213 0.878519i −0.492752 0.870170i \(-0.664009\pi\)
0.999965 0.00834907i \(-0.00265762\pi\)
\(752\) 3.39213 + 5.87534i 0.123698 + 0.214252i
\(753\) 0 0
\(754\) 0 0
\(755\) −0.534528 −0.0194535
\(756\) 0 0
\(757\) 19.0816 0.693533 0.346766 0.937952i \(-0.387280\pi\)
0.346766 + 0.937952i \(0.387280\pi\)
\(758\) −4.64331 + 8.04246i −0.168653 + 0.292115i
\(759\) 0 0
\(760\) 0.944570 + 1.63604i 0.0342632 + 0.0593455i
\(761\) 23.6093 40.8925i 0.855837 1.48235i −0.0200287 0.999799i \(-0.506376\pi\)
0.875866 0.482554i \(-0.160291\pi\)
\(762\) 0 0
\(763\) 10.2265 2.22030i 0.370223 0.0803802i
\(764\) 4.77354 0.172701
\(765\) 0 0
\(766\) 1.81197 + 3.13843i 0.0654693 + 0.113396i
\(767\) 0 0
\(768\) 0 0
\(769\) −9.56852 −0.345050 −0.172525 0.985005i \(-0.555192\pi\)
−0.172525 + 0.985005i \(0.555192\pi\)
\(770\) 2.86977 + 3.15943i 0.103419 + 0.113858i
\(771\) 0 0
\(772\) −1.55780 + 2.69819i −0.0560664 + 0.0971099i
\(773\) 7.97764 + 13.8177i 0.286936 + 0.496988i 0.973077 0.230481i \(-0.0740300\pi\)
−0.686141 + 0.727469i \(0.740697\pi\)
\(774\) 0 0
\(775\) 7.60251 13.1679i 0.273090 0.473006i
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 7.16031 0.256710
\(779\) 2.89512 5.01449i 0.103728 0.179663i
\(780\) 0 0
\(781\) 7.75654 + 13.4347i 0.277551 + 0.480732i
\(782\) −13.0608 + 22.6220i −0.467053 + 0.808959i
\(783\) 0 0
\(784\) 6.36977 2.90275i 0.227492 0.103670i
\(785\) 32.2098 1.14962
\(786\) 0 0
\(787\) −24.9276 43.1758i −0.888572 1.53905i −0.841564 0.540157i \(-0.818365\pi\)
−0.0470081 0.998895i \(-0.514969\pi\)
\(788\) −2.41449 4.18201i −0.0860125 0.148978i
\(789\) 0 0
\(790\) −9.05543 −0.322178
\(791\) −3.50237 + 10.9411i −0.124530 + 0.389021i
\(792\) 0 0