Properties

Label 1386.2.k.v.991.2
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 991.2
Root \(0.500000 - 3.05087i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.v.793.2

$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.627352 0.778736i \(-0.284139\pi\)
−0.988081 + 0.153935i \(0.950805\pi\)
\(6\) 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 −0.0509059 + 0.998703i \(0.516211\pi\)
−0.839450 + 0.543438i \(0.817122\pi\)
\(18\) 0 0
\(19\) −0.585515 1.01414i −0.134326 0.232660i 0.791014 0.611799i \(-0.209554\pi\)
−0.925340 + 0.379139i \(0.876220\pi\)
\(20\) 1.61323 0.360729
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 1.77890 + 3.08115i 0.370926 + 0.642463i 0.989708 0.143100i \(-0.0457069\pi\)
−0.618782 + 0.785563i \(0.712374\pi\)
\(24\) 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 0.427078 + 0.904215i \(0.359543\pi\)
−0.996612 + 0.0822467i \(0.973790\pi\)
\(32\) 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 0.726015 0.687679i \(-0.241370\pi\)
−0.958555 + 0.284908i \(0.908037\pi\)
\(38\) 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 0.999982 0.00600214i \(-0.00191055\pi\)
−0.505189 + 0.863009i \(0.668577\pi\)
\(48\) 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 −0.448871 0.893597i \(-0.648174\pi\)
0.998313 0.0580651i \(-0.0184931\pi\)
\(54\) 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 −0.686660 0.726979i \(-0.740924\pi\)
0.972912 + 0.231175i \(0.0742572\pi\)
\(60\) 0 0
\(61\) 5.97764 + 10.3536i 0.765359 + 1.32564i 0.940057 + 0.341019i \(0.110772\pi\)
−0.174698 + 0.984622i \(0.555895\pi\)
\(62\) −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 −0.941835 0.336075i \(-0.890900\pi\)
0.761967 + 0.647616i \(0.224234\pi\)
\(68\) −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 −0.676624 0.736329i \(-0.736558\pi\)
0.975991 + 0.217809i \(0.0698909\pi\)
\(74\) 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 0.663832 0.747882i \(-0.268929\pi\)
−0.979601 + 0.200954i \(0.935596\pi\)
\(80\) −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 0.844799 0.535085i \(-0.179720\pi\)
−0.885796 + 0.464075i \(0.846387\pi\)
\(90\) 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 −0.297820 0.954622i \(-0.596260\pi\)
0.975637 0.219391i \(-0.0704071\pi\)
\(102\) 0 0
\(103\) 6.17103 + 10.6885i 0.608050 + 1.05317i 0.991562 + 0.129637i \(0.0413812\pi\)
−0.383512 + 0.923536i \(0.625285\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) −7.86977 13.6308i −0.760800 1.31774i −0.942439 0.334379i \(-0.891474\pi\)
0.181639 0.983365i \(-0.441860\pi\)
\(108\) 0 0
\(109\) −1.97764 + 3.42538i −0.189424 + 0.328092i −0.945058 0.326902i \(-0.893995\pi\)
0.755634 + 0.654994i \(0.227329\pi\)
\(110\) 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 0.810324 0.585982i \(-0.199291\pi\)
−0.912637 + 0.408770i \(0.865958\pi\)
\(132\) 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 −0.788847 0.614590i \(-0.789321\pi\)
0.926674 + 0.375866i \(0.122655\pi\)
\(138\) 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 0.917079 + 0.398705i \(0.130540\pi\)
−0.113251 + 0.993566i \(0.536126\pi\)
\(150\) 0 0
\(151\) 0.165670 0.286949i 0.0134820 0.0233516i −0.859206 0.511630i \(-0.829042\pi\)
0.872688 + 0.488279i \(0.162375\pi\)
\(152\) 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 0.125004 + 0.992156i \(0.460106\pi\)
−0.921735 + 0.387821i \(0.873228\pi\)
\(158\) 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 −0.895126 0.445814i \(-0.852914\pi\)
0.0614771 0.998108i \(-0.480419\pi\)
\(164\) 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 0.895816 0.444424i \(-0.146592\pi\)
−0.832791 + 0.553588i \(0.813258\pi\)
\(174\) 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 −0.434423 0.900709i \(-0.643048\pi\)
0.997248 0.0741327i \(-0.0236188\pi\)
\(180\) 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 0.766663 0.642050i \(-0.221916\pi\)
−0.939363 + 0.342924i \(0.888583\pi\)
\(192\) 0 0
\(193\) −1.55780 + 2.69819i −0.112133 + 0.194220i −0.916630 0.399737i \(-0.869102\pi\)
0.804497 + 0.593957i \(0.202435\pi\)
\(194\) 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 −0.951316 0.308216i \(-0.900268\pi\)
0.742581 + 0.669756i \(0.233601\pi\)
\(200\) −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 −0.940314 0.340307i \(-0.889469\pi\)
0.764872 + 0.644183i \(0.222802\pi\)
\(228\) 0 0
\(229\) 2.44220 + 4.23001i 0.161385 + 0.279527i 0.935366 0.353682i \(-0.115071\pi\)
−0.773981 + 0.633209i \(0.781737\pi\)
\(230\) 5.73955 0.378455
\(231\) 0 0
\(232\) 10.3975 0.682629
\(233\) 4.89749 + 8.48270i 0.320845 + 0.555720i 0.980663 0.195706i \(-0.0626997\pi\)
−0.659817 + 0.751426i \(0.729366\pi\)
\(234\) 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 −0.894843 0.446380i \(-0.852713\pi\)
0.833998 + 0.551767i \(0.186046\pi\)
\(242\) 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 0.636131 0.771581i \(-0.280534\pi\)
−0.986274 + 0.165115i \(0.947201\pi\)
\(258\) 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 −0.884313 0.466895i \(-0.845373\pi\)
0.846499 + 0.532390i \(0.178706\pi\)
\(264\) 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 −0.684050 0.729435i \(-0.739783\pi\)
0.973734 + 0.227687i \(0.0731162\pi\)
\(270\) 0 0
\(271\) −1.61323 2.79420i −0.0979967 0.169735i 0.812859 0.582461i \(-0.197910\pi\)
−0.910855 + 0.412726i \(0.864577\pi\)
\(272\) 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 −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) 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 −0.187899 0.982188i \(-0.560168\pi\)
0.944550 0.328369i \(-0.106499\pi\)
\(284\) 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 −0.870684 0.491842i \(-0.836324\pi\)
0.861290 + 0.508114i \(0.169657\pi\)
\(312\) 0 0
\(313\) 7.19874 + 12.4686i 0.406897 + 0.704766i 0.994540 0.104354i \(-0.0332774\pi\)
−0.587643 + 0.809120i \(0.699944\pi\)
\(314\) −19.9660 −1.12675
\(315\) 0 0
\(316\) 5.61323 0.315769
\(317\) 8.76190 + 15.1761i 0.492118 + 0.852373i 0.999959 0.00907805i \(-0.00288967\pi\)
−0.507841 + 0.861451i \(0.669556\pi\)
\(318\) 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 0.962362 0.271772i \(-0.0876098\pi\)
−0.716543 + 0.697543i \(0.754276\pi\)
\(332\) 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 0.0915491 + 0.995801i \(0.470818\pi\)
−0.908163 + 0.418616i \(0.862515\pi\)
\(348\) 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 −0.789894 0.613244i \(-0.789864\pi\)
0.926032 + 0.377446i \(0.123198\pi\)
\(354\) 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 −0.913056 0.407834i \(-0.866284\pi\)
0.103333 0.994647i \(-0.467049\pi\)
\(360\) 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 −0.884421 0.466690i \(-0.845446\pi\)
0.846376 + 0.532586i \(0.178780\pi\)
\(368\) 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 0.845651 + 0.533736i \(0.179212\pi\)
0.0394037 + 0.999223i \(0.487454\pi\)
\(374\) 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 0.816012 0.578035i \(-0.196180\pi\)
−0.908599 + 0.417669i \(0.862847\pi\)
\(384\) 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 −0.760878 0.648895i \(-0.775231\pi\)
0.942399 + 0.334492i \(0.108565\pi\)
\(390\) 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 0.941400 + 0.337291i \(0.109511\pi\)
−0.178597 + 0.983922i \(0.557156\pi\)
\(398\) −5.88914 −0.295196
\(399\) 0 0
\(400\) −2.39749 −0.119874
\(401\) −6.01072 10.4109i −0.300161 0.519894i 0.676011 0.736891i \(-0.263707\pi\)
−0.976172 + 0.216997i \(0.930374\pi\)
\(402\) 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 −0.997243 0.0742099i \(-0.976357\pi\)
0.562889 + 0.826533i \(0.309690\pi\)
\(410\) −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 −0.994202 0.107531i \(-0.965706\pi\)
0.590225 + 0.807239i \(0.299039\pi\)
\(432\) 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 −0.925331 0.379160i \(-0.876213\pi\)
0.134303 0.990940i \(-0.457121\pi\)
\(440\) −1.61323 −0.0769077
\(441\) 0 0
\(442\) 0 0
\(443\) −6.02771 10.4403i −0.286385 0.496034i 0.686559 0.727074i \(-0.259120\pi\)
−0.972944 + 0.231040i \(0.925787\pi\)
\(444\) 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 −0.846172 0.532910i \(-0.821098\pi\)
−0.0384276 0.999261i \(-0.512235\pi\)
\(458\) −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 0.645677 0.763610i \(-0.276575\pi\)
−0.984145 + 0.177368i \(0.943242\pi\)
\(468\) 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 −0.879695 0.475538i \(-0.842253\pi\)
0.851676 + 0.524069i \(0.175587\pi\)
\(480\) 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 0.274243 + 0.961660i \(0.411573\pi\)
−0.969944 + 0.243329i \(0.921761\pi\)
\(488\) −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 0.958246 0.285945i \(-0.0923076\pi\)
−0.726759 + 0.686893i \(0.758974\pi\)
\(500\) 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 0.996848 + 0.0793318i \(0.0252787\pi\)
−0.429721 + 0.902962i \(0.641388\pi\)
\(510\) 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 −0.993011 0.118020i \(-0.962345\pi\)
0.598714 + 0.800963i \(0.295679\pi\)
\(522\) 0 0
\(523\) −15.1817 26.2956i −0.663852 1.14982i −0.979595 0.200980i \(-0.935587\pi\)
0.315744 0.948844i \(-0.397746\pi\)
\(524\) 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 0.848165 0.529732i \(-0.177708\pi\)
−0.882844 + 0.469666i \(0.844374\pi\)
\(542\) 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 −0.721417 0.692501i \(-0.756509\pi\)
0.960432 + 0.278515i \(0.0898423\pi\)
\(558\) 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 −0.557191 0.830384i \(-0.688121\pi\)
0.997729 + 0.0673499i \(0.0214544\pi\)
\(564\) 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 0.772169 0.635417i \(-0.219172\pi\)
−0.936372 + 0.351009i \(0.885839\pi\)
\(570\) 0 0
\(571\) −1.19874 + 2.07629i −0.0501659 + 0.0868899i −0.890018 0.455926i \(-0.849308\pi\)
0.839852 + 0.542815i \(0.182642\pi\)
\(572\) 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 0.465768 + 0.884907i \(0.345778\pi\)
−0.999236 + 0.0390869i \(0.987555\pi\)
\(578\) 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 0.985330 + 0.170660i \(0.0545898\pi\)
−0.344869 + 0.938651i \(0.612077\pi\)
\(594\) 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 0.346298 + 0.938125i \(0.387439\pi\)
−0.985589 + 0.169159i \(0.945895\pi\)
\(600\) 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 0.995782 0.0917548i \(-0.0292476\pi\)
−0.577353 + 0.816495i \(0.695914\pi\)
\(608\) −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 −0.661937 0.749560i \(-0.730265\pi\)
0.980106 + 0.198474i \(0.0635986\pi\)
\(614\) −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 −0.556264 0.831005i \(-0.687766\pi\)
0.997804 + 0.0662365i \(0.0210992\pi\)
\(620\) −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 −0.804733 0.593636i \(-0.797692\pi\)
0.916471 + 0.400101i \(0.131025\pi\)
\(642\) 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 −0.939732 0.341912i \(-0.888926\pi\)
0.765970 + 0.642876i \(0.222259\pi\)
\(648\) 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 0.515560 0.856853i \(-0.327584\pi\)
−0.999837 + 0.0180618i \(0.994250\pi\)
\(654\) 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 −0.705770 0.708441i \(-0.749399\pi\)
0.966413 + 0.256994i \(0.0827321\pi\)
\(662\) −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 0.602231 0.798322i \(-0.294279\pi\)
−0.992482 + 0.122387i \(0.960945\pi\)
\(678\) 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 −0.950282 0.311391i \(-0.899205\pi\)
0.744813 + 0.667273i \(0.232539\pi\)
\(684\) 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 0.803638 0.595119i \(-0.202895\pi\)
−0.917207 + 0.398411i \(0.869562\pi\)
\(692\) −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 −0.953300 0.302026i \(-0.902337\pi\)
0.215088 0.976595i \(-0.430996\pi\)
\(710\) −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 −0.980795 0.195039i \(-0.937517\pi\)
0.321489 0.946913i \(-0.395817\pi\)
\(720\) 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 −0.999364 0.0356568i \(-0.988648\pi\)
0.468802 0.883303i \(-0.344686\pi\)
\(734\) −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 −0.675690 0.737186i \(-0.736154\pi\)
0.976267 + 0.216572i \(0.0694877\pi\)
\(740\) −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 0.999965 + 0.00834907i \(0.00265762\pi\)
−0.492752 + 0.870170i \(0.664009\pi\)
\(752\) 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 0.875866 + 0.482554i \(0.160291\pi\)
−0.0200287 + 0.999799i \(0.506376\pi\)
\(762\) 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 −0.686141 0.727469i \(-0.740697\pi\)
0.973077 + 0.230481i \(0.0740300\pi\)
\(774\) 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 −0.0470081 + 0.998895i \(0.514969\pi\)
−0.841564 + 0.540157i \(0.818365\pi\)
\(788\) −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