Properties

Label 1470.2.g.k.589.6
Level $1470$
Weight $2$
Character 1470.589
Analytic conductor $11.738$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1698758656.6
Defining polynomial: \(x^{8} + 18 x^{6} + 97 x^{4} + 176 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.6
Root \(-2.16053i\) of defining polynomial
Character \(\chi\) \(=\) 1470.589
Dual form 1470.2.g.k.589.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.0743018 + 2.23483i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.0743018 + 2.23483i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(-2.23483 + 0.0743018i) q^{10} -3.05545 q^{11} +1.00000i q^{12} -1.64124i q^{13} +(2.23483 - 0.0743018i) q^{15} +1.00000 q^{16} -2.90685i q^{17} -1.00000i q^{18} -2.21016 q^{19} +(-0.0743018 - 2.23483i) q^{20} -3.05545i q^{22} -1.78984i q^{23} -1.00000 q^{24} +(-4.98896 + 0.332104i) q^{25} +1.64124 q^{26} +1.00000i q^{27} -5.58667 q^{29} +(0.0743018 + 2.23483i) q^{30} +0.944547 q^{31} +1.00000i q^{32} +3.05545i q^{33} +2.90685 q^{34} +1.00000 q^{36} -10.7123i q^{37} -2.21016i q^{38} -1.64124 q^{39} +(2.23483 - 0.0743018i) q^{40} +6.67982 q^{41} -10.5021i q^{43} +3.05545 q^{44} +(-0.0743018 - 2.23483i) q^{45} +1.78984 q^{46} +11.3765i q^{47} -1.00000i q^{48} +(-0.332104 - 4.98896i) q^{50} -2.90685 q^{51} +1.64124i q^{52} -5.78984i q^{53} -1.00000 q^{54} +(-0.227026 - 6.82843i) q^{55} +2.21016i q^{57} -5.58667i q^{58} +5.97792 q^{59} +(-2.23483 + 0.0743018i) q^{60} +0.445811 q^{61} +0.944547i q^{62} -1.00000 q^{64} +(3.66790 - 0.121947i) q^{65} -3.05545 q^{66} +1.26561i q^{67} +2.90685i q^{68} -1.78984 q^{69} -14.8523 q^{71} +1.00000i q^{72} -7.91636i q^{73} +10.7123 q^{74} +(0.332104 + 4.98896i) q^{75} +2.21016 q^{76} -1.64124i q^{78} -14.2990 q^{79} +(0.0743018 + 2.23483i) q^{80} +1.00000 q^{81} +6.67982i q^{82} -0.874366i q^{83} +(6.49632 - 0.215984i) q^{85} +10.5021 q^{86} +5.58667i q^{87} +3.05545i q^{88} -17.5083 q^{89} +(2.23483 - 0.0743018i) q^{90} +1.78984i q^{92} -0.944547i q^{93} -11.3765 q^{94} +(-0.164219 - 4.93933i) q^{95} +1.00000 q^{96} -10.4476i q^{97} +3.05545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + 8q^{16} - 24q^{19} - 4q^{20} - 8q^{24} + 4q^{25} + 16q^{29} + 4q^{30} + 32q^{31} - 8q^{34} + 8q^{36} + 24q^{41} - 4q^{45} + 8q^{46} - 4q^{50} + 8q^{51} - 8q^{54} - 40q^{59} + 24q^{61} - 8q^{64} + 28q^{65} - 8q^{69} - 40q^{71} + 16q^{74} + 4q^{75} + 24q^{76} + 16q^{79} + 4q^{80} + 8q^{81} + 28q^{85} + 8q^{86} - 88q^{89} - 24q^{94} + 24q^{95} + 8q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 0.0743018 + 2.23483i 0.0332288 + 0.999448i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −2.23483 + 0.0743018i −0.706716 + 0.0234963i
\(11\) −3.05545 −0.921254 −0.460627 0.887594i \(-0.652375\pi\)
−0.460627 + 0.887594i \(0.652375\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.64124i 0.455198i −0.973755 0.227599i \(-0.926912\pi\)
0.973755 0.227599i \(-0.0730875\pi\)
\(14\) 0 0
\(15\) 2.23483 0.0743018i 0.577031 0.0191846i
\(16\) 1.00000 0.250000
\(17\) 2.90685i 0.705014i −0.935809 0.352507i \(-0.885329\pi\)
0.935809 0.352507i \(-0.114671\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −2.21016 −0.507045 −0.253522 0.967330i \(-0.581589\pi\)
−0.253522 + 0.967330i \(0.581589\pi\)
\(20\) −0.0743018 2.23483i −0.0166144 0.499724i
\(21\) 0 0
\(22\) 3.05545i 0.651425i
\(23\) 1.78984i 0.373208i −0.982435 0.186604i \(-0.940252\pi\)
0.982435 0.186604i \(-0.0597481\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.98896 + 0.332104i −0.997792 + 0.0664208i
\(26\) 1.64124 0.321873
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −5.58667 −1.03742 −0.518710 0.854951i \(-0.673587\pi\)
−0.518710 + 0.854951i \(0.673587\pi\)
\(30\) 0.0743018 + 2.23483i 0.0135656 + 0.408023i
\(31\) 0.944547 0.169646 0.0848228 0.996396i \(-0.472968\pi\)
0.0848228 + 0.996396i \(0.472968\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.05545i 0.531886i
\(34\) 2.90685 0.498521
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 10.7123i 1.76109i −0.473960 0.880546i \(-0.657176\pi\)
0.473960 0.880546i \(-0.342824\pi\)
\(38\) 2.21016i 0.358535i
\(39\) −1.64124 −0.262809
\(40\) 2.23483 0.0743018i 0.353358 0.0117481i
\(41\) 6.67982 1.04321 0.521607 0.853186i \(-0.325333\pi\)
0.521607 + 0.853186i \(0.325333\pi\)
\(42\) 0 0
\(43\) 10.5021i 1.60156i −0.598957 0.800781i \(-0.704418\pi\)
0.598957 0.800781i \(-0.295582\pi\)
\(44\) 3.05545 0.460627
\(45\) −0.0743018 2.23483i −0.0110763 0.333149i
\(46\) 1.78984 0.263898
\(47\) 11.3765i 1.65944i 0.558183 + 0.829718i \(0.311499\pi\)
−0.558183 + 0.829718i \(0.688501\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) −0.332104 4.98896i −0.0469666 0.705545i
\(51\) −2.90685 −0.407040
\(52\) 1.64124i 0.227599i
\(53\) 5.78984i 0.795296i −0.917538 0.397648i \(-0.869827\pi\)
0.917538 0.397648i \(-0.130173\pi\)
\(54\) −1.00000 −0.136083
\(55\) −0.227026 6.82843i −0.0306121 0.920745i
\(56\) 0 0
\(57\) 2.21016i 0.292742i
\(58\) 5.58667i 0.733566i
\(59\) 5.97792 0.778259 0.389129 0.921183i \(-0.372776\pi\)
0.389129 + 0.921183i \(0.372776\pi\)
\(60\) −2.23483 + 0.0743018i −0.288516 + 0.00959232i
\(61\) 0.445811 0.0570802 0.0285401 0.999593i \(-0.490914\pi\)
0.0285401 + 0.999593i \(0.490914\pi\)
\(62\) 0.944547i 0.119958i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.66790 0.121947i 0.454946 0.0151257i
\(66\) −3.05545 −0.376100
\(67\) 1.26561i 0.154619i 0.997007 + 0.0773094i \(0.0246329\pi\)
−0.997007 + 0.0773094i \(0.975367\pi\)
\(68\) 2.90685i 0.352507i
\(69\) −1.78984 −0.215472
\(70\) 0 0
\(71\) −14.8523 −1.76264 −0.881321 0.472518i \(-0.843345\pi\)
−0.881321 + 0.472518i \(0.843345\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 7.91636i 0.926540i −0.886217 0.463270i \(-0.846676\pi\)
0.886217 0.463270i \(-0.153324\pi\)
\(74\) 10.7123 1.24528
\(75\) 0.332104 + 4.98896i 0.0383481 + 0.576075i
\(76\) 2.21016 0.253522
\(77\) 0 0
\(78\) 1.64124i 0.185834i
\(79\) −14.2990 −1.60876 −0.804380 0.594115i \(-0.797503\pi\)
−0.804380 + 0.594115i \(0.797503\pi\)
\(80\) 0.0743018 + 2.23483i 0.00830719 + 0.249862i
\(81\) 1.00000 0.111111
\(82\) 6.67982i 0.737663i
\(83\) 0.874366i 0.0959741i −0.998848 0.0479871i \(-0.984719\pi\)
0.998848 0.0479871i \(-0.0152806\pi\)
\(84\) 0 0
\(85\) 6.49632 0.215984i 0.704625 0.0234268i
\(86\) 10.5021 1.13248
\(87\) 5.58667i 0.598954i
\(88\) 3.05545i 0.325712i
\(89\) −17.5083 −1.85587 −0.927935 0.372741i \(-0.878418\pi\)
−0.927935 + 0.372741i \(0.878418\pi\)
\(90\) 2.23483 0.0743018i 0.235572 0.00783210i
\(91\) 0 0
\(92\) 1.78984i 0.186604i
\(93\) 0.944547i 0.0979450i
\(94\) −11.3765 −1.17340
\(95\) −0.164219 4.93933i −0.0168485 0.506765i
\(96\) 1.00000 0.102062
\(97\) 10.4476i 1.06079i −0.847750 0.530396i \(-0.822043\pi\)
0.847750 0.530396i \(-0.177957\pi\)
\(98\) 0 0
\(99\) 3.05545 0.307085
\(100\) 4.98896 0.332104i 0.498896 0.0332104i
\(101\) 15.4549 1.53782 0.768912 0.639355i \(-0.220798\pi\)
0.768912 + 0.639355i \(0.220798\pi\)
\(102\) 2.90685i 0.287821i
\(103\) 3.12563i 0.307978i −0.988073 0.153989i \(-0.950788\pi\)
0.988073 0.153989i \(-0.0492120\pi\)
\(104\) −1.64124 −0.160937
\(105\) 0 0
\(106\) 5.78984 0.562359
\(107\) 4.78249i 0.462341i −0.972913 0.231170i \(-0.925745\pi\)
0.972913 0.231170i \(-0.0742555\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 9.10355 0.871962 0.435981 0.899956i \(-0.356401\pi\)
0.435981 + 0.899956i \(0.356401\pi\)
\(110\) 6.82843 0.227026i 0.651065 0.0216460i
\(111\) −10.7123 −1.01677
\(112\) 0 0
\(113\) 14.3982i 1.35447i −0.735766 0.677236i \(-0.763178\pi\)
0.735766 0.677236i \(-0.236822\pi\)
\(114\) −2.21016 −0.207000
\(115\) 4.00000 0.132989i 0.373002 0.0124012i
\(116\) 5.58667 0.518710
\(117\) 1.64124i 0.151733i
\(118\) 5.97792i 0.550312i
\(119\) 0 0
\(120\) −0.0743018 2.23483i −0.00678279 0.204011i
\(121\) −1.66421 −0.151292
\(122\) 0.445811i 0.0403618i
\(123\) 6.67982i 0.602299i
\(124\) −0.944547 −0.0848228
\(125\) −1.11289 11.1248i −0.0995396 0.995034i
\(126\) 0 0
\(127\) 8.45405i 0.750176i −0.926989 0.375088i \(-0.877613\pi\)
0.926989 0.375088i \(-0.122387\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −10.5021 −0.924663
\(130\) 0.121947 + 3.66790i 0.0106955 + 0.321696i
\(131\) 8.32106 0.727015 0.363507 0.931591i \(-0.381579\pi\)
0.363507 + 0.931591i \(0.381579\pi\)
\(132\) 3.05545i 0.265943i
\(133\) 0 0
\(134\) −1.26561 −0.109332
\(135\) −2.23483 + 0.0743018i −0.192344 + 0.00639488i
\(136\) −2.90685 −0.249260
\(137\) 9.86701i 0.842996i 0.906829 + 0.421498i \(0.138495\pi\)
−0.906829 + 0.421498i \(0.861505\pi\)
\(138\) 1.78984i 0.152362i
\(139\) −16.9632 −1.43880 −0.719399 0.694597i \(-0.755583\pi\)
−0.719399 + 0.694597i \(0.755583\pi\)
\(140\) 0 0
\(141\) 11.3765 0.958075
\(142\) 14.8523i 1.24638i
\(143\) 5.01473i 0.419353i
\(144\) −1.00000 −0.0833333
\(145\) −0.415100 12.4853i −0.0344722 1.03685i
\(146\) 7.91636 0.655163
\(147\) 0 0
\(148\) 10.7123i 0.880546i
\(149\) −8.04810 −0.659326 −0.329663 0.944099i \(-0.606935\pi\)
−0.329663 + 0.944099i \(0.606935\pi\)
\(150\) −4.98896 + 0.332104i −0.407347 + 0.0271162i
\(151\) −9.97792 −0.811991 −0.405996 0.913875i \(-0.633075\pi\)
−0.405996 + 0.913875i \(0.633075\pi\)
\(152\) 2.21016i 0.179267i
\(153\) 2.90685i 0.235005i
\(154\) 0 0
\(155\) 0.0701816 + 2.11091i 0.00563712 + 0.169552i
\(156\) 1.64124 0.131404
\(157\) 12.6676i 1.01099i −0.862831 0.505493i \(-0.831311\pi\)
0.862831 0.505493i \(-0.168689\pi\)
\(158\) 14.2990i 1.13757i
\(159\) −5.78984 −0.459164
\(160\) −2.23483 + 0.0743018i −0.176679 + 0.00587407i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 23.5646i 1.84572i 0.385134 + 0.922861i \(0.374155\pi\)
−0.385134 + 0.922861i \(0.625845\pi\)
\(164\) −6.67982 −0.521607
\(165\) −6.82843 + 0.227026i −0.531592 + 0.0176739i
\(166\) 0.874366 0.0678639
\(167\) 18.0818i 1.39921i 0.714528 + 0.699607i \(0.246642\pi\)
−0.714528 + 0.699607i \(0.753358\pi\)
\(168\) 0 0
\(169\) 10.3063 0.792795
\(170\) 0.215984 + 6.49632i 0.0165652 + 0.498245i
\(171\) 2.21016 0.169015
\(172\) 10.5021i 0.800781i
\(173\) 1.93845i 0.147377i 0.997281 + 0.0736887i \(0.0234771\pi\)
−0.997281 + 0.0736887i \(0.976523\pi\)
\(174\) −5.58667 −0.423525
\(175\) 0 0
\(176\) −3.05545 −0.230313
\(177\) 5.97792i 0.449328i
\(178\) 17.5083i 1.31230i
\(179\) 24.4463 1.82720 0.913602 0.406609i \(-0.133289\pi\)
0.913602 + 0.406609i \(0.133289\pi\)
\(180\) 0.0743018 + 2.23483i 0.00553813 + 0.166575i
\(181\) −16.9788 −1.26202 −0.631012 0.775773i \(-0.717360\pi\)
−0.631012 + 0.775773i \(0.717360\pi\)
\(182\) 0 0
\(183\) 0.445811i 0.0329553i
\(184\) −1.78984 −0.131949
\(185\) 23.9402 0.795944i 1.76012 0.0585189i
\(186\) 0.944547 0.0692576
\(187\) 8.88174i 0.649497i
\(188\) 11.3765i 0.829718i
\(189\) 0 0
\(190\) 4.93933 0.164219i 0.358337 0.0119137i
\(191\) 0.741377 0.0536442 0.0268221 0.999640i \(-0.491461\pi\)
0.0268221 + 0.999640i \(0.491461\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 6.11091i 0.439873i 0.975514 + 0.219936i \(0.0705850\pi\)
−0.975514 + 0.219936i \(0.929415\pi\)
\(194\) 10.4476 0.750093
\(195\) −0.121947 3.66790i −0.00873281 0.262663i
\(196\) 0 0
\(197\) 20.6832i 1.47362i 0.676100 + 0.736810i \(0.263669\pi\)
−0.676100 + 0.736810i \(0.736331\pi\)
\(198\) 3.05545i 0.217142i
\(199\) −12.0702 −0.855632 −0.427816 0.903866i \(-0.640717\pi\)
−0.427816 + 0.903866i \(0.640717\pi\)
\(200\) 0.332104 + 4.98896i 0.0234833 + 0.352773i
\(201\) 1.26561 0.0892692
\(202\) 15.4549i 1.08741i
\(203\) 0 0
\(204\) 2.90685 0.203520
\(205\) 0.496323 + 14.9283i 0.0346647 + 1.04264i
\(206\) 3.12563 0.217773
\(207\) 1.78984i 0.124403i
\(208\) 1.64124i 0.113799i
\(209\) 6.75303 0.467117
\(210\) 0 0
\(211\) 2.95153 0.203192 0.101596 0.994826i \(-0.467605\pi\)
0.101596 + 0.994826i \(0.467605\pi\)
\(212\) 5.78984i 0.397648i
\(213\) 14.8523i 1.01766i
\(214\) 4.78249 0.326924
\(215\) 23.4706 0.780329i 1.60068 0.0532180i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 9.10355i 0.616570i
\(219\) −7.91636 −0.534938
\(220\) 0.227026 + 6.82843i 0.0153061 + 0.460372i
\(221\) −4.77083 −0.320921
\(222\) 10.7123i 0.718963i
\(223\) 11.7678i 0.788027i 0.919105 + 0.394014i \(0.128914\pi\)
−0.919105 + 0.394014i \(0.871086\pi\)
\(224\) 0 0
\(225\) 4.98896 0.332104i 0.332597 0.0221403i
\(226\) 14.3982 0.957756
\(227\) 13.2365i 0.878540i 0.898355 + 0.439270i \(0.144763\pi\)
−0.898355 + 0.439270i \(0.855237\pi\)
\(228\) 2.21016i 0.146371i
\(229\) −25.2448 −1.66822 −0.834111 0.551597i \(-0.814019\pi\)
−0.834111 + 0.551597i \(0.814019\pi\)
\(230\) 0.132989 + 4.00000i 0.00876900 + 0.263752i
\(231\) 0 0
\(232\) 5.58667i 0.366783i
\(233\) 3.32842i 0.218052i −0.994039 0.109026i \(-0.965227\pi\)
0.994039 0.109026i \(-0.0347732\pi\)
\(234\) −1.64124 −0.107291
\(235\) −25.4246 + 0.845296i −1.65852 + 0.0551410i
\(236\) −5.97792 −0.389129
\(237\) 14.2990i 0.928819i
\(238\) 0 0
\(239\) −24.8713 −1.60879 −0.804396 0.594094i \(-0.797511\pi\)
−0.804396 + 0.594094i \(0.797511\pi\)
\(240\) 2.23483 0.0743018i 0.144258 0.00479616i
\(241\) 10.3535 0.666931 0.333465 0.942762i \(-0.391782\pi\)
0.333465 + 0.942762i \(0.391782\pi\)
\(242\) 1.66421i 0.106979i
\(243\) 1.00000i 0.0641500i
\(244\) −0.445811 −0.0285401
\(245\) 0 0
\(246\) 6.67982 0.425890
\(247\) 3.62740i 0.230806i
\(248\) 0.944547i 0.0599788i
\(249\) −0.874366 −0.0554107
\(250\) 11.1248 1.11289i 0.703595 0.0703851i
\(251\) 16.5502 1.04464 0.522321 0.852749i \(-0.325066\pi\)
0.522321 + 0.852749i \(0.325066\pi\)
\(252\) 0 0
\(253\) 5.46878i 0.343819i
\(254\) 8.45405 0.530454
\(255\) −0.215984 6.49632i −0.0135254 0.406816i
\(256\) 1.00000 0.0625000
\(257\) 24.4546i 1.52543i −0.646732 0.762717i \(-0.723865\pi\)
0.646732 0.762717i \(-0.276135\pi\)
\(258\) 10.5021i 0.653835i
\(259\) 0 0
\(260\) −3.66790 + 0.121947i −0.227473 + 0.00756283i
\(261\) 5.58667 0.345806
\(262\) 8.32106i 0.514077i
\(263\) 12.5091i 0.771346i 0.922635 + 0.385673i \(0.126031\pi\)
−0.922635 + 0.385673i \(0.873969\pi\)
\(264\) 3.05545 0.188050
\(265\) 12.9393 0.430196i 0.794857 0.0264267i
\(266\) 0 0
\(267\) 17.5083i 1.07149i
\(268\) 1.26561i 0.0773094i
\(269\) 18.9666 1.15641 0.578207 0.815890i \(-0.303753\pi\)
0.578207 + 0.815890i \(0.303753\pi\)
\(270\) −0.0743018 2.23483i −0.00452186 0.136008i
\(271\) 19.6638 1.19449 0.597247 0.802058i \(-0.296261\pi\)
0.597247 + 0.802058i \(0.296261\pi\)
\(272\) 2.90685i 0.176254i
\(273\) 0 0
\(274\) −9.86701 −0.596088
\(275\) 15.2435 1.01473i 0.919219 0.0611904i
\(276\) 1.78984 0.107736
\(277\) 6.13998i 0.368915i −0.982840 0.184458i \(-0.940947\pi\)
0.982840 0.184458i \(-0.0590529\pi\)
\(278\) 16.9632i 1.01738i
\(279\) −0.944547 −0.0565486
\(280\) 0 0
\(281\) −12.1330 −0.723793 −0.361897 0.932218i \(-0.617871\pi\)
−0.361897 + 0.932218i \(0.617871\pi\)
\(282\) 11.3765i 0.677462i
\(283\) 17.4172i 1.03535i 0.855578 + 0.517674i \(0.173202\pi\)
−0.855578 + 0.517674i \(0.826798\pi\)
\(284\) 14.8523 0.881321
\(285\) −4.93933 + 0.164219i −0.292581 + 0.00972747i
\(286\) −5.01473 −0.296527
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 8.55023 0.502955
\(290\) 12.4853 0.415100i 0.733161 0.0243755i
\(291\) −10.4476 −0.612448
\(292\) 7.91636i 0.463270i
\(293\) 23.7521i 1.38762i 0.720160 + 0.693808i \(0.244068\pi\)
−0.720160 + 0.693808i \(0.755932\pi\)
\(294\) 0 0
\(295\) 0.444170 + 13.3596i 0.0258606 + 0.777829i
\(296\) −10.7123 −0.622640
\(297\) 3.05545i 0.177295i
\(298\) 8.04810i 0.466214i
\(299\) −2.93756 −0.169883
\(300\) −0.332104 4.98896i −0.0191740 0.288038i
\(301\) 0 0
\(302\) 9.97792i 0.574165i
\(303\) 15.4549i 0.887863i
\(304\) −2.21016 −0.126761
\(305\) 0.0331245 + 0.996313i 0.00189671 + 0.0570487i
\(306\) −2.90685 −0.166174
\(307\) 7.90812i 0.451340i −0.974204 0.225670i \(-0.927543\pi\)
0.974204 0.225670i \(-0.0724572\pi\)
\(308\) 0 0
\(309\) −3.12563 −0.177811
\(310\) −2.11091 + 0.0701816i −0.119891 + 0.00398604i
\(311\) −10.0772 −0.571424 −0.285712 0.958316i \(-0.592230\pi\)
−0.285712 + 0.958316i \(0.592230\pi\)
\(312\) 1.64124i 0.0929169i
\(313\) 20.3844i 1.15219i −0.817381 0.576097i \(-0.804575\pi\)
0.817381 0.576097i \(-0.195425\pi\)
\(314\) 12.6676 0.714875
\(315\) 0 0
\(316\) 14.2990 0.804380
\(317\) 0.321063i 0.0180327i −0.999959 0.00901634i \(-0.997130\pi\)
0.999959 0.00901634i \(-0.00287003\pi\)
\(318\) 5.78984i 0.324678i
\(319\) 17.0698 0.955726
\(320\) −0.0743018 2.23483i −0.00415360 0.124931i
\(321\) −4.78249 −0.266932
\(322\) 0 0
\(323\) 6.42459i 0.357474i
\(324\) −1.00000 −0.0555556
\(325\) 0.545062 + 8.18807i 0.0302346 + 0.454193i
\(326\) −23.5646 −1.30512
\(327\) 9.10355i 0.503428i
\(328\) 6.67982i 0.368832i
\(329\) 0 0
\(330\) −0.227026 6.82843i −0.0124973 0.375893i
\(331\) −16.6084 −0.912880 −0.456440 0.889754i \(-0.650876\pi\)
−0.456440 + 0.889754i \(0.650876\pi\)
\(332\) 0.874366i 0.0479871i
\(333\) 10.7123i 0.587031i
\(334\) −18.0818 −0.989394
\(335\) −2.82843 + 0.0940371i −0.154533 + 0.00513780i
\(336\) 0 0
\(337\) 1.91118i 0.104108i −0.998644 0.0520542i \(-0.983423\pi\)
0.998644 0.0520542i \(-0.0165769\pi\)
\(338\) 10.3063i 0.560591i
\(339\) −14.3982 −0.782005
\(340\) −6.49632 + 0.215984i −0.352313 + 0.0117134i
\(341\) −2.88602 −0.156287
\(342\) 2.21016i 0.119512i
\(343\) 0 0
\(344\) −10.5021 −0.566238
\(345\) −0.132989 4.00000i −0.00715986 0.215353i
\(346\) −1.93845 −0.104212
\(347\) 7.90812i 0.424530i −0.977212 0.212265i \(-0.931916\pi\)
0.977212 0.212265i \(-0.0680840\pi\)
\(348\) 5.58667i 0.299477i
\(349\) 23.5273 1.25939 0.629693 0.776844i \(-0.283181\pi\)
0.629693 + 0.776844i \(0.283181\pi\)
\(350\) 0 0
\(351\) 1.64124 0.0876029
\(352\) 3.05545i 0.162856i
\(353\) 22.9718i 1.22267i 0.791373 + 0.611333i \(0.209366\pi\)
−0.791373 + 0.611333i \(0.790634\pi\)
\(354\) 5.97792 0.317723
\(355\) −1.10355 33.1924i −0.0585704 1.76167i
\(356\) 17.5083 0.927935
\(357\) 0 0
\(358\) 24.4463i 1.29203i
\(359\) −11.0264 −0.581950 −0.290975 0.956731i \(-0.593980\pi\)
−0.290975 + 0.956731i \(0.593980\pi\)
\(360\) −2.23483 + 0.0743018i −0.117786 + 0.00391605i
\(361\) −14.1152 −0.742906
\(362\) 16.9788i 0.892386i
\(363\) 1.66421i 0.0873483i
\(364\) 0 0
\(365\) 17.6918 0.588200i 0.926029 0.0307878i
\(366\) 0.445811 0.0233029
\(367\) 10.1446i 0.529546i 0.964311 + 0.264773i \(0.0852970\pi\)
−0.964311 + 0.264773i \(0.914703\pi\)
\(368\) 1.78984i 0.0933020i
\(369\) −6.67982 −0.347738
\(370\) 0.795944 + 23.9402i 0.0413791 + 1.24459i
\(371\) 0 0
\(372\) 0.944547i 0.0489725i
\(373\) 26.5021i 1.37223i 0.727493 + 0.686115i \(0.240685\pi\)
−0.727493 + 0.686115i \(0.759315\pi\)
\(374\) −8.88174 −0.459264
\(375\) −11.1248 + 1.11289i −0.574483 + 0.0574692i
\(376\) 11.3765 0.586699
\(377\) 9.16907i 0.472231i
\(378\) 0 0
\(379\) −29.4142 −1.51091 −0.755453 0.655203i \(-0.772583\pi\)
−0.755453 + 0.655203i \(0.772583\pi\)
\(380\) 0.164219 + 4.93933i 0.00842424 + 0.253382i
\(381\) −8.45405 −0.433114
\(382\) 0.741377i 0.0379322i
\(383\) 3.64249i 0.186123i −0.995660 0.0930613i \(-0.970335\pi\)
0.995660 0.0930613i \(-0.0296653\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −6.11091 −0.311037
\(387\) 10.5021i 0.533854i
\(388\) 10.4476i 0.530396i
\(389\) 23.7938 1.20639 0.603196 0.797593i \(-0.293894\pi\)
0.603196 + 0.797593i \(0.293894\pi\)
\(390\) 3.66790 0.121947i 0.185731 0.00617503i
\(391\) −5.20280 −0.263117
\(392\) 0 0
\(393\) 8.32106i 0.419742i
\(394\) −20.6832 −1.04201
\(395\) −1.06244 31.9558i −0.0534572 1.60787i
\(396\) −3.05545 −0.153542
\(397\) 9.76129i 0.489905i 0.969535 + 0.244953i \(0.0787724\pi\)
−0.969535 + 0.244953i \(0.921228\pi\)
\(398\) 12.0702i 0.605024i
\(399\) 0 0
\(400\) −4.98896 + 0.332104i −0.249448 + 0.0166052i
\(401\) 9.97792 0.498273 0.249137 0.968468i \(-0.419853\pi\)
0.249137 + 0.968468i \(0.419853\pi\)
\(402\) 1.26561i 0.0631229i
\(403\) 1.55023i 0.0772224i
\(404\) −15.4549 −0.768912
\(405\) 0.0743018 + 2.23483i 0.00369209 + 0.111050i
\(406\) 0 0
\(407\) 32.7309i 1.62241i
\(408\) 2.90685i 0.143910i
\(409\) −35.1837 −1.73972 −0.869862 0.493295i \(-0.835792\pi\)
−0.869862 + 0.493295i \(0.835792\pi\)
\(410\) −14.9283 + 0.496323i −0.737256 + 0.0245116i
\(411\) 9.86701 0.486704
\(412\) 3.12563i 0.153989i
\(413\) 0 0
\(414\) −1.78984 −0.0879660
\(415\) 1.95406 0.0649669i 0.0959211 0.00318910i
\(416\) 1.64124 0.0804684
\(417\) 16.9632i 0.830691i
\(418\) 6.75303i 0.330302i
\(419\) −18.6274 −0.910009 −0.455004 0.890489i \(-0.650362\pi\)
−0.455004 + 0.890489i \(0.650362\pi\)
\(420\) 0 0
\(421\) 31.6464 1.54235 0.771176 0.636622i \(-0.219669\pi\)
0.771176 + 0.636622i \(0.219669\pi\)
\(422\) 2.95153i 0.143678i
\(423\) 11.3765i 0.553145i
\(424\) −5.78984 −0.281180
\(425\) 0.965377 + 14.5021i 0.0468277 + 0.703458i
\(426\) −14.8523 −0.719595
\(427\) 0 0
\(428\) 4.78249i 0.231170i
\(429\) 5.01473 0.242113
\(430\) 0.780329 + 23.4706i 0.0376308 + 1.13185i
\(431\) −14.8046 −0.713111 −0.356556 0.934274i \(-0.616049\pi\)
−0.356556 + 0.934274i \(0.616049\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 4.24731i 0.204113i −0.994779 0.102056i \(-0.967458\pi\)
0.994779 0.102056i \(-0.0325422\pi\)
\(434\) 0 0
\(435\) −12.4853 + 0.415100i −0.598623 + 0.0199025i
\(436\) −9.10355 −0.435981
\(437\) 3.95583i 0.189233i
\(438\) 7.91636i 0.378258i
\(439\) 2.22880 0.106375 0.0531874 0.998585i \(-0.483062\pi\)
0.0531874 + 0.998585i \(0.483062\pi\)
\(440\) −6.82843 + 0.227026i −0.325532 + 0.0108230i
\(441\) 0 0
\(442\) 4.77083i 0.226925i
\(443\) 4.64213i 0.220554i 0.993901 + 0.110277i \(0.0351738\pi\)
−0.993901 + 0.110277i \(0.964826\pi\)
\(444\) 10.7123 0.508384
\(445\) −1.30089 39.1280i −0.0616683 1.85485i
\(446\) −11.7678 −0.557220
\(447\) 8.04810i 0.380662i
\(448\) 0 0
\(449\) 3.69059 0.174170 0.0870849 0.996201i \(-0.472245\pi\)
0.0870849 + 0.996201i \(0.472245\pi\)
\(450\) 0.332104 + 4.98896i 0.0156555 + 0.235182i
\(451\) −20.4099 −0.961064
\(452\) 14.3982i 0.677236i
\(453\) 9.97792i 0.468803i
\(454\) −13.2365 −0.621222
\(455\) 0 0
\(456\) 2.21016 0.103500
\(457\) 2.72972i 0.127691i −0.997960 0.0638455i \(-0.979664\pi\)
0.997960 0.0638455i \(-0.0203365\pi\)
\(458\) 25.2448i 1.17961i
\(459\) 2.90685 0.135680
\(460\) −4.00000 + 0.132989i −0.186501 + 0.00620062i
\(461\) 11.8072 0.549918 0.274959 0.961456i \(-0.411336\pi\)
0.274959 + 0.961456i \(0.411336\pi\)
\(462\) 0 0
\(463\) 2.40561i 0.111798i −0.998436 0.0558990i \(-0.982198\pi\)
0.998436 0.0558990i \(-0.0178025\pi\)
\(464\) −5.58667 −0.259355
\(465\) 2.11091 0.0701816i 0.0978909 0.00325459i
\(466\) 3.32842 0.154186
\(467\) 14.6612i 0.678437i −0.940708 0.339219i \(-0.889837\pi\)
0.940708 0.339219i \(-0.110163\pi\)
\(468\) 1.64124i 0.0758663i
\(469\) 0 0
\(470\) −0.845296 25.4246i −0.0389906 1.17275i
\(471\) −12.6676 −0.583693
\(472\) 5.97792i 0.275156i
\(473\) 32.0888i 1.47545i
\(474\) −14.2990 −0.656774
\(475\) 11.0264 0.734003i 0.505925 0.0336783i
\(476\) 0 0
\(477\) 5.78984i 0.265099i
\(478\) 24.8713i 1.13759i
\(479\) −11.8934 −0.543422 −0.271711 0.962379i \(-0.587590\pi\)
−0.271711 + 0.962379i \(0.587590\pi\)
\(480\) 0.0743018 + 2.23483i 0.00339140 + 0.102006i
\(481\) −17.5815 −0.801645
\(482\) 10.3535i 0.471591i
\(483\) 0 0
\(484\) 1.66421 0.0756458
\(485\) 23.3486 0.776274i 1.06021 0.0352488i
\(486\) 1.00000 0.0453609
\(487\) 35.5018i 1.60874i −0.594129 0.804370i \(-0.702503\pi\)
0.594129 0.804370i \(-0.297497\pi\)
\(488\) 0.445811i 0.0201809i
\(489\) 23.5646 1.06563
\(490\) 0 0
\(491\) −0.978284 −0.0441493 −0.0220747 0.999756i \(-0.507027\pi\)
−0.0220747 + 0.999756i \(0.507027\pi\)
\(492\) 6.67982i 0.301150i
\(493\) 16.2396i 0.731395i
\(494\) −3.62740 −0.163204
\(495\) 0.227026 + 6.82843i 0.0102040 + 0.306915i
\(496\) 0.944547 0.0424114
\(497\) 0 0
\(498\) 0.874366i 0.0391813i
\(499\) −11.7340 −0.525287 −0.262644 0.964893i \(-0.584594\pi\)
−0.262644 + 0.964893i \(0.584594\pi\)
\(500\) 1.11289 + 11.1248i 0.0497698 + 0.497517i
\(501\) 18.0818 0.807837
\(502\) 16.5502i 0.738674i
\(503\) 17.3618i 0.774125i −0.922054 0.387062i \(-0.873490\pi\)
0.922054 0.387062i \(-0.126510\pi\)
\(504\) 0 0
\(505\) 1.14833 + 34.5392i 0.0511000 + 1.53697i
\(506\) −5.46878 −0.243117
\(507\) 10.3063i 0.457720i
\(508\) 8.45405i 0.375088i
\(509\) −25.8293 −1.14486 −0.572432 0.819952i \(-0.694000\pi\)
−0.572432 + 0.819952i \(0.694000\pi\)
\(510\) 6.49632 0.215984i 0.287662 0.00956394i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 2.21016i 0.0975808i
\(514\) 24.4546 1.07864
\(515\) 6.98527 0.232240i 0.307808 0.0102337i
\(516\) 10.5021 0.462331
\(517\) 34.7604i 1.52876i
\(518\) 0 0
\(519\) 1.93845 0.0850884
\(520\) −0.121947 3.66790i −0.00534773 0.160848i
\(521\) −24.7466 −1.08417 −0.542083 0.840325i \(-0.682364\pi\)
−0.542083 + 0.840325i \(0.682364\pi\)
\(522\) 5.58667i 0.244522i
\(523\) 1.61574i 0.0706515i 0.999376 + 0.0353258i \(0.0112469\pi\)
−0.999376 + 0.0353258i \(0.988753\pi\)
\(524\) −8.32106 −0.363507
\(525\) 0 0
\(526\) −12.5091 −0.545424
\(527\) 2.74566i 0.119603i
\(528\) 3.05545i 0.132972i
\(529\) 19.7965 0.860716
\(530\) 0.430196 + 12.9393i 0.0186865 + 0.562049i
\(531\) −5.97792 −0.259420
\(532\) 0 0
\(533\) 10.9632i 0.474868i
\(534\) −17.5083 −0.757656
\(535\) 10.6881 0.355347i 0.462085 0.0153630i
\(536\) 1.26561 0.0546660
\(537\) 24.4463i 1.05494i
\(538\) 18.9666i 0.817708i
\(539\) 0 0
\(540\) 2.23483 0.0743018i 0.0961719 0.00319744i
\(541\) 24.7530 1.06422 0.532108 0.846677i \(-0.321400\pi\)
0.532108 + 0.846677i \(0.321400\pi\)
\(542\) 19.6638i 0.844634i
\(543\) 16.9788i 0.728630i
\(544\) 2.90685 0.124630
\(545\) 0.676410 + 20.3449i 0.0289742 + 0.871481i
\(546\) 0 0
\(547\) 44.0524i 1.88354i −0.336253 0.941772i \(-0.609160\pi\)
0.336253 0.941772i \(-0.390840\pi\)
\(548\) 9.86701i 0.421498i
\(549\) −0.445811 −0.0190267
\(550\) 1.01473 + 15.2435i 0.0432682 + 0.649986i
\(551\) 12.3474 0.526018
\(552\) 1.78984i 0.0761808i
\(553\) 0 0
\(554\) 6.13998 0.260863
\(555\) −0.795944 23.9402i −0.0337859 1.01621i
\(556\) 16.9632 0.719399
\(557\) 2.06979i 0.0877000i −0.999038 0.0438500i \(-0.986038\pi\)
0.999038 0.0438500i \(-0.0139624\pi\)
\(558\) 0.944547i 0.0399859i
\(559\) −17.2365 −0.729028
\(560\) 0 0
\(561\) 8.88174 0.374987
\(562\) 12.1330i 0.511799i
\(563\) 9.84493i 0.414914i −0.978244 0.207457i \(-0.933481\pi\)
0.978244 0.207457i \(-0.0665188\pi\)
\(564\) −11.3765 −0.479038
\(565\) 32.1776 1.06981i 1.35372 0.0450074i
\(566\) −17.4172 −0.732101
\(567\) 0 0
\(568\) 14.8523i 0.623188i
\(569\) −13.7561 −0.576686 −0.288343 0.957527i \(-0.593104\pi\)
−0.288343 + 0.957527i \(0.593104\pi\)
\(570\) −0.164219 4.93933i −0.00687836 0.206886i
\(571\) 19.2071 0.803791 0.401896 0.915685i \(-0.368351\pi\)
0.401896 + 0.915685i \(0.368351\pi\)
\(572\) 5.01473i 0.209676i
\(573\) 0.741377i 0.0309715i
\(574\) 0 0
\(575\) 0.594414 + 8.92945i 0.0247888 + 0.372384i
\(576\) 1.00000 0.0416667
\(577\) 37.3072i 1.55312i −0.630043 0.776560i \(-0.716963\pi\)
0.630043 0.776560i \(-0.283037\pi\)
\(578\) 8.55023i 0.355643i
\(579\) 6.11091 0.253961
\(580\) 0.415100 + 12.4853i 0.0172361 + 0.518423i
\(581\) 0 0
\(582\) 10.4476i 0.433066i
\(583\) 17.6906i 0.732669i
\(584\) −7.91636 −0.327581
\(585\) −3.66790 + 0.121947i −0.151649 + 0.00504189i
\(586\) −23.7521 −0.981192
\(587\) 19.5459i 0.806748i −0.915035 0.403374i \(-0.867837\pi\)
0.915035 0.403374i \(-0.132163\pi\)
\(588\) 0 0
\(589\) −2.08760 −0.0860180
\(590\) −13.3596 + 0.444170i −0.550008 + 0.0182862i
\(591\) 20.6832 0.850795
\(592\) 10.7123i 0.440273i
\(593\) 28.9424i 1.18852i 0.804273 + 0.594260i \(0.202555\pi\)
−0.804273 + 0.594260i \(0.797445\pi\)
\(594\) 3.05545 0.125367
\(595\) 0 0
\(596\) 8.04810 0.329663
\(597\) 12.0702i 0.494000i
\(598\) 2.93756i 0.120126i
\(599\) 9.73170 0.397627 0.198813 0.980037i \(-0.436291\pi\)
0.198813 + 0.980037i \(0.436291\pi\)
\(600\) 4.98896 0.332104i 0.203673 0.0135581i
\(601\) 33.4038 1.36257 0.681284 0.732019i \(-0.261422\pi\)
0.681284 + 0.732019i \(0.261422\pi\)
\(602\) 0 0
\(603\) 1.26561i 0.0515396i
\(604\) 9.97792 0.405996
\(605\) −0.123654 3.71923i −0.00502724 0.151208i
\(606\) 15.4549 0.627814
\(607\) 43.2358i 1.75489i 0.479680 + 0.877444i \(0.340753\pi\)
−0.479680 + 0.877444i \(0.659247\pi\)
\(608\) 2.21016i 0.0896337i
\(609\) 0 0
\(610\) −0.996313 + 0.0331245i −0.0403395 + 0.00134117i
\(611\) 18.6716 0.755371
\(612\) 2.90685i 0.117502i
\(613\) 1.79023i 0.0723067i 0.999346 + 0.0361534i \(0.0115105\pi\)
−0.999346 + 0.0361534i \(0.988490\pi\)
\(614\) 7.90812 0.319146
\(615\) 14.9283 0.496323i 0.601967 0.0200137i
\(616\) 0 0
\(617\) 38.2665i 1.54055i −0.637712 0.770275i \(-0.720119\pi\)
0.637712 0.770275i \(-0.279881\pi\)
\(618\) 3.12563i 0.125731i
\(619\) −0.132989 −0.00534526 −0.00267263 0.999996i \(-0.500851\pi\)
−0.00267263 + 0.999996i \(0.500851\pi\)
\(620\) −0.0701816 2.11091i −0.00281856 0.0847760i
\(621\) 1.78984 0.0718239
\(622\) 10.0772i 0.404058i
\(623\) 0 0
\(624\) −1.64124 −0.0657022
\(625\) 24.7794 3.31371i 0.991177 0.132548i
\(626\) 20.3844 0.814724
\(627\) 6.75303i 0.269690i
\(628\) 12.6676i 0.505493i
\(629\) −31.1391 −1.24160
\(630\) 0 0
\(631\) −25.1850 −1.00260 −0.501299 0.865274i \(-0.667145\pi\)
−0.501299 + 0.865274i \(0.667145\pi\)
\(632\) 14.2990i 0.568783i
\(633\) 2.95153i 0.117313i
\(634\) 0.321063 0.0127510
\(635\) 18.8934 0.628151i 0.749761 0.0249274i
\(636\) 5.78984 0.229582
\(637\) 0 0
\(638\) 17.0698i 0.675800i
\(639\) 14.8523 0.587547
\(640\) 2.23483 0.0743018i 0.0883395 0.00293704i
\(641\) −24.5906 −0.971270 −0.485635 0.874162i \(-0.661412\pi\)
−0.485635 + 0.874162i \(0.661412\pi\)
\(642\) 4.78249i 0.188750i
\(643\) 9.15126i 0.360891i −0.983585 0.180445i \(-0.942246\pi\)
0.983585 0.180445i \(-0.0577539\pi\)
\(644\) 0 0
\(645\) −0.780329 23.4706i −0.0307254 0.924152i
\(646\) −6.42459 −0.252772
\(647\) 31.9268i 1.25517i −0.778548 0.627585i \(-0.784043\pi\)
0.778548 0.627585i \(-0.215957\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −18.2652 −0.716973
\(650\) −8.18807 + 0.545062i −0.321163 + 0.0213791i
\(651\) 0 0
\(652\) 23.5646i 0.922861i
\(653\) 3.06244i 0.119843i −0.998203 0.0599213i \(-0.980915\pi\)
0.998203 0.0599213i \(-0.0190850\pi\)
\(654\) 9.10355 0.355977
\(655\) 0.618270 + 18.5962i 0.0241578 + 0.726613i
\(656\) 6.67982 0.260803
\(657\) 7.91636i 0.308847i
\(658\) 0 0
\(659\) 9.16636 0.357071 0.178535 0.983934i \(-0.442864\pi\)
0.178535 + 0.983934i \(0.442864\pi\)
\(660\) 6.82843 0.227026i 0.265796 0.00883696i
\(661\) 31.4181 1.22202 0.611012 0.791621i \(-0.290763\pi\)
0.611012 + 0.791621i \(0.290763\pi\)
\(662\) 16.6084i 0.645503i
\(663\) 4.77083i 0.185284i
\(664\) −0.874366 −0.0339320
\(665\) 0 0
\(666\) −10.7123 −0.415093
\(667\) 9.99927i 0.387173i
\(668\) 18.0818i 0.699607i
\(669\) 11.7678 0.454968
\(670\) −0.0940371 2.82843i −0.00363297 0.109272i
\(671\) −1.36215 −0.0525854
\(672\) 0 0
\(673\) 6.45100i 0.248668i −0.992240 0.124334i \(-0.960321\pi\)
0.992240 0.124334i \(-0.0396794\pi\)
\(674\) 1.91118 0.0736158
\(675\) −0.332104 4.98896i −0.0127827 0.192025i
\(676\) −10.3063 −0.396397
\(677\) 6.01384i 0.231131i −0.993300 0.115565i \(-0.963132\pi\)
0.993300 0.115565i \(-0.0368680\pi\)
\(678\) 14.3982i 0.552961i
\(679\) 0 0
\(680\) −0.215984 6.49632i −0.00828261 0.249123i
\(681\) 13.2365 0.507225
\(682\) 2.88602i 0.110511i
\(683\) 8.92208i 0.341394i −0.985324 0.170697i \(-0.945398\pi\)
0.985324 0.170697i \(-0.0546019\pi\)
\(684\) −2.21016 −0.0845075
\(685\) −22.0511 + 0.733137i −0.842530 + 0.0280117i
\(686\) 0 0
\(687\) 25.2448i 0.963148i
\(688\) 10.5021i 0.400391i
\(689\) −9.50252 −0.362017
\(690\) 4.00000 0.132989i 0.152277 0.00506279i
\(691\) 47.6581 1.81300 0.906499 0.422207i \(-0.138745\pi\)
0.906499 + 0.422207i \(0.138745\pi\)
\(692\) 1.93845i 0.0736887i
\(693\) 0 0
\(694\) 7.90812 0.300188
\(695\) −1.26040 37.9099i −0.0478095 1.43800i
\(696\) 5.58667 0.211762
\(697\) 19.4172i 0.735480i
\(698\) 23.5273i 0.890521i
\(699\) −3.32842 −0.125892
\(700\) 0 0
\(701\) 31.0788 1.17383 0.586914 0.809649i \(-0.300343\pi\)
0.586914 + 0.809649i \(0.300343\pi\)
\(702\) 1.64124i 0.0619446i
\(703\) 23.6759i 0.892953i
\(704\) 3.05545 0.115157
\(705\) 0.845296 + 25.4246i 0.0318357 + 0.957546i
\(706\) −22.9718 −0.864556
\(707\) 0 0
\(708\) 5.97792i 0.224664i
\(709\) 12.1815 0.457485 0.228742 0.973487i \(-0.426539\pi\)
0.228742 + 0.973487i \(0.426539\pi\)
\(710\) 33.1924 1.10355i 1.24569 0.0414155i
\(711\) 14.2990 0.536254
\(712\) 17.5083i 0.656149i
\(713\) 1.69059i 0.0633131i
\(714\) 0 0
\(715\) −11.2071 + 0.372603i −0.419121 + 0.0139346i
\(716\) −24.4463 −0.913602
\(717\) 24.8713i 0.928836i
\(718\) 11.0264i 0.411501i
\(719\) 31.9896 1.19301 0.596505 0.802609i \(-0.296556\pi\)
0.596505 + 0.802609i \(0.296556\pi\)
\(720\) −0.0743018 2.23483i −0.00276906 0.0832873i
\(721\) 0 0
\(722\) 14.1152i 0.525314i
\(723\) 10.3535i 0.385053i
\(724\) 16.9788 0.631012
\(725\) 27.8717 1.85536i 1.03513 0.0689063i
\(726\) −1.66421 −0.0617646
\(727\) 22.9992i 0.852995i −0.904489 0.426497i \(-0.859747\pi\)
0.904489 0.426497i \(-0.140253\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0.588200 + 17.6918i 0.0217703 + 0.654801i
\(731\) −30.5282 −1.12912
\(732\) 0.445811i 0.0164776i
\(733\) 17.6001i 0.650076i 0.945701 + 0.325038i \(0.105377\pi\)
−0.945701 + 0.325038i \(0.894623\pi\)
\(734\) −10.1446 −0.374446
\(735\) 0 0
\(736\) 1.78984 0.0659745
\(737\) 3.86701i 0.142443i
\(738\) 6.67982i 0.245888i
\(739\) 0.174100 0.00640437 0.00320218 0.999995i \(-0.498981\pi\)
0.00320218 + 0.999995i \(0.498981\pi\)
\(740\) −23.9402 + 0.795944i −0.880060 + 0.0292595i
\(741\) 3.62740 0.133256
\(742\) 0 0
\(743\) 53.6360i 1.96771i −0.178957 0.983857i \(-0.557272\pi\)
0.178957 0.983857i \(-0.442728\pi\)
\(744\) −0.944547 −0.0346288
\(745\) −0.597988 17.9862i −0.0219086 0.658962i
\(746\) −26.5021 −0.970313
\(747\) 0.874366i 0.0319914i
\(748\) 8.88174i 0.324749i
\(749\) 0 0
\(750\) −1.11289 11.1248i −0.0406369 0.406221i
\(751\) 29.0931 1.06162 0.530812 0.847490i \(-0.321887\pi\)
0.530812 + 0.847490i \(0.321887\pi\)
\(752\) 11.3765i 0.414859i
\(753\) 16.5502i 0.603125i
\(754\) −9.16907 −0.333918
\(755\) −0.741377 22.2990i −0.0269815 0.811543i
\(756\) 0 0
\(757\) 34.0842i 1.23881i −0.785072 0.619405i \(-0.787374\pi\)
0.785072 0.619405i \(-0.212626\pi\)
\(758\) 29.4142i 1.06837i
\(759\) 5.46878 0.198504
\(760\) −4.93933 + 0.164219i −0.179168 + 0.00595684i
\(761\) −7.62959 −0.276572 −0.138286 0.990392i \(-0.544159\pi\)
−0.138286 + 0.990392i \(0.544159\pi\)
\(762\) 8.45405i 0.306258i
\(763\) 0 0
\(764\) −0.741377 −0.0268221
\(765\) −6.49632 + 0.215984i −0.234875 + 0.00780892i
\(766\) 3.64249 0.131609
\(767\) 9.81119i 0.354262i
\(768\) 1.00000i 0.0360844i
\(769\) 37.8241 1.36397 0.681986 0.731365i \(-0.261117\pi\)
0.681986 + 0.731365i \(0.261117\pi\)
\(770\) 0 0
\(771\) −24.4546 −0.880710
\(772\) 6.11091i 0.219936i
\(773\) 25.2349i 0.907636i 0.891094 + 0.453818i \(0.149938\pi\)
−0.891094 + 0.453818i \(0.850062\pi\)
\(774\) −10.5021 −0.377492
\(775\) −4.71231 + 0.313688i −0.169271 + 0.0112680i
\(776\) −10.4476 −0.375046
\(777\) 0 0
\(778\) 23.7938i 0.853048i
\(779\) −14.7635 −0.528956
\(780\) 0.121947 + 3.66790i 0.00436640 + 0.131332i
\(781\) 45.3804 1.62384
\(782\) 5.20280i 0.186052i
\(783\) 5.58667i 0.199651i
\(784\) 0 0
\(785\) 28.3100 0.941227i 1.01043 0.0335938i
\(786\) 8.32106 0.296802
\(787\) 22.7193i 0.809855i −0.914349 0.404928i \(-0.867297\pi\)
0.914349 0.404928i \(-0.132703\pi\)
\(788\) 20.6832i 0.736810i
\(789\) 12.5091 0.445337
\(790\) 31.9558 1.06244i 1.13694 0.0377999i
\(791\) 0 0
\(792\) 3.05545i