Properties

Label 4020.2.q.k.3781.7
Level 4020
Weight 2
Character 4020.3781
Analytic conductor 32.100
Analytic rank 0
Dimension 14
CM No
Inner twists 2

Related objects

Downloads

Learn more about

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 3781.7
Root \(-0.647766 - 1.12196i\)
Character \(\chi\) = 4020.3781
Dual form 4020.2.q.k.841.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +(2.01447 + 3.48916i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +(2.01447 + 3.48916i) q^{7} +1.00000 q^{9} +(1.47884 + 2.56142i) q^{11} +(-0.795531 + 1.37790i) q^{13} -1.00000 q^{15} +(-2.62284 + 4.54289i) q^{17} +(0.339201 - 0.587513i) q^{19} +(-2.01447 - 3.48916i) q^{21} +(-0.358507 + 0.620953i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.40670 + 5.90058i) q^{29} +(1.61034 + 2.78918i) q^{31} +(-1.47884 - 2.56142i) q^{33} +(2.01447 + 3.48916i) q^{35} +(-1.94572 + 3.37008i) q^{37} +(0.795531 - 1.37790i) q^{39} +(-0.662081 - 1.14676i) q^{41} -10.8759 q^{43} +1.00000 q^{45} +(-3.03954 - 5.26464i) q^{47} +(-4.61614 + 7.99539i) q^{49} +(2.62284 - 4.54289i) q^{51} +1.84141 q^{53} +(1.47884 + 2.56142i) q^{55} +(-0.339201 + 0.587513i) q^{57} +3.21856 q^{59} +(0.514400 - 0.890968i) q^{61} +(2.01447 + 3.48916i) q^{63} +(-0.795531 + 1.37790i) q^{65} +(-2.98224 - 7.62274i) q^{67} +(0.358507 - 0.620953i) q^{69} +(-6.97238 - 12.0765i) q^{71} +(-3.44466 + 5.96633i) q^{73} -1.00000 q^{75} +(-5.95814 + 10.3198i) q^{77} +(5.19415 + 8.99654i) q^{79} +1.00000 q^{81} +(3.85758 - 6.68153i) q^{83} +(-2.62284 + 4.54289i) q^{85} +(-3.40670 - 5.90058i) q^{87} -0.969090 q^{89} -6.41028 q^{91} +(-1.61034 - 2.78918i) q^{93} +(0.339201 - 0.587513i) q^{95} +(4.77014 - 8.26213i) q^{97} +(1.47884 + 2.56142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + 6q^{11} + 9q^{13} - 14q^{15} - 12q^{17} + 14q^{19} - 3q^{21} + 6q^{23} + 14q^{25} - 14q^{27} - q^{29} + 7q^{31} - 6q^{33} + 3q^{35} - 2q^{37} - 9q^{39} - 18q^{41} - 6q^{43} + 14q^{45} + 7q^{47} + 12q^{51} - 12q^{53} + 6q^{55} - 14q^{57} - 2q^{59} + 3q^{63} + 9q^{65} + 25q^{67} - 6q^{69} + 22q^{71} - 15q^{73} - 14q^{75} + q^{77} + 9q^{79} + 14q^{81} - q^{83} - 12q^{85} + q^{87} - 12q^{89} - 38q^{91} - 7q^{93} + 14q^{95} + 16q^{97} + 6q^{99} + O(q^{100}) \)

Character Values

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

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(7\) 2.01447 + 3.48916i 0.761396 + 1.31878i 0.942131 + 0.335245i \(0.108819\pi\)
−0.180735 + 0.983532i \(0.557848\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.47884 + 2.56142i 0.445887 + 0.772298i 0.998114 0.0613955i \(-0.0195551\pi\)
−0.552227 + 0.833694i \(0.686222\pi\)
\(12\) 0 0
\(13\) −0.795531 + 1.37790i −0.220641 + 0.382161i −0.955003 0.296597i \(-0.904148\pi\)
0.734362 + 0.678758i \(0.237481\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −2.62284 + 4.54289i −0.636131 + 1.10181i 0.350143 + 0.936696i \(0.386133\pi\)
−0.986274 + 0.165115i \(0.947200\pi\)
\(18\) 0 0
\(19\) 0.339201 0.587513i 0.0778180 0.134785i −0.824490 0.565876i \(-0.808538\pi\)
0.902308 + 0.431091i \(0.141871\pi\)
\(20\) 0 0
\(21\) −2.01447 3.48916i −0.439592 0.761396i
\(22\) 0 0
\(23\) −0.358507 + 0.620953i −0.0747539 + 0.129478i −0.900979 0.433862i \(-0.857150\pi\)
0.826225 + 0.563340i \(0.190484\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.40670 + 5.90058i 0.632608 + 1.09571i 0.987016 + 0.160619i \(0.0513490\pi\)
−0.354408 + 0.935091i \(0.615318\pi\)
\(30\) 0 0
\(31\) 1.61034 + 2.78918i 0.289225 + 0.500952i 0.973625 0.228155i \(-0.0732692\pi\)
−0.684400 + 0.729107i \(0.739936\pi\)
\(32\) 0 0
\(33\) −1.47884 2.56142i −0.257433 0.445887i
\(34\) 0 0
\(35\) 2.01447 + 3.48916i 0.340507 + 0.589775i
\(36\) 0 0
\(37\) −1.94572 + 3.37008i −0.319874 + 0.554038i −0.980461 0.196711i \(-0.936974\pi\)
0.660588 + 0.750749i \(0.270307\pi\)
\(38\) 0 0
\(39\) 0.795531 1.37790i 0.127387 0.220641i
\(40\) 0 0
\(41\) −0.662081 1.14676i −0.103400 0.179094i 0.809684 0.586867i \(-0.199639\pi\)
−0.913083 + 0.407773i \(0.866305\pi\)
\(42\) 0 0
\(43\) −10.8759 −1.65856 −0.829282 0.558830i \(-0.811250\pi\)
−0.829282 + 0.558830i \(0.811250\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −3.03954 5.26464i −0.443363 0.767927i 0.554574 0.832135i \(-0.312881\pi\)
−0.997937 + 0.0642075i \(0.979548\pi\)
\(48\) 0 0
\(49\) −4.61614 + 7.99539i −0.659449 + 1.14220i
\(50\) 0 0
\(51\) 2.62284 4.54289i 0.367271 0.636131i
\(52\) 0 0
\(53\) 1.84141 0.252937 0.126468 0.991971i \(-0.459636\pi\)
0.126468 + 0.991971i \(0.459636\pi\)
\(54\) 0 0
\(55\) 1.47884 + 2.56142i 0.199407 + 0.345382i
\(56\) 0 0
\(57\) −0.339201 + 0.587513i −0.0449282 + 0.0778180i
\(58\) 0 0
\(59\) 3.21856 0.419021 0.209511 0.977806i \(-0.432813\pi\)
0.209511 + 0.977806i \(0.432813\pi\)
\(60\) 0 0
\(61\) 0.514400 0.890968i 0.0658622 0.114077i −0.831214 0.555953i \(-0.812354\pi\)
0.897076 + 0.441876i \(0.145687\pi\)
\(62\) 0 0
\(63\) 2.01447 + 3.48916i 0.253799 + 0.439592i
\(64\) 0 0
\(65\) −0.795531 + 1.37790i −0.0986735 + 0.170908i
\(66\) 0 0
\(67\) −2.98224 7.62274i −0.364339 0.931266i
\(68\) 0 0
\(69\) 0.358507 0.620953i 0.0431592 0.0747539i
\(70\) 0 0
\(71\) −6.97238 12.0765i −0.827469 1.43322i −0.900018 0.435853i \(-0.856447\pi\)
0.0725490 0.997365i \(-0.476887\pi\)
\(72\) 0 0
\(73\) −3.44466 + 5.96633i −0.403167 + 0.698306i −0.994106 0.108410i \(-0.965424\pi\)
0.590939 + 0.806716i \(0.298757\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) −5.95814 + 10.3198i −0.678993 + 1.17605i
\(78\) 0 0
\(79\) 5.19415 + 8.99654i 0.584388 + 1.01219i 0.994951 + 0.100358i \(0.0319987\pi\)
−0.410563 + 0.911832i \(0.634668\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.85758 6.68153i 0.423425 0.733393i −0.572847 0.819662i \(-0.694161\pi\)
0.996272 + 0.0862691i \(0.0274945\pi\)
\(84\) 0 0
\(85\) −2.62284 + 4.54289i −0.284487 + 0.492745i
\(86\) 0 0
\(87\) −3.40670 5.90058i −0.365237 0.632608i
\(88\) 0 0
\(89\) −0.969090 −0.102723 −0.0513617 0.998680i \(-0.516356\pi\)
−0.0513617 + 0.998680i \(0.516356\pi\)
\(90\) 0 0
\(91\) −6.41028 −0.671980
\(92\) 0 0
\(93\) −1.61034 2.78918i −0.166984 0.289225i
\(94\) 0 0
\(95\) 0.339201 0.587513i 0.0348012 0.0602775i
\(96\) 0 0
\(97\) 4.77014 8.26213i 0.484335 0.838893i −0.515503 0.856888i \(-0.672395\pi\)
0.999838 + 0.0179951i \(0.00572832\pi\)
\(98\) 0 0
\(99\) 1.47884 + 2.56142i 0.148629 + 0.257433i
\(100\) 0 0
\(101\) −2.10709 3.64959i −0.209663 0.363147i 0.741945 0.670460i \(-0.233903\pi\)
−0.951608 + 0.307313i \(0.900570\pi\)
\(102\) 0 0
\(103\) 1.25035 + 2.16566i 0.123200 + 0.213389i 0.921028 0.389496i \(-0.127351\pi\)
−0.797828 + 0.602886i \(0.794018\pi\)
\(104\) 0 0
\(105\) −2.01447 3.48916i −0.196592 0.340507i
\(106\) 0 0
\(107\) −0.117103 −0.0113208 −0.00566041 0.999984i \(-0.501802\pi\)
−0.00566041 + 0.999984i \(0.501802\pi\)
\(108\) 0 0
\(109\) 6.47281 0.619983 0.309992 0.950739i \(-0.399674\pi\)
0.309992 + 0.950739i \(0.399674\pi\)
\(110\) 0 0
\(111\) 1.94572 3.37008i 0.184679 0.319874i
\(112\) 0 0
\(113\) −9.71169 16.8211i −0.913599 1.58240i −0.808939 0.587892i \(-0.799958\pi\)
−0.104660 0.994508i \(-0.533375\pi\)
\(114\) 0 0
\(115\) −0.358507 + 0.620953i −0.0334310 + 0.0579042i
\(116\) 0 0
\(117\) −0.795531 + 1.37790i −0.0735469 + 0.127387i
\(118\) 0 0
\(119\) −21.1345 −1.93739
\(120\) 0 0
\(121\) 1.12607 1.95041i 0.102370 0.177310i
\(122\) 0 0
\(123\) 0.662081 + 1.14676i 0.0596979 + 0.103400i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −1.70520 2.95350i −0.151312 0.262081i 0.780398 0.625283i \(-0.215017\pi\)
−0.931710 + 0.363203i \(0.881683\pi\)
\(128\) 0 0
\(129\) 10.8759 0.957573
\(130\) 0 0
\(131\) 11.5182 1.00635 0.503173 0.864185i \(-0.332166\pi\)
0.503173 + 0.864185i \(0.332166\pi\)
\(132\) 0 0
\(133\) 2.73323 0.237001
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −2.14095 −0.182913 −0.0914567 0.995809i \(-0.529152\pi\)
−0.0914567 + 0.995809i \(0.529152\pi\)
\(138\) 0 0
\(139\) −5.56402 −0.471934 −0.235967 0.971761i \(-0.575826\pi\)
−0.235967 + 0.971761i \(0.575826\pi\)
\(140\) 0 0
\(141\) 3.03954 + 5.26464i 0.255976 + 0.443363i
\(142\) 0 0
\(143\) −4.70585 −0.393523
\(144\) 0 0
\(145\) 3.40670 + 5.90058i 0.282911 + 0.490016i
\(146\) 0 0
\(147\) 4.61614 7.99539i 0.380733 0.659449i
\(148\) 0 0
\(149\) 11.7958 0.966348 0.483174 0.875524i \(-0.339484\pi\)
0.483174 + 0.875524i \(0.339484\pi\)
\(150\) 0 0
\(151\) 1.51228 2.61935i 0.123068 0.213160i −0.797908 0.602779i \(-0.794060\pi\)
0.920976 + 0.389619i \(0.127393\pi\)
\(152\) 0 0
\(153\) −2.62284 + 4.54289i −0.212044 + 0.367271i
\(154\) 0 0
\(155\) 1.61034 + 2.78918i 0.129345 + 0.224033i
\(156\) 0 0
\(157\) −1.96108 + 3.39669i −0.156511 + 0.271086i −0.933608 0.358295i \(-0.883358\pi\)
0.777097 + 0.629381i \(0.216691\pi\)
\(158\) 0 0
\(159\) −1.84141 −0.146033
\(160\) 0 0
\(161\) −2.88880 −0.227670
\(162\) 0 0
\(163\) 2.37206 + 4.10853i 0.185794 + 0.321805i 0.943844 0.330392i \(-0.107181\pi\)
−0.758050 + 0.652197i \(0.773848\pi\)
\(164\) 0 0
\(165\) −1.47884 2.56142i −0.115127 0.199407i
\(166\) 0 0
\(167\) −1.13784 1.97079i −0.0880485 0.152504i 0.818638 0.574310i \(-0.194730\pi\)
−0.906686 + 0.421806i \(0.861396\pi\)
\(168\) 0 0
\(169\) 5.23426 + 9.06600i 0.402635 + 0.697385i
\(170\) 0 0
\(171\) 0.339201 0.587513i 0.0259393 0.0449282i
\(172\) 0 0
\(173\) 0.382324 0.662205i 0.0290676 0.0503465i −0.851126 0.524962i \(-0.824080\pi\)
0.880193 + 0.474615i \(0.157413\pi\)
\(174\) 0 0
\(175\) 2.01447 + 3.48916i 0.152279 + 0.263755i
\(176\) 0 0
\(177\) −3.21856 −0.241922
\(178\) 0 0
\(179\) −15.9147 −1.18952 −0.594759 0.803904i \(-0.702753\pi\)
−0.594759 + 0.803904i \(0.702753\pi\)
\(180\) 0 0
\(181\) 2.99097 + 5.18051i 0.222317 + 0.385064i 0.955511 0.294955i \(-0.0953047\pi\)
−0.733194 + 0.680019i \(0.761971\pi\)
\(182\) 0 0
\(183\) −0.514400 + 0.890968i −0.0380256 + 0.0658622i
\(184\) 0 0
\(185\) −1.94572 + 3.37008i −0.143052 + 0.247773i
\(186\) 0 0
\(187\) −15.5150 −1.13457
\(188\) 0 0
\(189\) −2.01447 3.48916i −0.146531 0.253799i
\(190\) 0 0
\(191\) 1.91365 3.31454i 0.138467 0.239832i −0.788450 0.615099i \(-0.789116\pi\)
0.926916 + 0.375268i \(0.122449\pi\)
\(192\) 0 0
\(193\) −7.18305 −0.517047 −0.258523 0.966005i \(-0.583236\pi\)
−0.258523 + 0.966005i \(0.583236\pi\)
\(194\) 0 0
\(195\) 0.795531 1.37790i 0.0569692 0.0986735i
\(196\) 0 0
\(197\) 11.5593 + 20.0213i 0.823566 + 1.42646i 0.903011 + 0.429618i \(0.141352\pi\)
−0.0794451 + 0.996839i \(0.525315\pi\)
\(198\) 0 0
\(199\) −13.4217 + 23.2470i −0.951436 + 1.64794i −0.209114 + 0.977891i \(0.567058\pi\)
−0.742321 + 0.670044i \(0.766275\pi\)
\(200\) 0 0
\(201\) 2.98224 + 7.62274i 0.210351 + 0.537667i
\(202\) 0 0
\(203\) −13.7254 + 23.7730i −0.963331 + 1.66854i
\(204\) 0 0
\(205\) −0.662081 1.14676i −0.0462418 0.0800931i
\(206\) 0 0
\(207\) −0.358507 + 0.620953i −0.0249180 + 0.0431592i
\(208\) 0 0
\(209\) 2.00649 0.138792
\(210\) 0 0
\(211\) −1.30980 + 2.26864i −0.0901704 + 0.156180i −0.907583 0.419873i \(-0.862075\pi\)
0.817412 + 0.576053i \(0.195408\pi\)
\(212\) 0 0
\(213\) 6.97238 + 12.0765i 0.477739 + 0.827469i
\(214\) 0 0
\(215\) −10.8759 −0.741733
\(216\) 0 0
\(217\) −6.48793 + 11.2374i −0.440429 + 0.762846i
\(218\) 0 0
\(219\) 3.44466 5.96633i 0.232769 0.403167i
\(220\) 0 0
\(221\) −4.17310 7.22802i −0.280713 0.486209i
\(222\) 0 0
\(223\) −17.5929 −1.17811 −0.589055 0.808093i \(-0.700500\pi\)
−0.589055 + 0.808093i \(0.700500\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 1.78070 + 3.08427i 0.118189 + 0.204710i 0.919050 0.394140i \(-0.128958\pi\)
−0.800861 + 0.598851i \(0.795624\pi\)
\(228\) 0 0
\(229\) −11.9704 + 20.7333i −0.791025 + 1.37010i 0.134307 + 0.990940i \(0.457119\pi\)
−0.925333 + 0.379157i \(0.876214\pi\)
\(230\) 0 0
\(231\) 5.95814 10.3198i 0.392017 0.678993i
\(232\) 0 0
\(233\) 11.5277 + 19.9665i 0.755203 + 1.30805i 0.945274 + 0.326279i \(0.105795\pi\)
−0.190071 + 0.981770i \(0.560872\pi\)
\(234\) 0 0
\(235\) −3.03954 5.26464i −0.198278 0.343427i
\(236\) 0 0
\(237\) −5.19415 8.99654i −0.337397 0.584388i
\(238\) 0 0
\(239\) −0.785887 1.36120i −0.0508348 0.0880484i 0.839488 0.543378i \(-0.182855\pi\)
−0.890323 + 0.455329i \(0.849522\pi\)
\(240\) 0 0
\(241\) 0.751633 0.0484170 0.0242085 0.999707i \(-0.492293\pi\)
0.0242085 + 0.999707i \(0.492293\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −4.61614 + 7.99539i −0.294914 + 0.510807i
\(246\) 0 0
\(247\) 0.539689 + 0.934769i 0.0343396 + 0.0594780i
\(248\) 0 0
\(249\) −3.85758 + 6.68153i −0.244464 + 0.423425i
\(250\) 0 0
\(251\) 15.1397 26.2227i 0.955607 1.65516i 0.222634 0.974902i \(-0.428534\pi\)
0.732973 0.680258i \(-0.238132\pi\)
\(252\) 0 0
\(253\) −2.12070 −0.133327
\(254\) 0 0
\(255\) 2.62284 4.54289i 0.164248 0.284487i
\(256\) 0 0
\(257\) 4.51598 + 7.82191i 0.281699 + 0.487917i 0.971803 0.235793i \(-0.0757687\pi\)
−0.690104 + 0.723710i \(0.742435\pi\)
\(258\) 0 0
\(259\) −15.6783 −0.974203
\(260\) 0 0
\(261\) 3.40670 + 5.90058i 0.210869 + 0.365237i
\(262\) 0 0
\(263\) −13.4758 −0.830952 −0.415476 0.909604i \(-0.636385\pi\)
−0.415476 + 0.909604i \(0.636385\pi\)
\(264\) 0 0
\(265\) 1.84141 0.113117
\(266\) 0 0
\(267\) 0.969090 0.0593074
\(268\) 0 0
\(269\) −3.93750 −0.240074 −0.120037 0.992769i \(-0.538301\pi\)
−0.120037 + 0.992769i \(0.538301\pi\)
\(270\) 0 0
\(271\) 6.11307 0.371342 0.185671 0.982612i \(-0.440554\pi\)
0.185671 + 0.982612i \(0.440554\pi\)
\(272\) 0 0
\(273\) 6.41028 0.387968
\(274\) 0 0
\(275\) 1.47884 + 2.56142i 0.0891773 + 0.154460i
\(276\) 0 0
\(277\) 10.2321 0.614786 0.307393 0.951583i \(-0.400543\pi\)
0.307393 + 0.951583i \(0.400543\pi\)
\(278\) 0 0
\(279\) 1.61034 + 2.78918i 0.0964082 + 0.166984i
\(280\) 0 0
\(281\) 0.432633 0.749342i 0.0258087 0.0447020i −0.852833 0.522184i \(-0.825117\pi\)
0.878641 + 0.477482i \(0.158451\pi\)
\(282\) 0 0
\(283\) −31.6110 −1.87908 −0.939541 0.342437i \(-0.888748\pi\)
−0.939541 + 0.342437i \(0.888748\pi\)
\(284\) 0 0
\(285\) −0.339201 + 0.587513i −0.0200925 + 0.0348012i
\(286\) 0 0
\(287\) 2.66748 4.62021i 0.157456 0.272722i
\(288\) 0 0
\(289\) −5.25854 9.10806i −0.309326 0.535768i
\(290\) 0 0
\(291\) −4.77014 + 8.26213i −0.279631 + 0.484335i
\(292\) 0 0
\(293\) 22.7027 1.32631 0.663154 0.748483i \(-0.269217\pi\)
0.663154 + 0.748483i \(0.269217\pi\)
\(294\) 0 0
\(295\) 3.21856 0.187392
\(296\) 0 0
\(297\) −1.47884 2.56142i −0.0858109 0.148629i
\(298\) 0 0
\(299\) −0.570408 0.987975i −0.0329875 0.0571361i
\(300\) 0 0
\(301\) −21.9092 37.9478i −1.26282 2.18728i
\(302\) 0 0
\(303\) 2.10709 + 3.64959i 0.121049 + 0.209663i
\(304\) 0 0
\(305\) 0.514400 0.890968i 0.0294545 0.0510167i
\(306\) 0 0
\(307\) −16.1406 + 27.9564i −0.921193 + 1.59555i −0.123621 + 0.992329i \(0.539451\pi\)
−0.797572 + 0.603224i \(0.793883\pi\)
\(308\) 0 0
\(309\) −1.25035 2.16566i −0.0711297 0.123200i
\(310\) 0 0
\(311\) −6.42942 −0.364579 −0.182289 0.983245i \(-0.558351\pi\)
−0.182289 + 0.983245i \(0.558351\pi\)
\(312\) 0 0
\(313\) −1.54276 −0.0872018 −0.0436009 0.999049i \(-0.513883\pi\)
−0.0436009 + 0.999049i \(0.513883\pi\)
\(314\) 0 0
\(315\) 2.01447 + 3.48916i 0.113502 + 0.196592i
\(316\) 0 0
\(317\) −0.825808 + 1.43034i −0.0463820 + 0.0803360i −0.888284 0.459294i \(-0.848102\pi\)
0.841902 + 0.539630i \(0.181436\pi\)
\(318\) 0 0
\(319\) −10.0759 + 17.4520i −0.564143 + 0.977125i
\(320\) 0 0
\(321\) 0.117103 0.00653608
\(322\) 0 0
\(323\) 1.77934 + 3.08190i 0.0990049 + 0.171481i
\(324\) 0 0
\(325\) −0.795531 + 1.37790i −0.0441281 + 0.0764322i
\(326\) 0 0
\(327\) −6.47281 −0.357947
\(328\) 0 0
\(329\) 12.2461 21.2109i 0.675150 1.16939i
\(330\) 0 0
\(331\) 6.91944 + 11.9848i 0.380327 + 0.658745i 0.991109 0.133054i \(-0.0424783\pi\)
−0.610782 + 0.791799i \(0.709145\pi\)
\(332\) 0 0
\(333\) −1.94572 + 3.37008i −0.106625 + 0.184679i
\(334\) 0 0
\(335\) −2.98224 7.62274i −0.162937 0.416475i
\(336\) 0 0
\(337\) −6.03143 + 10.4467i −0.328553 + 0.569070i −0.982225 0.187708i \(-0.939894\pi\)
0.653672 + 0.756778i \(0.273228\pi\)
\(338\) 0 0
\(339\) 9.71169 + 16.8211i 0.527467 + 0.913599i
\(340\) 0 0
\(341\) −4.76285 + 8.24950i −0.257923 + 0.446736i
\(342\) 0 0
\(343\) −8.99370 −0.485614
\(344\) 0 0
\(345\) 0.358507 0.620953i 0.0193014 0.0334310i
\(346\) 0 0
\(347\) 12.2895 + 21.2860i 0.659735 + 1.14269i 0.980684 + 0.195598i \(0.0626647\pi\)
−0.320950 + 0.947096i \(0.604002\pi\)
\(348\) 0 0
\(349\) 7.16779 0.383683 0.191841 0.981426i \(-0.438554\pi\)
0.191841 + 0.981426i \(0.438554\pi\)
\(350\) 0 0
\(351\) 0.795531 1.37790i 0.0424623 0.0735469i
\(352\) 0 0
\(353\) −0.327236 + 0.566790i −0.0174170 + 0.0301672i −0.874603 0.484841i \(-0.838878\pi\)
0.857186 + 0.515008i \(0.172211\pi\)
\(354\) 0 0
\(355\) −6.97238 12.0765i −0.370055 0.640955i
\(356\) 0 0
\(357\) 21.1345 1.11855
\(358\) 0 0
\(359\) −3.17595 −0.167620 −0.0838100 0.996482i \(-0.526709\pi\)
−0.0838100 + 0.996482i \(0.526709\pi\)
\(360\) 0 0
\(361\) 9.26989 + 16.0559i 0.487889 + 0.845048i
\(362\) 0 0
\(363\) −1.12607 + 1.95041i −0.0591034 + 0.102370i
\(364\) 0 0
\(365\) −3.44466 + 5.96633i −0.180302 + 0.312292i
\(366\) 0 0
\(367\) −4.51684 7.82339i −0.235777 0.408378i 0.723721 0.690092i \(-0.242430\pi\)
−0.959498 + 0.281715i \(0.909097\pi\)
\(368\) 0 0
\(369\) −0.662081 1.14676i −0.0344666 0.0596979i
\(370\) 0 0
\(371\) 3.70945 + 6.42496i 0.192585 + 0.333567i
\(372\) 0 0
\(373\) 10.5611 + 18.2923i 0.546831 + 0.947140i 0.998489 + 0.0549485i \(0.0174995\pi\)
−0.451658 + 0.892191i \(0.649167\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −10.8405 −0.558316
\(378\) 0 0
\(379\) −3.31206 + 5.73666i −0.170129 + 0.294673i −0.938465 0.345375i \(-0.887752\pi\)
0.768336 + 0.640047i \(0.221085\pi\)
\(380\) 0 0
\(381\) 1.70520 + 2.95350i 0.0873603 + 0.151312i
\(382\) 0 0
\(383\) 0.133978 0.232057i 0.00684598 0.0118576i −0.862582 0.505917i \(-0.831154\pi\)
0.869428 + 0.494059i \(0.164488\pi\)
\(384\) 0 0
\(385\) −5.95814 + 10.3198i −0.303655 + 0.525946i
\(386\) 0 0
\(387\) −10.8759 −0.552855
\(388\) 0 0
\(389\) 6.38734 11.0632i 0.323851 0.560926i −0.657428 0.753517i \(-0.728356\pi\)
0.981279 + 0.192591i \(0.0616890\pi\)
\(390\) 0 0
\(391\) −1.88061 3.25732i −0.0951066 0.164730i
\(392\) 0 0
\(393\) −11.5182 −0.581015
\(394\) 0 0
\(395\) 5.19415 + 8.99654i 0.261346 + 0.452665i
\(396\) 0 0
\(397\) 32.4347 1.62785 0.813924 0.580971i \(-0.197327\pi\)
0.813924 + 0.580971i \(0.197327\pi\)
\(398\) 0 0
\(399\) −2.73323 −0.136833
\(400\) 0 0
\(401\) 20.0300 1.00025 0.500126 0.865953i \(-0.333287\pi\)
0.500126 + 0.865953i \(0.333287\pi\)
\(402\) 0 0
\(403\) −5.12429 −0.255259
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −11.5096 −0.570510
\(408\) 0 0
\(409\) −12.2965 21.2982i −0.608024 1.05313i −0.991566 0.129605i \(-0.958629\pi\)
0.383542 0.923523i \(-0.374704\pi\)
\(410\) 0 0
\(411\) 2.14095 0.105605
\(412\) 0 0
\(413\) 6.48368 + 11.2301i 0.319041 + 0.552595i
\(414\) 0 0
\(415\) 3.85758 6.68153i 0.189361 0.327983i
\(416\) 0 0
\(417\) 5.56402 0.272471
\(418\) 0 0
\(419\) −1.19377 + 2.06766i −0.0583193 + 0.101012i −0.893711 0.448643i \(-0.851907\pi\)
0.835392 + 0.549655i \(0.185241\pi\)
\(420\) 0 0
\(421\) −0.238338 + 0.412813i −0.0116159 + 0.0201193i −0.871775 0.489907i \(-0.837031\pi\)
0.860159 + 0.510026i \(0.170364\pi\)
\(422\) 0 0
\(423\) −3.03954 5.26464i −0.147788 0.255976i
\(424\) 0 0
\(425\) −2.62284 + 4.54289i −0.127226 + 0.220362i
\(426\) 0 0
\(427\) 4.14497 0.200589
\(428\) 0 0
\(429\) 4.70585 0.227201
\(430\) 0 0
\(431\) 3.80478 + 6.59007i 0.183270 + 0.317433i 0.942992 0.332815i \(-0.107998\pi\)
−0.759722 + 0.650248i \(0.774665\pi\)
\(432\) 0 0
\(433\) 0.433672 + 0.751142i 0.0208409 + 0.0360976i 0.876258 0.481843i \(-0.160032\pi\)
−0.855417 + 0.517940i \(0.826699\pi\)
\(434\) 0 0
\(435\) −3.40670 5.90058i −0.163339 0.282911i
\(436\) 0 0
\(437\) 0.243212 + 0.421255i 0.0116344 + 0.0201514i
\(438\) 0 0
\(439\) 15.4885 26.8268i 0.739224 1.28037i −0.213621 0.976917i \(-0.568526\pi\)
0.952845 0.303457i \(-0.0981409\pi\)
\(440\) 0 0
\(441\) −4.61614 + 7.99539i −0.219816 + 0.380733i
\(442\) 0 0
\(443\) −15.0873 26.1320i −0.716820 1.24157i −0.962253 0.272155i \(-0.912263\pi\)
0.245433 0.969414i \(-0.421070\pi\)
\(444\) 0 0
\(445\) −0.969090 −0.0459393
\(446\) 0 0
\(447\) −11.7958 −0.557921
\(448\) 0 0
\(449\) 5.98151 + 10.3603i 0.282285 + 0.488932i 0.971947 0.235199i \(-0.0755743\pi\)
−0.689662 + 0.724131i \(0.742241\pi\)
\(450\) 0 0
\(451\) 1.95822 3.39174i 0.0922091 0.159711i
\(452\) 0 0
\(453\) −1.51228 + 2.61935i −0.0710533 + 0.123068i
\(454\) 0 0
\(455\) −6.41028 −0.300519
\(456\) 0 0
\(457\) −7.14859 12.3817i −0.334397 0.579192i 0.648972 0.760812i \(-0.275199\pi\)
−0.983369 + 0.181620i \(0.941866\pi\)
\(458\) 0 0
\(459\) 2.62284 4.54289i 0.122424 0.212044i
\(460\) 0 0
\(461\) 17.9836 0.837582 0.418791 0.908083i \(-0.362454\pi\)
0.418791 + 0.908083i \(0.362454\pi\)
\(462\) 0 0
\(463\) −10.2327 + 17.7236i −0.475555 + 0.823686i −0.999608 0.0279998i \(-0.991086\pi\)
0.524053 + 0.851686i \(0.324420\pi\)
\(464\) 0 0
\(465\) −1.61034 2.78918i −0.0746775 0.129345i
\(466\) 0 0
\(467\) 2.59920 4.50194i 0.120277 0.208325i −0.799600 0.600533i \(-0.794955\pi\)
0.919877 + 0.392208i \(0.128289\pi\)
\(468\) 0 0
\(469\) 20.5893 25.7613i 0.950727 1.18954i
\(470\) 0 0
\(471\) 1.96108 3.39669i 0.0903619 0.156511i
\(472\) 0 0
\(473\) −16.0838 27.8579i −0.739532 1.28091i
\(474\) 0 0
\(475\) 0.339201 0.587513i 0.0155636 0.0269569i
\(476\) 0 0
\(477\) 1.84141 0.0843123
\(478\) 0 0
\(479\) 6.34803 10.9951i 0.290049 0.502379i −0.683772 0.729695i \(-0.739662\pi\)
0.973821 + 0.227316i \(0.0729952\pi\)
\(480\) 0 0
\(481\) −3.09576 5.36201i −0.141154 0.244487i
\(482\) 0 0
\(483\) 2.88880 0.131445
\(484\) 0 0
\(485\) 4.77014 8.26213i 0.216601 0.375164i
\(486\) 0 0
\(487\) −7.08345 + 12.2689i −0.320982 + 0.555957i −0.980691 0.195564i \(-0.937346\pi\)
0.659709 + 0.751521i \(0.270680\pi\)
\(488\) 0 0
\(489\) −2.37206 4.10853i −0.107268 0.185794i
\(490\) 0 0
\(491\) 32.0080 1.44450 0.722250 0.691632i \(-0.243108\pi\)
0.722250 + 0.691632i \(0.243108\pi\)
\(492\) 0 0
\(493\) −35.7409 −1.60969
\(494\) 0 0
\(495\) 1.47884 + 2.56142i 0.0664689 + 0.115127i
\(496\) 0 0
\(497\) 28.0912 48.6554i 1.26006 2.18249i
\(498\) 0 0
\(499\) −16.2186 + 28.0914i −0.726043 + 1.25754i 0.232500 + 0.972596i \(0.425309\pi\)
−0.958543 + 0.284947i \(0.908024\pi\)
\(500\) 0 0
\(501\) 1.13784 + 1.97079i 0.0508348 + 0.0880485i
\(502\) 0 0
\(503\) 16.7195 + 28.9591i 0.745487 + 1.29122i 0.949967 + 0.312350i \(0.101116\pi\)
−0.204480 + 0.978871i \(0.565550\pi\)
\(504\) 0 0
\(505\) −2.10709 3.64959i −0.0937642 0.162404i
\(506\) 0 0
\(507\) −5.23426 9.06600i −0.232462 0.402635i
\(508\) 0 0
\(509\) −17.2804 −0.765940 −0.382970 0.923761i \(-0.625099\pi\)
−0.382970 + 0.923761i \(0.625099\pi\)
\(510\) 0 0
\(511\) −27.7566 −1.22788
\(512\) 0 0
\(513\) −0.339201 + 0.587513i −0.0149761 + 0.0259393i
\(514\) 0 0
\(515\) 1.25035 + 2.16566i 0.0550968 + 0.0954305i
\(516\) 0 0
\(517\) 8.98999 15.5711i 0.395379 0.684817i
\(518\) 0 0
\(519\) −0.382324 + 0.662205i −0.0167822 + 0.0290676i
\(520\) 0 0
\(521\) −11.5957 −0.508015 −0.254008 0.967202i \(-0.581749\pi\)
−0.254008 + 0.967202i \(0.581749\pi\)
\(522\) 0 0
\(523\) 4.86867 8.43278i 0.212892 0.368740i −0.739726 0.672908i \(-0.765045\pi\)
0.952618 + 0.304168i \(0.0983784\pi\)
\(524\) 0 0
\(525\) −2.01447 3.48916i −0.0879185 0.152279i
\(526\) 0 0
\(527\) −16.8946 −0.735940
\(528\) 0 0
\(529\) 11.2429 + 19.4734i 0.488824 + 0.846667i
\(530\) 0 0
\(531\) 3.21856 0.139674
\(532\) 0 0
\(533\) 2.10683 0.0912568
\(534\) 0 0
\(535\) −0.117103 −0.00506283
\(536\) 0 0
\(537\) 15.9147 0.686769
\(538\) 0 0
\(539\) −27.3061 −1.17616
\(540\) 0 0
\(541\) 12.8255 0.551411 0.275706 0.961242i \(-0.411088\pi\)
0.275706 + 0.961242i \(0.411088\pi\)
\(542\) 0 0
\(543\) −2.99097 5.18051i −0.128355 0.222317i
\(544\) 0 0
\(545\) 6.47281 0.277265
\(546\) 0 0
\(547\) 7.47486 + 12.9468i 0.319602 + 0.553567i 0.980405 0.196992i \(-0.0631174\pi\)
−0.660803 + 0.750559i \(0.729784\pi\)
\(548\) 0 0
\(549\) 0.514400 0.890968i 0.0219541 0.0380256i
\(550\) 0 0
\(551\) 4.62222 0.196913
\(552\) 0 0
\(553\) −20.9269 + 36.2464i −0.889902 + 1.54136i
\(554\) 0 0
\(555\) 1.94572 3.37008i 0.0825911 0.143052i
\(556\) 0 0
\(557\) 19.2541 + 33.3490i 0.815821 + 1.41304i 0.908737 + 0.417369i \(0.137048\pi\)
−0.0929167 + 0.995674i \(0.529619\pi\)
\(558\) 0 0
\(559\) 8.65215 14.9860i 0.365947 0.633838i
\(560\) 0 0
\(561\) 15.5150 0.655044
\(562\) 0 0
\(563\) −3.97968 −0.167724 −0.0838618 0.996477i \(-0.526725\pi\)
−0.0838618 + 0.996477i \(0.526725\pi\)
\(564\) 0 0
\(565\) −9.71169 16.8211i −0.408574 0.707671i
\(566\) 0 0
\(567\) 2.01447 + 3.48916i 0.0845996 + 0.146531i
\(568\) 0 0
\(569\) −21.8974 37.9274i −0.917987 1.59000i −0.802468 0.596696i \(-0.796480\pi\)
−0.115520 0.993305i \(-0.536853\pi\)
\(570\) 0 0
\(571\) −4.86063 8.41885i −0.203411 0.352318i 0.746214 0.665706i \(-0.231869\pi\)
−0.949625 + 0.313388i \(0.898536\pi\)
\(572\) 0 0
\(573\) −1.91365 + 3.31454i −0.0799439 + 0.138467i
\(574\) 0 0
\(575\) −0.358507 + 0.620953i −0.0149508 + 0.0258955i
\(576\) 0 0
\(577\) −13.9145 24.1006i −0.579267 1.00332i −0.995564 0.0940915i \(-0.970005\pi\)
0.416296 0.909229i \(-0.363328\pi\)
\(578\) 0 0
\(579\) 7.18305 0.298517
\(580\) 0 0
\(581\) 31.0839 1.28958
\(582\) 0 0
\(583\) 2.72315 + 4.71663i 0.112781 + 0.195343i
\(584\) 0 0
\(585\) −0.795531 + 1.37790i −0.0328912 + 0.0569692i
\(586\) 0 0
\(587\) 3.88217 6.72411i 0.160234 0.277534i −0.774718 0.632306i \(-0.782108\pi\)
0.934953 + 0.354773i \(0.115442\pi\)
\(588\) 0 0
\(589\) 2.18491 0.0900275
\(590\) 0 0
\(591\) −11.5593 20.0213i −0.475486 0.823566i
\(592\) 0 0
\(593\) 5.59382 9.68879i 0.229711 0.397871i −0.728012 0.685565i \(-0.759555\pi\)
0.957722 + 0.287694i \(0.0928886\pi\)
\(594\) 0 0
\(595\) −21.1345 −0.866428
\(596\) 0 0
\(597\) 13.4217 23.2470i 0.549312 0.951436i
\(598\) 0 0
\(599\) 1.91450 + 3.31600i 0.0782242 + 0.135488i 0.902484 0.430724i \(-0.141742\pi\)
−0.824260 + 0.566212i \(0.808408\pi\)
\(600\) 0 0
\(601\) 13.2689 22.9825i 0.541251 0.937474i −0.457582 0.889168i \(-0.651284\pi\)
0.998833 0.0483065i \(-0.0153824\pi\)
\(602\) 0 0
\(603\) −2.98224 7.62274i −0.121446 0.310422i
\(604\) 0 0
\(605\) 1.12607 1.95041i 0.0457813 0.0792956i
\(606\) 0 0
\(607\) −20.4414 35.4055i −0.829690 1.43707i −0.898282 0.439420i \(-0.855184\pi\)
0.0685917 0.997645i \(-0.478149\pi\)
\(608\) 0 0
\(609\) 13.7254 23.7730i 0.556180 0.963331i
\(610\) 0 0
\(611\) 9.67221 0.391296
\(612\) 0 0
\(613\) −11.3259 + 19.6170i −0.457448 + 0.792324i −0.998825 0.0484563i \(-0.984570\pi\)
0.541377 + 0.840780i \(0.317903\pi\)
\(614\) 0 0
\(615\) 0.662081 + 1.14676i 0.0266977 + 0.0462418i
\(616\) 0 0
\(617\) 40.4341 1.62782 0.813908 0.580994i \(-0.197336\pi\)
0.813908 + 0.580994i \(0.197336\pi\)
\(618\) 0 0
\(619\) 5.51336 9.54942i 0.221601 0.383823i −0.733694 0.679480i \(-0.762205\pi\)
0.955294 + 0.295657i \(0.0955386\pi\)
\(620\) 0 0
\(621\) 0.358507 0.620953i 0.0143864 0.0249180i
\(622\) 0 0
\(623\) −1.95220 3.38131i −0.0782132 0.135469i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −2.00649 −0.0801316
\(628\) 0 0
\(629\) −10.2066 17.6783i −0.406964 0.704882i
\(630\) 0 0
\(631\) −9.30826 + 16.1224i −0.370556 + 0.641821i −0.989651 0.143494i \(-0.954166\pi\)
0.619095 + 0.785316i \(0.287499\pi\)
\(632\) 0 0
\(633\) 1.30980 2.26864i 0.0520599 0.0901704i
\(634\) 0 0
\(635\) −1.70520 2.95350i −0.0676690 0.117206i
\(636\) 0 0
\(637\) −7.34457 12.7212i −0.291002 0.504031i
\(638\) 0 0
\(639\) −6.97238 12.0765i −0.275823 0.477739i
\(640\) 0 0
\(641\) −12.3550 21.3996i −0.487995 0.845232i 0.511910 0.859039i \(-0.328938\pi\)
−0.999905 + 0.0138072i \(0.995605\pi\)
\(642\) 0 0
\(643\) 33.5875 1.32456 0.662282 0.749255i \(-0.269588\pi\)
0.662282 + 0.749255i \(0.269588\pi\)
\(644\) 0 0
\(645\) 10.8759 0.428239
\(646\) 0 0
\(647\) −22.6888 + 39.2982i −0.891990 + 1.54497i −0.0545048 + 0.998514i \(0.517358\pi\)
−0.837486 + 0.546459i \(0.815975\pi\)
\(648\) 0 0
\(649\) 4.75973 + 8.24410i 0.186836 + 0.323609i
\(650\) 0 0
\(651\) 6.48793 11.2374i 0.254282 0.440429i
\(652\) 0 0
\(653\) 4.60834 7.98188i 0.180338 0.312355i −0.761657 0.647980i \(-0.775614\pi\)
0.941996 + 0.335625i \(0.108947\pi\)
\(654\) 0 0
\(655\) 11.5182 0.450052
\(656\) 0 0
\(657\) −3.44466 + 5.96633i −0.134389 + 0.232769i
\(658\) 0 0
\(659\) 5.09361 + 8.82238i 0.198419 + 0.343671i 0.948016 0.318223i \(-0.103086\pi\)
−0.749597 + 0.661894i \(0.769753\pi\)
\(660\) 0 0
\(661\) 32.9987 1.28350 0.641751 0.766913i \(-0.278208\pi\)
0.641751 + 0.766913i \(0.278208\pi\)
\(662\) 0 0
\(663\) 4.17310 + 7.22802i 0.162070 + 0.280713i
\(664\) 0 0
\(665\) 2.73323 0.105990
\(666\) 0 0
\(667\) −4.88531 −0.189160
\(668\) 0 0
\(669\) 17.5929 0.680182
\(670\) 0 0
\(671\) 3.04286 0.117468
\(672\) 0 0
\(673\) −28.6692 −1.10512 −0.552558 0.833475i \(-0.686348\pi\)
−0.552558 + 0.833475i \(0.686348\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 6.59788 + 11.4279i 0.253577 + 0.439208i 0.964508 0.264053i \(-0.0850595\pi\)
−0.710931 + 0.703262i \(0.751726\pi\)
\(678\) 0 0
\(679\) 38.4372 1.47508
\(680\) 0 0
\(681\) −1.78070 3.08427i −0.0682367 0.118189i
\(682\) 0 0
\(683\) −8.35528 + 14.4718i −0.319706 + 0.553747i −0.980427 0.196885i \(-0.936917\pi\)
0.660721 + 0.750632i \(0.270251\pi\)
\(684\) 0 0
\(685\) −2.14095 −0.0818013
\(686\) 0 0
\(687\) 11.9704 20.7333i 0.456699 0.791025i
\(688\) 0 0
\(689\) −1.46490 + 2.53728i −0.0558082 + 0.0966626i
\(690\) 0 0
\(691\) 18.3246 + 31.7392i 0.697101 + 1.20742i 0.969467 + 0.245221i \(0.0788606\pi\)
−0.272366 + 0.962194i \(0.587806\pi\)
\(692\) 0 0
\(693\) −5.95814 + 10.3198i −0.226331 + 0.392017i
\(694\) 0 0
\(695\) −5.56402 −0.211055
\(696\) 0 0
\(697\) 6.94613 0.263103
\(698\) 0 0
\(699\) −11.5277 19.9665i −0.436016 0.755203i
\(700\) 0 0
\(701\) −0.0317333 0.0549637i −0.00119855 0.00207595i 0.865426 0.501038i \(-0.167048\pi\)
−0.866624 + 0.498962i \(0.833715\pi\)
\(702\) 0 0
\(703\) 1.31998 + 2.28627i 0.0497839 + 0.0862282i
\(704\) 0 0
\(705\) 3.03954 + 5.26464i 0.114476 + 0.198278i
\(706\) 0 0
\(707\) 8.48932 14.7039i 0.319274 0.552998i
\(708\) 0 0
\(709\) −5.92424 + 10.2611i −0.222490 + 0.385363i −0.955563 0.294786i \(-0.904752\pi\)
0.733074 + 0.680149i \(0.238085\pi\)
\(710\) 0 0
\(711\) 5.19415 + 8.99654i 0.194796 + 0.337397i
\(712\) 0 0
\(713\) −2.30927 −0.0864828
\(714\) 0 0
\(715\) −4.70585 −0.175989
\(716\) 0 0
\(717\) 0.785887 + 1.36120i 0.0293495 + 0.0508348i
\(718\) 0 0
\(719\) 13.5290 23.4328i 0.504545 0.873897i −0.495441 0.868641i \(-0.664994\pi\)
0.999986 0.00525586i \(-0.00167300\pi\)
\(720\) 0 0
\(721\) −5.03756 + 8.72531i −0.187609 + 0.324947i
\(722\) 0 0
\(723\) −0.751633 −0.0279535
\(724\) 0 0
\(725\) 3.40670 + 5.90058i 0.126522 + 0.219142i
\(726\) 0 0
\(727\) −3.11684 + 5.39852i −0.115597 + 0.200220i −0.918018 0.396538i \(-0.870211\pi\)
0.802421 + 0.596758i \(0.203545\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 28.5258 49.4081i 1.05506 1.82743i
\(732\) 0 0
\(733\) 22.7516 + 39.4069i 0.840349 + 1.45553i 0.889600 + 0.456741i \(0.150983\pi\)
−0.0492511 + 0.998786i \(0.515683\pi\)
\(734\) 0 0
\(735\) 4.61614 7.99539i 0.170269 0.294914i
\(736\) 0 0
\(737\) 15.1148 18.9116i 0.556762 0.696618i
\(738\) 0 0
\(739\) −5.89645 + 10.2130i −0.216904 + 0.375690i −0.953860 0.300252i \(-0.902929\pi\)
0.736956 + 0.675941i \(0.236263\pi\)
\(740\) 0 0
\(741\) −0.539689 0.934769i −0.0198260 0.0343396i
\(742\) 0 0
\(743\) 14.3166 24.7970i 0.525224 0.909715i −0.474344 0.880339i \(-0.657315\pi\)
0.999568 0.0293756i \(-0.00935189\pi\)
\(744\) 0 0
\(745\) 11.7958 0.432164
\(746\) 0 0
\(747\) 3.85758 6.68153i 0.141142 0.244464i
\(748\) 0 0
\(749\) −0.235901 0.408592i −0.00861963 0.0149296i
\(750\) 0 0
\(751\) 18.0352 0.658112 0.329056 0.944310i \(-0.393269\pi\)
0.329056 + 0.944310i \(0.393269\pi\)
\(752\) 0 0
\(753\) −15.1397 + 26.2227i −0.551720 + 0.955607i
\(754\) 0 0
\(755\) 1.51228 2.61935i 0.0550377 0.0953280i
\(756\) 0 0
\(757\) −5.56650 9.64145i −0.202318 0.350425i 0.746957 0.664872i \(-0.231514\pi\)
−0.949275 + 0.314448i \(0.898181\pi\)
\(758\) 0 0
\(759\) 2.12070 0.0769765
\(760\) 0 0
\(761\) −4.62039 −0.167489 −0.0837446 0.996487i \(-0.526688\pi\)
−0.0837446 + 0.996487i \(0.526688\pi\)
\(762\) 0 0
\(763\) 13.0393 + 22.5847i 0.472053 + 0.817620i
\(764\) 0 0
\(765\) −2.62284 + 4.54289i −0.0948289 + 0.164248i
\(766\) 0 0
\(767\) −2.56047 + 4.43486i −0.0924531 + 0.160133i
\(768\) 0 0
\(769\) 3.44864 + 5.97321i 0.124361 + 0.215400i 0.921483 0.388419i \(-0.126979\pi\)
−0.797122 + 0.603818i \(0.793645\pi\)
\(770\) 0 0
\(771\) −4.51598 7.82191i −0.162639 0.281699i
\(772\) 0 0
\(773\) 10.0363 + 17.3833i 0.360980 + 0.625235i 0.988122 0.153669i \(-0.0491090\pi\)
−0.627143 + 0.778904i \(0.715776\pi\)
\(774\) 0 0
\(775\) 1.61034 + 2.78918i 0.0578449 + 0.100190i
\(776\) 0 0
\(777\) 15.6783 0.562457
\(778\) 0 0
\(779\) −0.898314 −0.0321854
\(780\) 0 0
\(781\) 20.6220 35.7184i 0.737915 1.27811i
\(782\) 0 0
\(783\) −3.40670 5.90058i −0.121746 0.210869i
\(784\) 0 0
\(785\) −1.96108 + 3.39669i −0.0699940 + 0.121233i
\(786\) 0 0
\(787\) −4.64960 + 8.05335i −0.165740 + 0.287071i −0.936918 0.349549i \(-0.886335\pi\)
0.771178 + 0.636620i \(0.219668\pi\)
\(788\) 0 0
\(789\) 13.4758 0.479751
\(790\) 0 0
\(791\) 39.1277 67.7712i 1.39122 2.40967i
\(792\) 0 0
\(793\) 0.818443 + 1.41759i 0.0290638 + 0.0503399i