Properties

Label 4020.2.q.k.841.2
Level 4020
Weight 2
Character 4020.841
Analytic conductor 32.100
Analytic rank 0
Dimension 14
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.q (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 841.2
Root \(-0.288886 + 0.500366i\)
Character \(\chi\) = 4020.841
Dual form 4020.2.q.k.3781.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +(-1.13810 + 1.97125i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +(-1.13810 + 1.97125i) q^{7} +1.00000 q^{9} +(1.34203 - 2.32447i) q^{11} +(-0.0777729 - 0.134707i) q^{13} -1.00000 q^{15} +(-0.386637 - 0.669675i) q^{17} +(-0.333089 - 0.576927i) q^{19} +(1.13810 - 1.97125i) q^{21} +(-2.24130 - 3.88205i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.790296 - 1.36883i) q^{29} +(-2.92455 + 5.06547i) q^{31} +(-1.34203 + 2.32447i) q^{33} +(-1.13810 + 1.97125i) q^{35} +(-4.60808 - 7.98142i) q^{37} +(0.0777729 + 0.134707i) q^{39} +(-4.88835 + 8.46687i) q^{41} -4.88135 q^{43} +1.00000 q^{45} +(4.20309 - 7.27996i) q^{47} +(0.909436 + 1.57519i) q^{49} +(0.386637 + 0.669675i) q^{51} +7.78200 q^{53} +(1.34203 - 2.32447i) q^{55} +(0.333089 + 0.576927i) q^{57} -10.5918 q^{59} +(1.14396 + 1.98139i) q^{61} +(-1.13810 + 1.97125i) q^{63} +(-0.0777729 - 0.134707i) q^{65} +(-1.48295 + 8.04990i) q^{67} +(2.24130 + 3.88205i) q^{69} +(6.37678 - 11.0449i) q^{71} +(-3.73675 - 6.47224i) q^{73} -1.00000 q^{75} +(3.05474 + 5.29097i) q^{77} +(-6.85569 + 11.8744i) q^{79} +1.00000 q^{81} +(-4.19414 - 7.26447i) q^{83} +(-0.386637 - 0.669675i) q^{85} +(-0.790296 + 1.36883i) q^{87} +5.03057 q^{89} +0.354055 q^{91} +(2.92455 - 5.06547i) q^{93} +(-0.333089 - 0.576927i) q^{95} +(-5.24485 - 9.08435i) q^{97} +(1.34203 - 2.32447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + 6q^{11} + 9q^{13} - 14q^{15} - 12q^{17} + 14q^{19} - 3q^{21} + 6q^{23} + 14q^{25} - 14q^{27} - q^{29} + 7q^{31} - 6q^{33} + 3q^{35} - 2q^{37} - 9q^{39} - 18q^{41} - 6q^{43} + 14q^{45} + 7q^{47} + 12q^{51} - 12q^{53} + 6q^{55} - 14q^{57} - 2q^{59} + 3q^{63} + 9q^{65} + 25q^{67} - 6q^{69} + 22q^{71} - 15q^{73} - 14q^{75} + q^{77} + 9q^{79} + 14q^{81} - q^{83} - 12q^{85} + q^{87} - 12q^{89} - 38q^{91} - 7q^{93} + 14q^{95} + 16q^{97} + 6q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.13810 + 1.97125i −0.430163 + 0.745064i −0.996887 0.0788435i \(-0.974877\pi\)
0.566724 + 0.823908i \(0.308211\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.34203 2.32447i 0.404638 0.700853i −0.589642 0.807665i \(-0.700731\pi\)
0.994279 + 0.106812i \(0.0340643\pi\)
\(12\) 0 0
\(13\) −0.0777729 0.134707i −0.0215703 0.0373609i 0.855039 0.518564i \(-0.173533\pi\)
−0.876609 + 0.481203i \(0.840200\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −0.386637 0.669675i −0.0937732 0.162420i 0.815323 0.579007i \(-0.196560\pi\)
−0.909096 + 0.416587i \(0.863226\pi\)
\(18\) 0 0
\(19\) −0.333089 0.576927i −0.0764159 0.132356i 0.825285 0.564716i \(-0.191014\pi\)
−0.901701 + 0.432360i \(0.857681\pi\)
\(20\) 0 0
\(21\) 1.13810 1.97125i 0.248355 0.430163i
\(22\) 0 0
\(23\) −2.24130 3.88205i −0.467344 0.809464i 0.531960 0.846770i \(-0.321456\pi\)
−0.999304 + 0.0373060i \(0.988122\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.790296 1.36883i 0.146754 0.254186i −0.783272 0.621679i \(-0.786451\pi\)
0.930026 + 0.367494i \(0.119784\pi\)
\(30\) 0 0
\(31\) −2.92455 + 5.06547i −0.525265 + 0.909786i 0.474302 + 0.880362i \(0.342700\pi\)
−0.999567 + 0.0294235i \(0.990633\pi\)
\(32\) 0 0
\(33\) −1.34203 + 2.32447i −0.233618 + 0.404638i
\(34\) 0 0
\(35\) −1.13810 + 1.97125i −0.192375 + 0.333203i
\(36\) 0 0
\(37\) −4.60808 7.98142i −0.757563 1.31214i −0.944090 0.329688i \(-0.893057\pi\)
0.186527 0.982450i \(-0.440277\pi\)
\(38\) 0 0
\(39\) 0.0777729 + 0.134707i 0.0124536 + 0.0215703i
\(40\) 0 0
\(41\) −4.88835 + 8.46687i −0.763432 + 1.32230i 0.177640 + 0.984096i \(0.443154\pi\)
−0.941072 + 0.338207i \(0.890179\pi\)
\(42\) 0 0
\(43\) −4.88135 −0.744399 −0.372199 0.928153i \(-0.621396\pi\)
−0.372199 + 0.928153i \(0.621396\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 4.20309 7.27996i 0.613083 1.06189i −0.377634 0.925955i \(-0.623262\pi\)
0.990718 0.135936i \(-0.0434043\pi\)
\(48\) 0 0
\(49\) 0.909436 + 1.57519i 0.129919 + 0.225027i
\(50\) 0 0
\(51\) 0.386637 + 0.669675i 0.0541400 + 0.0937732i
\(52\) 0 0
\(53\) 7.78200 1.06894 0.534470 0.845188i \(-0.320511\pi\)
0.534470 + 0.845188i \(0.320511\pi\)
\(54\) 0 0
\(55\) 1.34203 2.32447i 0.180959 0.313431i
\(56\) 0 0
\(57\) 0.333089 + 0.576927i 0.0441187 + 0.0764159i
\(58\) 0 0
\(59\) −10.5918 −1.37893 −0.689465 0.724319i \(-0.742154\pi\)
−0.689465 + 0.724319i \(0.742154\pi\)
\(60\) 0 0
\(61\) 1.14396 + 1.98139i 0.146468 + 0.253691i 0.929920 0.367762i \(-0.119876\pi\)
−0.783451 + 0.621453i \(0.786543\pi\)
\(62\) 0 0
\(63\) −1.13810 + 1.97125i −0.143388 + 0.248355i
\(64\) 0 0
\(65\) −0.0777729 0.134707i −0.00964654 0.0167083i
\(66\) 0 0
\(67\) −1.48295 + 8.04990i −0.181172 + 0.983451i
\(68\) 0 0
\(69\) 2.24130 + 3.88205i 0.269821 + 0.467344i
\(70\) 0 0
\(71\) 6.37678 11.0449i 0.756785 1.31079i −0.187697 0.982227i \(-0.560102\pi\)
0.944482 0.328563i \(-0.106564\pi\)
\(72\) 0 0
\(73\) −3.73675 6.47224i −0.437353 0.757518i 0.560131 0.828404i \(-0.310751\pi\)
−0.997484 + 0.0708858i \(0.977417\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 3.05474 + 5.29097i 0.348120 + 0.602962i
\(78\) 0 0
\(79\) −6.85569 + 11.8744i −0.771326 + 1.33598i 0.165511 + 0.986208i \(0.447073\pi\)
−0.936836 + 0.349768i \(0.886261\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.19414 7.26447i −0.460367 0.797379i 0.538612 0.842554i \(-0.318949\pi\)
−0.998979 + 0.0451747i \(0.985616\pi\)
\(84\) 0 0
\(85\) −0.386637 0.669675i −0.0419367 0.0726364i
\(86\) 0 0
\(87\) −0.790296 + 1.36883i −0.0847286 + 0.146754i
\(88\) 0 0
\(89\) 5.03057 0.533239 0.266619 0.963802i \(-0.414093\pi\)
0.266619 + 0.963802i \(0.414093\pi\)
\(90\) 0 0
\(91\) 0.354055 0.0371150
\(92\) 0 0
\(93\) 2.92455 5.06547i 0.303262 0.525265i
\(94\) 0 0
\(95\) −0.333089 0.576927i −0.0341742 0.0591915i
\(96\) 0 0
\(97\) −5.24485 9.08435i −0.532534 0.922376i −0.999278 0.0379835i \(-0.987907\pi\)
0.466745 0.884392i \(-0.345427\pi\)
\(98\) 0 0
\(99\) 1.34203 2.32447i 0.134879 0.233618i
\(100\) 0 0
\(101\) 0.530519 0.918886i 0.0527886 0.0914326i −0.838424 0.545019i \(-0.816522\pi\)
0.891212 + 0.453587i \(0.149856\pi\)
\(102\) 0 0
\(103\) 6.85611 11.8751i 0.675553 1.17009i −0.300754 0.953702i \(-0.597238\pi\)
0.976307 0.216390i \(-0.0694284\pi\)
\(104\) 0 0
\(105\) 1.13810 1.97125i 0.111068 0.192375i
\(106\) 0 0
\(107\) −18.1522 −1.75484 −0.877420 0.479723i \(-0.840737\pi\)
−0.877420 + 0.479723i \(0.840737\pi\)
\(108\) 0 0
\(109\) −1.05330 −0.100887 −0.0504437 0.998727i \(-0.516064\pi\)
−0.0504437 + 0.998727i \(0.516064\pi\)
\(110\) 0 0
\(111\) 4.60808 + 7.98142i 0.437379 + 0.757563i
\(112\) 0 0
\(113\) 7.44853 12.9012i 0.700698 1.21365i −0.267523 0.963551i \(-0.586205\pi\)
0.968222 0.250094i \(-0.0804614\pi\)
\(114\) 0 0
\(115\) −2.24130 3.88205i −0.209003 0.362003i
\(116\) 0 0
\(117\) −0.0777729 0.134707i −0.00719011 0.0124536i
\(118\) 0 0
\(119\) 1.76013 0.161351
\(120\) 0 0
\(121\) 1.89790 + 3.28727i 0.172537 + 0.298842i
\(122\) 0 0
\(123\) 4.88835 8.46687i 0.440768 0.763432i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 5.45909 9.45542i 0.484416 0.839033i −0.515424 0.856935i \(-0.672366\pi\)
0.999840 + 0.0179027i \(0.00569891\pi\)
\(128\) 0 0
\(129\) 4.88135 0.429779
\(130\) 0 0
\(131\) −4.93164 −0.430880 −0.215440 0.976517i \(-0.569119\pi\)
−0.215440 + 0.976517i \(0.569119\pi\)
\(132\) 0 0
\(133\) 1.51636 0.131485
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 9.40754 0.803741 0.401870 0.915697i \(-0.368360\pi\)
0.401870 + 0.915697i \(0.368360\pi\)
\(138\) 0 0
\(139\) −9.64017 −0.817668 −0.408834 0.912609i \(-0.634065\pi\)
−0.408834 + 0.912609i \(0.634065\pi\)
\(140\) 0 0
\(141\) −4.20309 + 7.27996i −0.353964 + 0.613083i
\(142\) 0 0
\(143\) −0.417495 −0.0349127
\(144\) 0 0
\(145\) 0.790296 1.36883i 0.0656305 0.113675i
\(146\) 0 0
\(147\) −0.909436 1.57519i −0.0750090 0.129919i
\(148\) 0 0
\(149\) −12.3962 −1.01554 −0.507769 0.861493i \(-0.669530\pi\)
−0.507769 + 0.861493i \(0.669530\pi\)
\(150\) 0 0
\(151\) −2.27804 3.94569i −0.185385 0.321095i 0.758321 0.651881i \(-0.226020\pi\)
−0.943706 + 0.330785i \(0.892686\pi\)
\(152\) 0 0
\(153\) −0.386637 0.669675i −0.0312577 0.0541400i
\(154\) 0 0
\(155\) −2.92455 + 5.06547i −0.234906 + 0.406869i
\(156\) 0 0
\(157\) 1.44535 + 2.50342i 0.115352 + 0.199795i 0.917920 0.396765i \(-0.129867\pi\)
−0.802569 + 0.596560i \(0.796534\pi\)
\(158\) 0 0
\(159\) −7.78200 −0.617152
\(160\) 0 0
\(161\) 10.2033 0.804137
\(162\) 0 0
\(163\) 7.15348 12.3902i 0.560304 0.970475i −0.437166 0.899381i \(-0.644018\pi\)
0.997470 0.0710940i \(-0.0226490\pi\)
\(164\) 0 0
\(165\) −1.34203 + 2.32447i −0.104477 + 0.180959i
\(166\) 0 0
\(167\) −12.0904 + 20.9412i −0.935584 + 1.62048i −0.161994 + 0.986792i \(0.551793\pi\)
−0.773590 + 0.633687i \(0.781541\pi\)
\(168\) 0 0
\(169\) 6.48790 11.2374i 0.499069 0.864414i
\(170\) 0 0
\(171\) −0.333089 0.576927i −0.0254720 0.0441187i
\(172\) 0 0
\(173\) −11.6805 20.2313i −0.888054 1.53815i −0.842173 0.539208i \(-0.818724\pi\)
−0.0458811 0.998947i \(-0.514610\pi\)
\(174\) 0 0
\(175\) −1.13810 + 1.97125i −0.0860326 + 0.149013i
\(176\) 0 0
\(177\) 10.5918 0.796125
\(178\) 0 0
\(179\) −7.46602 −0.558036 −0.279018 0.960286i \(-0.590009\pi\)
−0.279018 + 0.960286i \(0.590009\pi\)
\(180\) 0 0
\(181\) −4.45233 + 7.71165i −0.330939 + 0.573203i −0.982696 0.185225i \(-0.940699\pi\)
0.651757 + 0.758427i \(0.274032\pi\)
\(182\) 0 0
\(183\) −1.14396 1.98139i −0.0845636 0.146468i
\(184\) 0 0
\(185\) −4.60808 7.98142i −0.338792 0.586806i
\(186\) 0 0
\(187\) −2.07552 −0.151777
\(188\) 0 0
\(189\) 1.13810 1.97125i 0.0827849 0.143388i
\(190\) 0 0
\(191\) 9.74545 + 16.8796i 0.705156 + 1.22137i 0.966635 + 0.256157i \(0.0824563\pi\)
−0.261479 + 0.965209i \(0.584210\pi\)
\(192\) 0 0
\(193\) 9.62585 0.692884 0.346442 0.938071i \(-0.387390\pi\)
0.346442 + 0.938071i \(0.387390\pi\)
\(194\) 0 0
\(195\) 0.0777729 + 0.134707i 0.00556943 + 0.00964654i
\(196\) 0 0
\(197\) 1.58812 2.75070i 0.113149 0.195979i −0.803889 0.594779i \(-0.797240\pi\)
0.917038 + 0.398799i \(0.130573\pi\)
\(198\) 0 0
\(199\) −3.11819 5.40087i −0.221043 0.382858i 0.734082 0.679061i \(-0.237613\pi\)
−0.955125 + 0.296203i \(0.904279\pi\)
\(200\) 0 0
\(201\) 1.48295 8.04990i 0.104600 0.567796i
\(202\) 0 0
\(203\) 1.79888 + 3.11575i 0.126257 + 0.218683i
\(204\) 0 0
\(205\) −4.88835 + 8.46687i −0.341417 + 0.591352i
\(206\) 0 0
\(207\) −2.24130 3.88205i −0.155781 0.269821i
\(208\) 0 0
\(209\) −1.78806 −0.123683
\(210\) 0 0
\(211\) −10.5562 18.2838i −0.726718 1.25871i −0.958263 0.285888i \(-0.907712\pi\)
0.231545 0.972824i \(-0.425622\pi\)
\(212\) 0 0
\(213\) −6.37678 + 11.0449i −0.436930 + 0.756785i
\(214\) 0 0
\(215\) −4.88135 −0.332905
\(216\) 0 0
\(217\) −6.65689 11.5301i −0.451899 0.782712i
\(218\) 0 0
\(219\) 3.73675 + 6.47224i 0.252506 + 0.437353i
\(220\) 0 0
\(221\) −0.0601397 + 0.104165i −0.00404544 + 0.00700690i
\(222\) 0 0
\(223\) −25.1746 −1.68581 −0.842906 0.538060i \(-0.819157\pi\)
−0.842906 + 0.538060i \(0.819157\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 14.8271 25.6813i 0.984110 1.70453i 0.338284 0.941044i \(-0.390153\pi\)
0.645826 0.763485i \(-0.276513\pi\)
\(228\) 0 0
\(229\) −12.8348 22.2305i −0.848148 1.46904i −0.882859 0.469638i \(-0.844384\pi\)
0.0347106 0.999397i \(-0.488949\pi\)
\(230\) 0 0
\(231\) −3.05474 5.29097i −0.200987 0.348120i
\(232\) 0 0
\(233\) −10.4330 + 18.0706i −0.683492 + 1.18384i 0.290417 + 0.956900i \(0.406206\pi\)
−0.973908 + 0.226942i \(0.927127\pi\)
\(234\) 0 0
\(235\) 4.20309 7.27996i 0.274179 0.474892i
\(236\) 0 0
\(237\) 6.85569 11.8744i 0.445325 0.771326i
\(238\) 0 0
\(239\) 8.15344 14.1222i 0.527402 0.913488i −0.472087 0.881552i \(-0.656499\pi\)
0.999490 0.0319362i \(-0.0101673\pi\)
\(240\) 0 0
\(241\) 5.68032 0.365902 0.182951 0.983122i \(-0.441435\pi\)
0.182951 + 0.983122i \(0.441435\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0.909436 + 1.57519i 0.0581018 + 0.100635i
\(246\) 0 0
\(247\) −0.0518106 + 0.0897386i −0.00329663 + 0.00570993i
\(248\) 0 0
\(249\) 4.19414 + 7.26447i 0.265793 + 0.460367i
\(250\) 0 0
\(251\) −7.53313 13.0478i −0.475487 0.823568i 0.524119 0.851645i \(-0.324395\pi\)
−0.999606 + 0.0280776i \(0.991061\pi\)
\(252\) 0 0
\(253\) −12.0316 −0.756420
\(254\) 0 0
\(255\) 0.386637 + 0.669675i 0.0242121 + 0.0419367i
\(256\) 0 0
\(257\) −3.23525 + 5.60361i −0.201809 + 0.349544i −0.949111 0.314941i \(-0.898015\pi\)
0.747302 + 0.664484i \(0.231349\pi\)
\(258\) 0 0
\(259\) 20.9779 1.30350
\(260\) 0 0
\(261\) 0.790296 1.36883i 0.0489181 0.0847286i
\(262\) 0 0
\(263\) −15.6255 −0.963511 −0.481755 0.876306i \(-0.660001\pi\)
−0.481755 + 0.876306i \(0.660001\pi\)
\(264\) 0 0
\(265\) 7.78200 0.478044
\(266\) 0 0
\(267\) −5.03057 −0.307866
\(268\) 0 0
\(269\) 15.9632 0.973296 0.486648 0.873598i \(-0.338219\pi\)
0.486648 + 0.873598i \(0.338219\pi\)
\(270\) 0 0
\(271\) −27.7137 −1.68349 −0.841745 0.539876i \(-0.818471\pi\)
−0.841745 + 0.539876i \(0.818471\pi\)
\(272\) 0 0
\(273\) −0.354055 −0.0214284
\(274\) 0 0
\(275\) 1.34203 2.32447i 0.0809275 0.140171i
\(276\) 0 0
\(277\) 0.357694 0.0214918 0.0107459 0.999942i \(-0.496579\pi\)
0.0107459 + 0.999942i \(0.496579\pi\)
\(278\) 0 0
\(279\) −2.92455 + 5.06547i −0.175088 + 0.303262i
\(280\) 0 0
\(281\) 11.6739 + 20.2197i 0.696405 + 1.20621i 0.969705 + 0.244280i \(0.0785515\pi\)
−0.273300 + 0.961929i \(0.588115\pi\)
\(282\) 0 0
\(283\) −14.7440 −0.876443 −0.438221 0.898867i \(-0.644391\pi\)
−0.438221 + 0.898867i \(0.644391\pi\)
\(284\) 0 0
\(285\) 0.333089 + 0.576927i 0.0197305 + 0.0341742i
\(286\) 0 0
\(287\) −11.1269 19.2724i −0.656800 1.13761i
\(288\) 0 0
\(289\) 8.20102 14.2046i 0.482413 0.835564i
\(290\) 0 0
\(291\) 5.24485 + 9.08435i 0.307459 + 0.532534i
\(292\) 0 0
\(293\) 8.24349 0.481590 0.240795 0.970576i \(-0.422592\pi\)
0.240795 + 0.970576i \(0.422592\pi\)
\(294\) 0 0
\(295\) −10.5918 −0.616676
\(296\) 0 0
\(297\) −1.34203 + 2.32447i −0.0778726 + 0.134879i
\(298\) 0 0
\(299\) −0.348625 + 0.603837i −0.0201615 + 0.0349208i
\(300\) 0 0
\(301\) 5.55549 9.62239i 0.320213 0.554625i
\(302\) 0 0
\(303\) −0.530519 + 0.918886i −0.0304775 + 0.0527886i
\(304\) 0 0
\(305\) 1.14396 + 1.98139i 0.0655027 + 0.113454i
\(306\) 0 0
\(307\) 1.12893 + 1.95537i 0.0644316 + 0.111599i 0.896442 0.443162i \(-0.146143\pi\)
−0.832010 + 0.554760i \(0.812810\pi\)
\(308\) 0 0
\(309\) −6.85611 + 11.8751i −0.390031 + 0.675553i
\(310\) 0 0
\(311\) 16.7611 0.950433 0.475216 0.879869i \(-0.342370\pi\)
0.475216 + 0.879869i \(0.342370\pi\)
\(312\) 0 0
\(313\) −17.9458 −1.01436 −0.507179 0.861841i \(-0.669312\pi\)
−0.507179 + 0.861841i \(0.669312\pi\)
\(314\) 0 0
\(315\) −1.13810 + 1.97125i −0.0641249 + 0.111068i
\(316\) 0 0
\(317\) 4.65490 + 8.06252i 0.261445 + 0.452836i 0.966626 0.256191i \(-0.0824676\pi\)
−0.705181 + 0.709027i \(0.749134\pi\)
\(318\) 0 0
\(319\) −2.12120 3.67403i −0.118765 0.205706i
\(320\) 0 0
\(321\) 18.1522 1.01316
\(322\) 0 0
\(323\) −0.257569 + 0.446123i −0.0143315 + 0.0248229i
\(324\) 0 0
\(325\) −0.0777729 0.134707i −0.00431406 0.00747218i
\(326\) 0 0
\(327\) 1.05330 0.0582474
\(328\) 0 0
\(329\) 9.56710 + 16.5707i 0.527451 + 0.913573i
\(330\) 0 0
\(331\) 5.34083 9.25059i 0.293559 0.508458i −0.681090 0.732200i \(-0.738494\pi\)
0.974649 + 0.223741i \(0.0718271\pi\)
\(332\) 0 0
\(333\) −4.60808 7.98142i −0.252521 0.437379i
\(334\) 0 0
\(335\) −1.48295 + 8.04990i −0.0810225 + 0.439813i
\(336\) 0 0
\(337\) −10.6164 18.3881i −0.578311 1.00166i −0.995673 0.0929234i \(-0.970379\pi\)
0.417363 0.908740i \(-0.362954\pi\)
\(338\) 0 0
\(339\) −7.44853 + 12.9012i −0.404548 + 0.700698i
\(340\) 0 0
\(341\) 7.84968 + 13.5960i 0.425084 + 0.736267i
\(342\) 0 0
\(343\) −20.0736 −1.08387
\(344\) 0 0
\(345\) 2.24130 + 3.88205i 0.120668 + 0.209003i
\(346\) 0 0
\(347\) −16.0343 + 27.7723i −0.860768 + 1.49089i 0.0104202 + 0.999946i \(0.496683\pi\)
−0.871188 + 0.490949i \(0.836650\pi\)
\(348\) 0 0
\(349\) −25.2370 −1.35091 −0.675453 0.737403i \(-0.736052\pi\)
−0.675453 + 0.737403i \(0.736052\pi\)
\(350\) 0 0
\(351\) 0.0777729 + 0.134707i 0.00415121 + 0.00719011i
\(352\) 0 0
\(353\) −5.05164 8.74969i −0.268872 0.465699i 0.699699 0.714438i \(-0.253317\pi\)
−0.968571 + 0.248738i \(0.919984\pi\)
\(354\) 0 0
\(355\) 6.37678 11.0449i 0.338444 0.586203i
\(356\) 0 0
\(357\) −1.76013 −0.0931561
\(358\) 0 0
\(359\) −11.1318 −0.587513 −0.293757 0.955880i \(-0.594905\pi\)
−0.293757 + 0.955880i \(0.594905\pi\)
\(360\) 0 0
\(361\) 9.27810 16.0701i 0.488321 0.845797i
\(362\) 0 0
\(363\) −1.89790 3.28727i −0.0996141 0.172537i
\(364\) 0 0
\(365\) −3.73675 6.47224i −0.195590 0.338772i
\(366\) 0 0
\(367\) 8.67010 15.0170i 0.452575 0.783883i −0.545970 0.837805i \(-0.683839\pi\)
0.998545 + 0.0539214i \(0.0171720\pi\)
\(368\) 0 0
\(369\) −4.88835 + 8.46687i −0.254477 + 0.440768i
\(370\) 0 0
\(371\) −8.85672 + 15.3403i −0.459818 + 0.796429i
\(372\) 0 0
\(373\) 7.58109 13.1308i 0.392534 0.679889i −0.600249 0.799813i \(-0.704932\pi\)
0.992783 + 0.119924i \(0.0382652\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −0.245854 −0.0126621
\(378\) 0 0
\(379\) 6.59791 + 11.4279i 0.338912 + 0.587012i 0.984228 0.176903i \(-0.0566078\pi\)
−0.645317 + 0.763915i \(0.723275\pi\)
\(380\) 0 0
\(381\) −5.45909 + 9.45542i −0.279678 + 0.484416i
\(382\) 0 0
\(383\) 10.0816 + 17.4619i 0.515147 + 0.892260i 0.999845 + 0.0175790i \(0.00559585\pi\)
−0.484699 + 0.874681i \(0.661071\pi\)
\(384\) 0 0
\(385\) 3.05474 + 5.29097i 0.155684 + 0.269653i
\(386\) 0 0
\(387\) −4.88135 −0.248133
\(388\) 0 0
\(389\) −8.55329 14.8147i −0.433669 0.751137i 0.563517 0.826105i \(-0.309448\pi\)
−0.997186 + 0.0749675i \(0.976115\pi\)
\(390\) 0 0
\(391\) −1.73314 + 3.00189i −0.0876487 + 0.151812i
\(392\) 0 0
\(393\) 4.93164 0.248769
\(394\) 0 0
\(395\) −6.85569 + 11.8744i −0.344947 + 0.597466i
\(396\) 0 0
\(397\) −3.18544 −0.159873 −0.0799364 0.996800i \(-0.525472\pi\)
−0.0799364 + 0.996800i \(0.525472\pi\)
\(398\) 0 0
\(399\) −1.51636 −0.0759130
\(400\) 0 0
\(401\) 13.3423 0.666283 0.333142 0.942877i \(-0.391891\pi\)
0.333142 + 0.942877i \(0.391891\pi\)
\(402\) 0 0
\(403\) 0.909803 0.0453205
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −24.7367 −1.22615
\(408\) 0 0
\(409\) 9.68190 16.7695i 0.478739 0.829201i −0.520964 0.853579i \(-0.674427\pi\)
0.999703 + 0.0243783i \(0.00776063\pi\)
\(410\) 0 0
\(411\) −9.40754 −0.464040
\(412\) 0 0
\(413\) 12.0545 20.8791i 0.593165 1.02739i
\(414\) 0 0
\(415\) −4.19414 7.26447i −0.205882 0.356599i
\(416\) 0 0
\(417\) 9.64017 0.472081
\(418\) 0 0
\(419\) −17.1638 29.7286i −0.838507 1.45234i −0.891143 0.453722i \(-0.850096\pi\)
0.0526366 0.998614i \(-0.483237\pi\)
\(420\) 0 0
\(421\) 16.4008 + 28.4070i 0.799324 + 1.38447i 0.920057 + 0.391785i \(0.128142\pi\)
−0.120732 + 0.992685i \(0.538524\pi\)
\(422\) 0 0
\(423\) 4.20309 7.27996i 0.204361 0.353964i
\(424\) 0 0
\(425\) −0.386637 0.669675i −0.0187546 0.0324840i
\(426\) 0 0
\(427\) −5.20776 −0.252021
\(428\) 0 0
\(429\) 0.417495 0.0201568
\(430\) 0 0
\(431\) −13.6080 + 23.5698i −0.655476 + 1.13532i 0.326298 + 0.945267i \(0.394199\pi\)
−0.981774 + 0.190051i \(0.939135\pi\)
\(432\) 0 0
\(433\) 1.39442 2.41520i 0.0670114 0.116067i −0.830573 0.556910i \(-0.811987\pi\)
0.897584 + 0.440843i \(0.145320\pi\)
\(434\) 0 0
\(435\) −0.790296 + 1.36883i −0.0378918 + 0.0656305i
\(436\) 0 0
\(437\) −1.49311 + 2.58614i −0.0714250 + 0.123712i
\(438\) 0 0
\(439\) −12.1856 21.1060i −0.581586 1.00734i −0.995292 0.0969252i \(-0.969099\pi\)
0.413706 0.910410i \(-0.364234\pi\)
\(440\) 0 0
\(441\) 0.909436 + 1.57519i 0.0433065 + 0.0750090i
\(442\) 0 0
\(443\) 17.4251 30.1812i 0.827893 1.43395i −0.0717957 0.997419i \(-0.522873\pi\)
0.899688 0.436533i \(-0.143794\pi\)
\(444\) 0 0
\(445\) 5.03057 0.238472
\(446\) 0 0
\(447\) 12.3962 0.586321
\(448\) 0 0
\(449\) −0.512740 + 0.888091i −0.0241977 + 0.0419116i −0.877871 0.478898i \(-0.841036\pi\)
0.853673 + 0.520809i \(0.174370\pi\)
\(450\) 0 0
\(451\) 13.1206 + 22.7256i 0.617827 + 1.07011i
\(452\) 0 0
\(453\) 2.27804 + 3.94569i 0.107032 + 0.185385i
\(454\) 0 0
\(455\) 0.354055 0.0165983
\(456\) 0 0
\(457\) 5.04794 8.74328i 0.236132 0.408993i −0.723469 0.690357i \(-0.757453\pi\)
0.959601 + 0.281364i \(0.0907867\pi\)
\(458\) 0 0
\(459\) 0.386637 + 0.669675i 0.0180467 + 0.0312577i
\(460\) 0 0
\(461\) −15.8337 −0.737447 −0.368723 0.929539i \(-0.620205\pi\)
−0.368723 + 0.929539i \(0.620205\pi\)
\(462\) 0 0
\(463\) −16.9607 29.3768i −0.788230 1.36525i −0.927050 0.374937i \(-0.877664\pi\)
0.138820 0.990318i \(-0.455669\pi\)
\(464\) 0 0
\(465\) 2.92455 5.06547i 0.135623 0.234906i
\(466\) 0 0
\(467\) 17.2039 + 29.7981i 0.796103 + 1.37889i 0.922137 + 0.386864i \(0.126442\pi\)
−0.126034 + 0.992026i \(0.540225\pi\)
\(468\) 0 0
\(469\) −14.1806 12.0849i −0.654801 0.558029i
\(470\) 0 0
\(471\) −1.44535 2.50342i −0.0665982 0.115352i
\(472\) 0 0
\(473\) −6.55093 + 11.3465i −0.301212 + 0.521714i
\(474\) 0 0
\(475\) −0.333089 0.576927i −0.0152832 0.0264712i
\(476\) 0 0
\(477\) 7.78200 0.356313
\(478\) 0 0
\(479\) −5.27156 9.13061i −0.240864 0.417188i 0.720097 0.693874i \(-0.244097\pi\)
−0.960961 + 0.276685i \(0.910764\pi\)
\(480\) 0 0
\(481\) −0.716767 + 1.24148i −0.0326818 + 0.0566065i
\(482\) 0 0
\(483\) −10.2033 −0.464268
\(484\) 0 0
\(485\) −5.24485 9.08435i −0.238156 0.412499i
\(486\) 0 0
\(487\) 14.2516 + 24.6845i 0.645802 + 1.11856i 0.984116 + 0.177529i \(0.0568102\pi\)
−0.338314 + 0.941033i \(0.609856\pi\)
\(488\) 0 0
\(489\) −7.15348 + 12.3902i −0.323492 + 0.560304i
\(490\) 0 0
\(491\) 27.4994 1.24103 0.620515 0.784195i \(-0.286924\pi\)
0.620515 + 0.784195i \(0.286924\pi\)
\(492\) 0 0
\(493\) −1.22223 −0.0550465
\(494\) 0 0
\(495\) 1.34203 2.32447i 0.0603198 0.104477i
\(496\) 0 0
\(497\) 14.5149 + 25.1405i 0.651082 + 1.12771i
\(498\) 0 0
\(499\) 14.1244 + 24.4641i 0.632294 + 1.09517i 0.987082 + 0.160218i \(0.0512198\pi\)
−0.354788 + 0.934947i \(0.615447\pi\)
\(500\) 0 0
\(501\) 12.0904 20.9412i 0.540160 0.935584i
\(502\) 0 0
\(503\) −12.4351 + 21.5382i −0.554454 + 0.960342i 0.443492 + 0.896278i \(0.353739\pi\)
−0.997946 + 0.0640637i \(0.979594\pi\)
\(504\) 0 0
\(505\) 0.530519 0.918886i 0.0236078 0.0408899i
\(506\) 0 0
\(507\) −6.48790 + 11.2374i −0.288138 + 0.499069i
\(508\) 0 0
\(509\) 37.5674 1.66514 0.832572 0.553917i \(-0.186867\pi\)
0.832572 + 0.553917i \(0.186867\pi\)
\(510\) 0 0
\(511\) 17.0112 0.752533
\(512\) 0 0
\(513\) 0.333089 + 0.576927i 0.0147062 + 0.0254720i
\(514\) 0 0
\(515\) 6.85611 11.8751i 0.302116 0.523281i
\(516\) 0 0
\(517\) −11.2813 19.5399i −0.496153 0.859362i
\(518\) 0 0
\(519\) 11.6805 + 20.2313i 0.512718 + 0.888054i
\(520\) 0 0
\(521\) 4.44091 0.194560 0.0972800 0.995257i \(-0.468986\pi\)
0.0972800 + 0.995257i \(0.468986\pi\)
\(522\) 0 0
\(523\) 7.35695 + 12.7426i 0.321697 + 0.557196i 0.980838 0.194823i \(-0.0624134\pi\)
−0.659141 + 0.752019i \(0.729080\pi\)
\(524\) 0 0
\(525\) 1.13810 1.97125i 0.0496710 0.0860326i
\(526\) 0 0
\(527\) 4.52296 0.197023
\(528\) 0 0
\(529\) 1.45312 2.51688i 0.0631791 0.109429i
\(530\) 0 0
\(531\) −10.5918 −0.459643
\(532\) 0 0
\(533\) 1.52072 0.0658699
\(534\) 0 0
\(535\) −18.1522 −0.784789
\(536\) 0 0
\(537\) 7.46602 0.322182
\(538\) 0 0
\(539\) 4.88197 0.210281
\(540\) 0 0
\(541\) −8.90460 −0.382839 −0.191419 0.981508i \(-0.561309\pi\)
−0.191419 + 0.981508i \(0.561309\pi\)
\(542\) 0 0
\(543\) 4.45233 7.71165i 0.191068 0.330939i
\(544\) 0 0
\(545\) −1.05330 −0.0451183
\(546\) 0 0
\(547\) 14.6728 25.4140i 0.627363 1.08663i −0.360715 0.932676i \(-0.617467\pi\)
0.988079 0.153949i \(-0.0491992\pi\)
\(548\) 0 0
\(549\) 1.14396 + 1.98139i 0.0488228 + 0.0845636i
\(550\) 0 0
\(551\) −1.05296 −0.0448574
\(552\) 0 0
\(553\) −15.6050 27.0286i −0.663592 1.14937i
\(554\) 0 0
\(555\) 4.60808 + 7.98142i 0.195602 + 0.338792i
\(556\) 0 0
\(557\) 2.59596 4.49633i 0.109994 0.190516i −0.805773 0.592224i \(-0.798250\pi\)
0.915768 + 0.401708i \(0.131583\pi\)
\(558\) 0 0
\(559\) 0.379637 + 0.657550i 0.0160569 + 0.0278114i
\(560\) 0 0
\(561\) 2.07552 0.0876283
\(562\) 0 0
\(563\) 10.9825 0.462859 0.231430 0.972852i \(-0.425660\pi\)
0.231430 + 0.972852i \(0.425660\pi\)
\(564\) 0 0
\(565\) 7.44853 12.9012i 0.313362 0.542759i
\(566\) 0 0
\(567\) −1.13810 + 1.97125i −0.0477959 + 0.0827849i
\(568\) 0 0
\(569\) 3.96707 6.87116i 0.166308 0.288054i −0.770811 0.637064i \(-0.780149\pi\)
0.937119 + 0.349010i \(0.113482\pi\)
\(570\) 0 0
\(571\) 16.8047 29.1067i 0.703257 1.21808i −0.264060 0.964506i \(-0.585062\pi\)
0.967317 0.253570i \(-0.0816049\pi\)
\(572\) 0 0
\(573\) −9.74545 16.8796i −0.407122 0.705156i
\(574\) 0 0
\(575\) −2.24130 3.88205i −0.0934688 0.161893i
\(576\) 0 0
\(577\) 0.0491809 0.0851838i 0.00204743 0.00354625i −0.865000 0.501772i \(-0.832682\pi\)
0.867047 + 0.498226i \(0.166015\pi\)
\(578\) 0 0
\(579\) −9.62585 −0.400037
\(580\) 0 0
\(581\) 19.0935 0.792132
\(582\) 0 0
\(583\) 10.4437 18.0890i 0.432533 0.749169i
\(584\) 0 0
\(585\) −0.0777729 0.134707i −0.00321551 0.00556943i
\(586\) 0 0
\(587\) 11.6866 + 20.2417i 0.482356 + 0.835465i 0.999795 0.0202548i \(-0.00644776\pi\)
−0.517439 + 0.855720i \(0.673114\pi\)
\(588\) 0 0
\(589\) 3.89655 0.160554
\(590\) 0 0
\(591\) −1.58812 + 2.75070i −0.0653265 + 0.113149i
\(592\) 0 0
\(593\) −10.1112 17.5130i −0.415215 0.719174i 0.580236 0.814449i \(-0.302960\pi\)
−0.995451 + 0.0952746i \(0.969627\pi\)
\(594\) 0 0
\(595\) 1.76013 0.0721584
\(596\) 0 0
\(597\) 3.11819 + 5.40087i 0.127619 + 0.221043i
\(598\) 0 0
\(599\) 0.326232 0.565051i 0.0133295 0.0230874i −0.859284 0.511499i \(-0.829090\pi\)
0.872613 + 0.488412i \(0.162424\pi\)
\(600\) 0 0
\(601\) 12.7792 + 22.1342i 0.521275 + 0.902874i 0.999694 + 0.0247426i \(0.00787662\pi\)
−0.478419 + 0.878132i \(0.658790\pi\)
\(602\) 0 0
\(603\) −1.48295 + 8.04990i −0.0603906 + 0.327817i
\(604\) 0 0
\(605\) 1.89790 + 3.28727i 0.0771608 + 0.133646i
\(606\) 0 0
\(607\) −6.76139 + 11.7111i −0.274436 + 0.475338i −0.969993 0.243134i \(-0.921825\pi\)
0.695556 + 0.718471i \(0.255158\pi\)
\(608\) 0 0
\(609\) −1.79888 3.11575i −0.0728942 0.126257i
\(610\) 0 0
\(611\) −1.30754 −0.0528976
\(612\) 0 0
\(613\) −1.81636 3.14602i −0.0733620 0.127067i 0.827011 0.562186i \(-0.190040\pi\)
−0.900373 + 0.435119i \(0.856706\pi\)
\(614\) 0 0
\(615\) 4.88835 8.46687i 0.197117 0.341417i
\(616\) 0 0
\(617\) −17.7653 −0.715203 −0.357602 0.933874i \(-0.616405\pi\)
−0.357602 + 0.933874i \(0.616405\pi\)
\(618\) 0 0
\(619\) −9.77863 16.9371i −0.393036 0.680759i 0.599812 0.800141i \(-0.295242\pi\)
−0.992848 + 0.119382i \(0.961909\pi\)
\(620\) 0 0
\(621\) 2.24130 + 3.88205i 0.0899404 + 0.155781i
\(622\) 0 0
\(623\) −5.72531 + 9.91653i −0.229380 + 0.397297i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 1.78806 0.0714084
\(628\) 0 0
\(629\) −3.56330 + 6.17182i −0.142078 + 0.246087i
\(630\) 0 0
\(631\) 15.6938 + 27.1824i 0.624759 + 1.08211i 0.988587 + 0.150648i \(0.0481360\pi\)
−0.363829 + 0.931466i \(0.618531\pi\)
\(632\) 0 0
\(633\) 10.5562 + 18.2838i 0.419571 + 0.726718i
\(634\) 0 0
\(635\) 5.45909 9.45542i 0.216637 0.375227i
\(636\) 0 0
\(637\) 0.141459 0.245014i 0.00560481 0.00970781i
\(638\) 0 0
\(639\) 6.37678 11.0449i 0.252262 0.436930i
\(640\) 0 0
\(641\) 0.370192 0.641191i 0.0146217 0.0253255i −0.858622 0.512609i \(-0.828679\pi\)
0.873244 + 0.487284i \(0.162012\pi\)
\(642\) 0 0
\(643\) −47.8156 −1.88566 −0.942832 0.333268i \(-0.891848\pi\)
−0.942832 + 0.333268i \(0.891848\pi\)
\(644\) 0 0
\(645\) 4.88135 0.192203
\(646\) 0 0
\(647\) 18.8521 + 32.6527i 0.741151 + 1.28371i 0.951972 + 0.306186i \(0.0990531\pi\)
−0.210821 + 0.977525i \(0.567614\pi\)
\(648\) 0 0
\(649\) −14.2145 + 24.6202i −0.557967 + 0.966427i
\(650\) 0 0
\(651\) 6.65689 + 11.5301i 0.260904 + 0.451899i
\(652\) 0 0
\(653\) 16.7316 + 28.9800i 0.654759 + 1.13408i 0.981954 + 0.189119i \(0.0605633\pi\)
−0.327195 + 0.944957i \(0.606103\pi\)
\(654\) 0 0
\(655\) −4.93164 −0.192695
\(656\) 0 0
\(657\) −3.73675 6.47224i −0.145784 0.252506i
\(658\) 0 0
\(659\) 17.0677 29.5620i 0.664861 1.15157i −0.314461 0.949270i \(-0.601824\pi\)
0.979323 0.202303i \(-0.0648427\pi\)
\(660\) 0 0
\(661\) −29.4211 −1.14435 −0.572175 0.820132i \(-0.693900\pi\)
−0.572175 + 0.820132i \(0.693900\pi\)
\(662\) 0 0
\(663\) 0.0601397 0.104165i 0.00233563 0.00404544i
\(664\) 0 0
\(665\) 1.51636 0.0588020
\(666\) 0 0
\(667\) −7.08517 −0.274339
\(668\) 0 0
\(669\) 25.1746 0.973305
\(670\) 0 0
\(671\) 6.14090 0.237067
\(672\) 0 0
\(673\) −45.3295 −1.74733 −0.873663 0.486532i \(-0.838262\pi\)
−0.873663 + 0.486532i \(0.838262\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 7.56313 13.0997i 0.290675 0.503464i −0.683295 0.730143i \(-0.739454\pi\)
0.973969 + 0.226679i \(0.0727869\pi\)
\(678\) 0 0
\(679\) 23.8767 0.916306
\(680\) 0 0
\(681\) −14.8271 + 25.6813i −0.568176 + 0.984110i
\(682\) 0 0
\(683\) 15.0573 + 26.0800i 0.576151 + 0.997923i 0.995916 + 0.0902896i \(0.0287793\pi\)
−0.419765 + 0.907633i \(0.637887\pi\)
\(684\) 0 0
\(685\) 9.40754 0.359444
\(686\) 0 0
\(687\) 12.8348 + 22.2305i 0.489679 + 0.848148i
\(688\) 0 0
\(689\) −0.605228 1.04829i −0.0230574 0.0399365i
\(690\) 0 0
\(691\) −23.7019 + 41.0528i −0.901661 + 1.56172i −0.0763236 + 0.997083i \(0.524318\pi\)
−0.825337 + 0.564640i \(0.809015\pi\)
\(692\) 0 0
\(693\) 3.05474 + 5.29097i 0.116040 + 0.200987i
\(694\) 0 0
\(695\) −9.64017 −0.365672
\(696\) 0 0
\(697\) 7.56007 0.286358
\(698\) 0 0
\(699\) 10.4330 18.0706i 0.394614 0.683492i
\(700\) 0 0
\(701\) −22.2350 + 38.5122i −0.839805 + 1.45459i 0.0502518 + 0.998737i \(0.483998\pi\)
−0.890057 + 0.455849i \(0.849336\pi\)
\(702\) 0 0
\(703\) −3.06980 + 5.31705i −0.115780 + 0.200536i
\(704\) 0 0
\(705\) −4.20309 + 7.27996i −0.158297 + 0.274179i
\(706\) 0 0
\(707\) 1.20757 + 2.09158i 0.0454154 + 0.0786618i
\(708\) 0 0
\(709\) 22.8950 + 39.6552i 0.859838 + 1.48928i 0.872083 + 0.489359i \(0.162769\pi\)
−0.0122444 + 0.999925i \(0.503898\pi\)
\(710\) 0 0
\(711\) −6.85569 + 11.8744i −0.257109 + 0.445325i
\(712\) 0 0
\(713\) 26.2192 0.981918
\(714\) 0 0
\(715\) −0.417495 −0.0156134
\(716\) 0 0
\(717\) −8.15344 + 14.1222i −0.304496 + 0.527402i
\(718\) 0 0
\(719\) −5.56816 9.64434i −0.207657 0.359673i 0.743319 0.668937i \(-0.233251\pi\)
−0.950976 + 0.309264i \(0.899917\pi\)
\(720\) 0 0
\(721\) 15.6059 + 27.0303i 0.581196 + 1.00666i
\(722\) 0 0
\(723\) −5.68032 −0.211254
\(724\) 0 0
\(725\) 0.790296 1.36883i 0.0293509 0.0508372i
\(726\) 0 0
\(727\) 3.06823 + 5.31433i 0.113794 + 0.197098i 0.917297 0.398203i \(-0.130366\pi\)
−0.803503 + 0.595301i \(0.797033\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.88731 + 3.26892i 0.0698047 + 0.120905i
\(732\) 0 0
\(733\) 8.05415 13.9502i 0.297487 0.515262i −0.678074 0.734994i \(-0.737185\pi\)
0.975560 + 0.219732i \(0.0705183\pi\)
\(734\) 0 0
\(735\) −0.909436 1.57519i −0.0335451 0.0581018i
\(736\) 0 0
\(737\) 16.7215 + 14.2503i 0.615946 + 0.524916i
\(738\) 0 0
\(739\) −2.96273 5.13160i −0.108986 0.188769i 0.806374 0.591406i \(-0.201427\pi\)
−0.915360 + 0.402637i \(0.868094\pi\)
\(740\) 0 0
\(741\) 0.0518106 0.0897386i 0.00190331 0.00329663i
\(742\) 0 0
\(743\) 4.76725 + 8.25711i 0.174893 + 0.302924i 0.940124 0.340832i \(-0.110709\pi\)
−0.765231 + 0.643756i \(0.777375\pi\)
\(744\) 0 0
\(745\) −12.3962 −0.454163
\(746\) 0 0
\(747\) −4.19414 7.26447i −0.153456 0.265793i
\(748\) 0 0
\(749\) 20.6591 35.7826i 0.754868 1.30747i
\(750\) 0 0
\(751\) 25.5634 0.932820 0.466410 0.884569i \(-0.345547\pi\)
0.466410 + 0.884569i \(0.345547\pi\)
\(752\) 0 0
\(753\) 7.53313 + 13.0478i 0.274523 + 0.475487i
\(754\) 0 0
\(755\) −2.27804 3.94569i −0.0829065 0.143598i
\(756\) 0 0
\(757\) −6.43229 + 11.1410i −0.233785 + 0.404928i −0.958919 0.283680i \(-0.908445\pi\)
0.725134 + 0.688608i \(0.241778\pi\)
\(758\) 0 0
\(759\) 12.0316 0.436719
\(760\) 0 0
\(761\) 41.3565 1.49917 0.749585 0.661908i \(-0.230253\pi\)
0.749585 + 0.661908i \(0.230253\pi\)
\(762\) 0 0
\(763\) 1.19876 2.07632i 0.0433981 0.0751677i
\(764\) 0 0
\(765\) −0.386637 0.669675i −0.0139789 0.0242121i
\(766\) 0 0
\(767\) 0.823752 + 1.42678i 0.0297439 + 0.0515180i
\(768\) 0 0
\(769\) −20.4554 + 35.4298i −0.737640 + 1.27763i 0.215915 + 0.976412i \(0.430727\pi\)
−0.953555 + 0.301218i \(0.902607\pi\)
\(770\) 0 0
\(771\) 3.23525 5.60361i 0.116515 0.201809i
\(772\) 0 0
\(773\) −16.4205 + 28.4412i −0.590605 + 1.02296i 0.403546 + 0.914960i \(0.367778\pi\)
−0.994151 + 0.107999i \(0.965556\pi\)
\(774\) 0 0
\(775\) −2.92455 + 5.06547i −0.105053 + 0.181957i
\(776\) 0 0
\(777\) −20.9779 −0.752578
\(778\) 0 0
\(779\) 6.51303 0.233353
\(780\) 0 0
\(781\) −17.1157 29.6452i −0.612447 1.06079i
\(782\) 0 0
\(783\) −0.790296 + 1.36883i −0.0282429 + 0.0489181i
\(784\) 0 0
\(785\) 1.44535 + 2.50342i 0.0515868 + 0.0893509i
\(786\) 0 0
\(787\) 6.21479 + 10.7643i 0.221533 + 0.383707i 0.955274 0.295723i \(-0.0955605\pi\)
−0.733740 + 0.679430i \(0.762227\pi\)
\(788\) 0 0
\(789\) 15.6255 0.556283
\(790\) 0 0
\(791\) 16.9544 + 29.3659i 0.602829 + 1.04413i
\(792\) 0 0
\(793\) 0.177937 0.308197i 0.00631874