Properties

Label 4020.2.q.k.3781.6
Level 4020
Weight 2
Character 4020.3781
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 3781.6
Root \(-1.36264 - 2.36015i\)
Character \(\chi\) = 4020.3781
Dual form 4020.2.q.k.841.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +(1.26463 + 2.19041i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +(1.26463 + 2.19041i) q^{7} +1.00000 q^{9} +(0.0636774 + 0.110293i) q^{11} +(-2.22527 + 3.85428i) q^{13} -1.00000 q^{15} +(0.129720 - 0.224682i) q^{17} +(3.21355 - 5.56603i) q^{19} +(-1.26463 - 2.19041i) q^{21} +(3.09212 - 5.35572i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-0.920164 - 1.59377i) q^{29} +(-2.61911 - 4.53644i) q^{31} +(-0.0636774 - 0.110293i) q^{33} +(1.26463 + 2.19041i) q^{35} +(4.92280 - 8.52654i) q^{37} +(2.22527 - 3.85428i) q^{39} +(0.579529 + 1.00377i) q^{41} +2.35137 q^{43} +1.00000 q^{45} +(5.48732 + 9.50432i) q^{47} +(0.301411 - 0.522059i) q^{49} +(-0.129720 + 0.224682i) q^{51} -2.37847 q^{53} +(0.0636774 + 0.110293i) q^{55} +(-3.21355 + 5.56603i) q^{57} -0.400614 q^{59} +(2.78302 - 4.82033i) q^{61} +(1.26463 + 2.19041i) q^{63} +(-2.22527 + 3.85428i) q^{65} +(7.76655 + 2.58469i) q^{67} +(-3.09212 + 5.35572i) q^{69} +(3.62714 + 6.28239i) q^{71} +(1.00399 - 1.73897i) q^{73} -1.00000 q^{75} +(-0.161057 + 0.278959i) q^{77} +(0.753802 + 1.30562i) q^{79} +1.00000 q^{81} +(-3.21009 + 5.56004i) q^{83} +(0.129720 - 0.224682i) q^{85} +(0.920164 + 1.59377i) q^{87} -1.27157 q^{89} -11.2566 q^{91} +(2.61911 + 4.53644i) q^{93} +(3.21355 - 5.56603i) q^{95} +(-2.93224 + 5.07880i) q^{97} +(0.0636774 + 0.110293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + 6q^{11} + 9q^{13} - 14q^{15} - 12q^{17} + 14q^{19} - 3q^{21} + 6q^{23} + 14q^{25} - 14q^{27} - q^{29} + 7q^{31} - 6q^{33} + 3q^{35} - 2q^{37} - 9q^{39} - 18q^{41} - 6q^{43} + 14q^{45} + 7q^{47} + 12q^{51} - 12q^{53} + 6q^{55} - 14q^{57} - 2q^{59} + 3q^{63} + 9q^{65} + 25q^{67} - 6q^{69} + 22q^{71} - 15q^{73} - 14q^{75} + q^{77} + 9q^{79} + 14q^{81} - q^{83} - 12q^{85} + q^{87} - 12q^{89} - 38q^{91} - 7q^{93} + 14q^{95} + 16q^{97} + 6q^{99} + O(q^{100}) \)

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
\(7\) 1.26463 + 2.19041i 0.477986 + 0.827896i 0.999682 0.0252357i \(-0.00803361\pi\)
−0.521695 + 0.853132i \(0.674700\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.0636774 + 0.110293i 0.0191995 + 0.0332544i 0.875466 0.483281i \(-0.160555\pi\)
−0.856266 + 0.516535i \(0.827222\pi\)
\(12\) 0 0
\(13\) −2.22527 + 3.85428i −0.617179 + 1.06899i 0.372819 + 0.927904i \(0.378391\pi\)
−0.989998 + 0.141081i \(0.954942\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 0.129720 0.224682i 0.0314618 0.0544935i −0.849866 0.526999i \(-0.823317\pi\)
0.881328 + 0.472506i \(0.156650\pi\)
\(18\) 0 0
\(19\) 3.21355 5.56603i 0.737239 1.27694i −0.216495 0.976284i \(-0.569463\pi\)
0.953734 0.300652i \(-0.0972041\pi\)
\(20\) 0 0
\(21\) −1.26463 2.19041i −0.275965 0.477986i
\(22\) 0 0
\(23\) 3.09212 5.35572i 0.644753 1.11674i −0.339606 0.940568i \(-0.610294\pi\)
0.984359 0.176176i \(-0.0563729\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −0.920164 1.59377i −0.170870 0.295956i 0.767854 0.640625i \(-0.221325\pi\)
−0.938724 + 0.344669i \(0.887991\pi\)
\(30\) 0 0
\(31\) −2.61911 4.53644i −0.470407 0.814768i 0.529021 0.848609i \(-0.322559\pi\)
−0.999427 + 0.0338409i \(0.989226\pi\)
\(32\) 0 0
\(33\) −0.0636774 0.110293i −0.0110848 0.0191995i
\(34\) 0 0
\(35\) 1.26463 + 2.19041i 0.213762 + 0.370246i
\(36\) 0 0
\(37\) 4.92280 8.52654i 0.809303 1.40175i −0.104044 0.994573i \(-0.533178\pi\)
0.913347 0.407182i \(-0.133488\pi\)
\(38\) 0 0
\(39\) 2.22527 3.85428i 0.356328 0.617179i
\(40\) 0 0
\(41\) 0.579529 + 1.00377i 0.0905072 + 0.156763i 0.907725 0.419566i \(-0.137818\pi\)
−0.817217 + 0.576329i \(0.804485\pi\)
\(42\) 0 0
\(43\) 2.35137 0.358580 0.179290 0.983796i \(-0.442620\pi\)
0.179290 + 0.983796i \(0.442620\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 5.48732 + 9.50432i 0.800408 + 1.38635i 0.919348 + 0.393446i \(0.128717\pi\)
−0.118940 + 0.992901i \(0.537950\pi\)
\(48\) 0 0
\(49\) 0.301411 0.522059i 0.0430587 0.0745798i
\(50\) 0 0
\(51\) −0.129720 + 0.224682i −0.0181645 + 0.0314618i
\(52\) 0 0
\(53\) −2.37847 −0.326708 −0.163354 0.986568i \(-0.552231\pi\)
−0.163354 + 0.986568i \(0.552231\pi\)
\(54\) 0 0
\(55\) 0.0636774 + 0.110293i 0.00858626 + 0.0148718i
\(56\) 0 0
\(57\) −3.21355 + 5.56603i −0.425645 + 0.737239i
\(58\) 0 0
\(59\) −0.400614 −0.0521555 −0.0260777 0.999660i \(-0.508302\pi\)
−0.0260777 + 0.999660i \(0.508302\pi\)
\(60\) 0 0
\(61\) 2.78302 4.82033i 0.356329 0.617180i −0.631015 0.775770i \(-0.717362\pi\)
0.987344 + 0.158590i \(0.0506949\pi\)
\(62\) 0 0
\(63\) 1.26463 + 2.19041i 0.159329 + 0.275965i
\(64\) 0 0
\(65\) −2.22527 + 3.85428i −0.276011 + 0.478065i
\(66\) 0 0
\(67\) 7.76655 + 2.58469i 0.948836 + 0.315771i
\(68\) 0 0
\(69\) −3.09212 + 5.35572i −0.372248 + 0.644753i
\(70\) 0 0
\(71\) 3.62714 + 6.28239i 0.430462 + 0.745582i 0.996913 0.0785133i \(-0.0250173\pi\)
−0.566451 + 0.824095i \(0.691684\pi\)
\(72\) 0 0
\(73\) 1.00399 1.73897i 0.117509 0.203531i −0.801271 0.598301i \(-0.795843\pi\)
0.918780 + 0.394770i \(0.129176\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) −0.161057 + 0.278959i −0.0183542 + 0.0317903i
\(78\) 0 0
\(79\) 0.753802 + 1.30562i 0.0848094 + 0.146894i 0.905310 0.424752i \(-0.139639\pi\)
−0.820501 + 0.571646i \(0.806305\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.21009 + 5.56004i −0.352353 + 0.610294i −0.986661 0.162786i \(-0.947952\pi\)
0.634308 + 0.773081i \(0.281285\pi\)
\(84\) 0 0
\(85\) 0.129720 0.224682i 0.0140702 0.0243702i
\(86\) 0 0
\(87\) 0.920164 + 1.59377i 0.0986520 + 0.170870i
\(88\) 0 0
\(89\) −1.27157 −0.134786 −0.0673932 0.997726i \(-0.521468\pi\)
−0.0673932 + 0.997726i \(0.521468\pi\)
\(90\) 0 0
\(91\) −11.2566 −1.18001
\(92\) 0 0
\(93\) 2.61911 + 4.53644i 0.271589 + 0.470407i
\(94\) 0 0
\(95\) 3.21355 5.56603i 0.329703 0.571063i
\(96\) 0 0
\(97\) −2.93224 + 5.07880i −0.297724 + 0.515674i −0.975615 0.219489i \(-0.929561\pi\)
0.677891 + 0.735163i \(0.262894\pi\)
\(98\) 0 0
\(99\) 0.0636774 + 0.110293i 0.00639982 + 0.0110848i
\(100\) 0 0
\(101\) 1.52837 + 2.64722i 0.152079 + 0.263408i 0.931992 0.362480i \(-0.118070\pi\)
−0.779913 + 0.625888i \(0.784737\pi\)
\(102\) 0 0
\(103\) 6.62209 + 11.4698i 0.652494 + 1.13015i 0.982516 + 0.186180i \(0.0596107\pi\)
−0.330021 + 0.943973i \(0.607056\pi\)
\(104\) 0 0
\(105\) −1.26463 2.19041i −0.123415 0.213762i
\(106\) 0 0
\(107\) 9.51097 0.919460 0.459730 0.888059i \(-0.347946\pi\)
0.459730 + 0.888059i \(0.347946\pi\)
\(108\) 0 0
\(109\) 6.74556 0.646107 0.323054 0.946381i \(-0.395291\pi\)
0.323054 + 0.946381i \(0.395291\pi\)
\(110\) 0 0
\(111\) −4.92280 + 8.52654i −0.467251 + 0.809303i
\(112\) 0 0
\(113\) −4.56883 7.91345i −0.429800 0.744435i 0.567056 0.823679i \(-0.308082\pi\)
−0.996855 + 0.0792448i \(0.974749\pi\)
\(114\) 0 0
\(115\) 3.09212 5.35572i 0.288342 0.499423i
\(116\) 0 0
\(117\) −2.22527 + 3.85428i −0.205726 + 0.356328i
\(118\) 0 0
\(119\) 0.656194 0.0601532
\(120\) 0 0
\(121\) 5.49189 9.51223i 0.499263 0.864748i
\(122\) 0 0
\(123\) −0.579529 1.00377i −0.0522544 0.0905072i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −1.10991 1.92242i −0.0984887 0.170587i 0.812571 0.582863i \(-0.198067\pi\)
−0.911059 + 0.412275i \(0.864734\pi\)
\(128\) 0 0
\(129\) −2.35137 −0.207026
\(130\) 0 0
\(131\) −21.0542 −1.83952 −0.919758 0.392487i \(-0.871615\pi\)
−0.919758 + 0.392487i \(0.871615\pi\)
\(132\) 0 0
\(133\) 16.2558 1.40956
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 7.65782 0.654252 0.327126 0.944981i \(-0.393920\pi\)
0.327126 + 0.944981i \(0.393920\pi\)
\(138\) 0 0
\(139\) 13.0649 1.10815 0.554074 0.832467i \(-0.313072\pi\)
0.554074 + 0.832467i \(0.313072\pi\)
\(140\) 0 0
\(141\) −5.48732 9.50432i −0.462116 0.800408i
\(142\) 0 0
\(143\) −0.566798 −0.0473980
\(144\) 0 0
\(145\) −0.920164 1.59377i −0.0764155 0.132355i
\(146\) 0 0
\(147\) −0.301411 + 0.522059i −0.0248599 + 0.0430587i
\(148\) 0 0
\(149\) −1.39911 −0.114619 −0.0573096 0.998356i \(-0.518252\pi\)
−0.0573096 + 0.998356i \(0.518252\pi\)
\(150\) 0 0
\(151\) −8.77578 + 15.2001i −0.714163 + 1.23697i 0.249118 + 0.968473i \(0.419859\pi\)
−0.963281 + 0.268494i \(0.913474\pi\)
\(152\) 0 0
\(153\) 0.129720 0.224682i 0.0104873 0.0181645i
\(154\) 0 0
\(155\) −2.61911 4.53644i −0.210372 0.364375i
\(156\) 0 0
\(157\) −2.24823 + 3.89404i −0.179428 + 0.310779i −0.941685 0.336496i \(-0.890758\pi\)
0.762257 + 0.647275i \(0.224091\pi\)
\(158\) 0 0
\(159\) 2.37847 0.188625
\(160\) 0 0
\(161\) 15.6416 1.23273
\(162\) 0 0
\(163\) 10.4296 + 18.0645i 0.816907 + 1.41492i 0.907951 + 0.419077i \(0.137646\pi\)
−0.0910440 + 0.995847i \(0.529020\pi\)
\(164\) 0 0
\(165\) −0.0636774 0.110293i −0.00495728 0.00858626i
\(166\) 0 0
\(167\) −6.14610 10.6454i −0.475600 0.823763i 0.524010 0.851712i \(-0.324436\pi\)
−0.999609 + 0.0279497i \(0.991102\pi\)
\(168\) 0 0
\(169\) −3.40366 5.89531i −0.261820 0.453485i
\(170\) 0 0
\(171\) 3.21355 5.56603i 0.245746 0.425645i
\(172\) 0 0
\(173\) 3.90299 6.76018i 0.296739 0.513967i −0.678649 0.734463i \(-0.737434\pi\)
0.975388 + 0.220496i \(0.0707676\pi\)
\(174\) 0 0
\(175\) 1.26463 + 2.19041i 0.0955972 + 0.165579i
\(176\) 0 0
\(177\) 0.400614 0.0301120
\(178\) 0 0
\(179\) 15.9995 1.19586 0.597929 0.801549i \(-0.295990\pi\)
0.597929 + 0.801549i \(0.295990\pi\)
\(180\) 0 0
\(181\) −10.8380 18.7720i −0.805583 1.39531i −0.915897 0.401414i \(-0.868519\pi\)
0.110314 0.993897i \(-0.464814\pi\)
\(182\) 0 0
\(183\) −2.78302 + 4.82033i −0.205727 + 0.356329i
\(184\) 0 0
\(185\) 4.92280 8.52654i 0.361931 0.626884i
\(186\) 0 0
\(187\) 0.0330410 0.00241620
\(188\) 0 0
\(189\) −1.26463 2.19041i −0.0919885 0.159329i
\(190\) 0 0
\(191\) −12.8281 + 22.2189i −0.928207 + 1.60770i −0.141888 + 0.989883i \(0.545317\pi\)
−0.786320 + 0.617820i \(0.788016\pi\)
\(192\) 0 0
\(193\) 17.9337 1.29090 0.645449 0.763804i \(-0.276670\pi\)
0.645449 + 0.763804i \(0.276670\pi\)
\(194\) 0 0
\(195\) 2.22527 3.85428i 0.159355 0.276011i
\(196\) 0 0
\(197\) −3.49225 6.04876i −0.248813 0.430956i 0.714384 0.699754i \(-0.246707\pi\)
−0.963197 + 0.268798i \(0.913374\pi\)
\(198\) 0 0
\(199\) −1.19684 + 2.07299i −0.0848417 + 0.146950i −0.905324 0.424722i \(-0.860372\pi\)
0.820482 + 0.571672i \(0.193705\pi\)
\(200\) 0 0
\(201\) −7.76655 2.58469i −0.547810 0.182310i
\(202\) 0 0
\(203\) 2.32734 4.03107i 0.163347 0.282926i
\(204\) 0 0
\(205\) 0.579529 + 1.00377i 0.0404761 + 0.0701066i
\(206\) 0 0
\(207\) 3.09212 5.35572i 0.214918 0.372248i
\(208\) 0 0
\(209\) 0.818522 0.0566184
\(210\) 0 0
\(211\) 1.40604 2.43533i 0.0967959 0.167655i −0.813561 0.581480i \(-0.802474\pi\)
0.910357 + 0.413824i \(0.135807\pi\)
\(212\) 0 0
\(213\) −3.62714 6.28239i −0.248527 0.430462i
\(214\) 0 0
\(215\) 2.35137 0.160362
\(216\) 0 0
\(217\) 6.62443 11.4738i 0.449695 0.778895i
\(218\) 0 0
\(219\) −1.00399 + 1.73897i −0.0678436 + 0.117509i
\(220\) 0 0
\(221\) 0.577326 + 0.999958i 0.0388352 + 0.0672645i
\(222\) 0 0
\(223\) −12.8891 −0.863117 −0.431558 0.902085i \(-0.642036\pi\)
−0.431558 + 0.902085i \(0.642036\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 4.67253 + 8.09306i 0.310127 + 0.537155i 0.978390 0.206770i \(-0.0662952\pi\)
−0.668263 + 0.743925i \(0.732962\pi\)
\(228\) 0 0
\(229\) 1.60442 2.77893i 0.106023 0.183637i −0.808133 0.589000i \(-0.799522\pi\)
0.914156 + 0.405363i \(0.132855\pi\)
\(230\) 0 0
\(231\) 0.161057 0.278959i 0.0105968 0.0183542i
\(232\) 0 0
\(233\) 5.73530 + 9.93383i 0.375732 + 0.650787i 0.990436 0.137971i \(-0.0440580\pi\)
−0.614704 + 0.788758i \(0.710725\pi\)
\(234\) 0 0
\(235\) 5.48732 + 9.50432i 0.357953 + 0.619993i
\(236\) 0 0
\(237\) −0.753802 1.30562i −0.0489647 0.0848094i
\(238\) 0 0
\(239\) −2.95082 5.11096i −0.190872 0.330601i 0.754667 0.656108i \(-0.227798\pi\)
−0.945540 + 0.325507i \(0.894465\pi\)
\(240\) 0 0
\(241\) 9.02817 0.581556 0.290778 0.956791i \(-0.406086\pi\)
0.290778 + 0.956791i \(0.406086\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0.301411 0.522059i 0.0192564 0.0333531i
\(246\) 0 0
\(247\) 14.3020 + 24.7719i 0.910017 + 1.57620i
\(248\) 0 0
\(249\) 3.21009 5.56004i 0.203431 0.352353i
\(250\) 0 0
\(251\) −2.88177 + 4.99137i −0.181896 + 0.315052i −0.942526 0.334133i \(-0.891557\pi\)
0.760630 + 0.649185i \(0.224890\pi\)
\(252\) 0 0
\(253\) 0.787594 0.0495156
\(254\) 0 0
\(255\) −0.129720 + 0.224682i −0.00812341 + 0.0140702i
\(256\) 0 0
\(257\) −14.0716 24.3727i −0.877761 1.52033i −0.853792 0.520614i \(-0.825703\pi\)
−0.0239683 0.999713i \(-0.507630\pi\)
\(258\) 0 0
\(259\) 24.9021 1.54734
\(260\) 0 0
\(261\) −0.920164 1.59377i −0.0569567 0.0986520i
\(262\) 0 0
\(263\) 14.3621 0.885607 0.442803 0.896619i \(-0.353984\pi\)
0.442803 + 0.896619i \(0.353984\pi\)
\(264\) 0 0
\(265\) −2.37847 −0.146108
\(266\) 0 0
\(267\) 1.27157 0.0778190
\(268\) 0 0
\(269\) 21.7111 1.32375 0.661873 0.749616i \(-0.269762\pi\)
0.661873 + 0.749616i \(0.269762\pi\)
\(270\) 0 0
\(271\) 10.7458 0.652758 0.326379 0.945239i \(-0.394171\pi\)
0.326379 + 0.945239i \(0.394171\pi\)
\(272\) 0 0
\(273\) 11.2566 0.681280
\(274\) 0 0
\(275\) 0.0636774 + 0.110293i 0.00383989 + 0.00665089i
\(276\) 0 0
\(277\) 27.2641 1.63814 0.819070 0.573693i \(-0.194490\pi\)
0.819070 + 0.573693i \(0.194490\pi\)
\(278\) 0 0
\(279\) −2.61911 4.53644i −0.156802 0.271589i
\(280\) 0 0
\(281\) −6.30782 + 10.9255i −0.376293 + 0.651758i −0.990520 0.137371i \(-0.956135\pi\)
0.614227 + 0.789130i \(0.289468\pi\)
\(282\) 0 0
\(283\) 22.7031 1.34956 0.674780 0.738019i \(-0.264239\pi\)
0.674780 + 0.738019i \(0.264239\pi\)
\(284\) 0 0
\(285\) −3.21355 + 5.56603i −0.190354 + 0.329703i
\(286\) 0 0
\(287\) −1.46578 + 2.53881i −0.0865224 + 0.149861i
\(288\) 0 0
\(289\) 8.46635 + 14.6641i 0.498020 + 0.862596i
\(290\) 0 0
\(291\) 2.93224 5.07880i 0.171891 0.297724i
\(292\) 0 0
\(293\) −10.2730 −0.600156 −0.300078 0.953915i \(-0.597013\pi\)
−0.300078 + 0.953915i \(0.597013\pi\)
\(294\) 0 0
\(295\) −0.400614 −0.0233246
\(296\) 0 0
\(297\) −0.0636774 0.110293i −0.00369494 0.00639982i
\(298\) 0 0
\(299\) 13.7616 + 23.8358i 0.795855 + 1.37846i
\(300\) 0 0
\(301\) 2.97362 + 5.15045i 0.171396 + 0.296867i
\(302\) 0 0
\(303\) −1.52837 2.64722i −0.0878028 0.152079i
\(304\) 0 0
\(305\) 2.78302 4.82033i 0.159355 0.276011i
\(306\) 0 0
\(307\) −5.66618 + 9.81412i −0.323386 + 0.560121i −0.981184 0.193073i \(-0.938155\pi\)
0.657798 + 0.753194i \(0.271488\pi\)
\(308\) 0 0
\(309\) −6.62209 11.4698i −0.376718 0.652494i
\(310\) 0 0
\(311\) 13.3637 0.757784 0.378892 0.925441i \(-0.376305\pi\)
0.378892 + 0.925441i \(0.376305\pi\)
\(312\) 0 0
\(313\) 22.3998 1.26611 0.633057 0.774105i \(-0.281800\pi\)
0.633057 + 0.774105i \(0.281800\pi\)
\(314\) 0 0
\(315\) 1.26463 + 2.19041i 0.0712540 + 0.123415i
\(316\) 0 0
\(317\) 13.0809 22.6568i 0.734699 1.27254i −0.220157 0.975464i \(-0.570657\pi\)
0.954855 0.297071i \(-0.0960097\pi\)
\(318\) 0 0
\(319\) 0.117187 0.202974i 0.00656123 0.0113644i
\(320\) 0 0
\(321\) −9.51097 −0.530850
\(322\) 0 0
\(323\) −0.833726 1.44406i −0.0463898 0.0803494i
\(324\) 0 0
\(325\) −2.22527 + 3.85428i −0.123436 + 0.213797i
\(326\) 0 0
\(327\) −6.74556 −0.373030
\(328\) 0 0
\(329\) −13.8789 + 24.0389i −0.765168 + 1.32531i
\(330\) 0 0
\(331\) 11.5888 + 20.0723i 0.636975 + 1.10327i 0.986093 + 0.166195i \(0.0531481\pi\)
−0.349117 + 0.937079i \(0.613519\pi\)
\(332\) 0 0
\(333\) 4.92280 8.52654i 0.269768 0.467251i
\(334\) 0 0
\(335\) 7.76655 + 2.58469i 0.424332 + 0.141217i
\(336\) 0 0
\(337\) −10.8157 + 18.7333i −0.589168 + 1.02047i 0.405173 + 0.914240i \(0.367211\pi\)
−0.994342 + 0.106230i \(0.966122\pi\)
\(338\) 0 0
\(339\) 4.56883 + 7.91345i 0.248145 + 0.429800i
\(340\) 0 0
\(341\) 0.333557 0.577737i 0.0180631 0.0312862i
\(342\) 0 0
\(343\) 19.2295 1.03830
\(344\) 0 0
\(345\) −3.09212 + 5.35572i −0.166474 + 0.288342i
\(346\) 0 0
\(347\) 0.804179 + 1.39288i 0.0431706 + 0.0747736i 0.886803 0.462147i \(-0.152921\pi\)
−0.843633 + 0.536921i \(0.819587\pi\)
\(348\) 0 0
\(349\) −14.7156 −0.787710 −0.393855 0.919173i \(-0.628859\pi\)
−0.393855 + 0.919173i \(0.628859\pi\)
\(350\) 0 0
\(351\) 2.22527 3.85428i 0.118776 0.205726i
\(352\) 0 0
\(353\) −10.3424 + 17.9136i −0.550473 + 0.953447i 0.447768 + 0.894150i \(0.352219\pi\)
−0.998240 + 0.0592968i \(0.981114\pi\)
\(354\) 0 0
\(355\) 3.62714 + 6.28239i 0.192508 + 0.333434i
\(356\) 0 0
\(357\) −0.656194 −0.0347295
\(358\) 0 0
\(359\) −14.3344 −0.756539 −0.378269 0.925696i \(-0.623481\pi\)
−0.378269 + 0.925696i \(0.623481\pi\)
\(360\) 0 0
\(361\) −11.1538 19.3190i −0.587043 1.01679i
\(362\) 0 0
\(363\) −5.49189 + 9.51223i −0.288249 + 0.499263i
\(364\) 0 0
\(365\) 1.00399 1.73897i 0.0525514 0.0910218i
\(366\) 0 0
\(367\) −13.2343 22.9225i −0.690825 1.19654i −0.971568 0.236760i \(-0.923914\pi\)
0.280744 0.959783i \(-0.409419\pi\)
\(368\) 0 0
\(369\) 0.579529 + 1.00377i 0.0301691 + 0.0522544i
\(370\) 0 0
\(371\) −3.00789 5.20981i −0.156162 0.270480i
\(372\) 0 0
\(373\) −19.0974 33.0776i −0.988824 1.71269i −0.623526 0.781803i \(-0.714300\pi\)
−0.365298 0.930891i \(-0.619033\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 8.19046 0.421830
\(378\) 0 0
\(379\) 11.6683 20.2101i 0.599361 1.03812i −0.393555 0.919301i \(-0.628755\pi\)
0.992916 0.118822i \(-0.0379119\pi\)
\(380\) 0 0
\(381\) 1.10991 + 1.92242i 0.0568625 + 0.0984887i
\(382\) 0 0
\(383\) 6.37068 11.0343i 0.325526 0.563828i −0.656092 0.754681i \(-0.727792\pi\)
0.981619 + 0.190852i \(0.0611251\pi\)
\(384\) 0 0
\(385\) −0.161057 + 0.278959i −0.00820823 + 0.0142171i
\(386\) 0 0
\(387\) 2.35137 0.119527
\(388\) 0 0
\(389\) 3.79864 6.57944i 0.192599 0.333591i −0.753512 0.657434i \(-0.771642\pi\)
0.946111 + 0.323843i \(0.104975\pi\)
\(390\) 0 0
\(391\) −0.802223 1.38949i −0.0405702 0.0702696i
\(392\) 0 0
\(393\) 21.0542 1.06204
\(394\) 0 0
\(395\) 0.753802 + 1.30562i 0.0379279 + 0.0656931i
\(396\) 0 0
\(397\) −9.30752 −0.467131 −0.233565 0.972341i \(-0.575039\pi\)
−0.233565 + 0.972341i \(0.575039\pi\)
\(398\) 0 0
\(399\) −16.2558 −0.813810
\(400\) 0 0
\(401\) −1.38966 −0.0693961 −0.0346980 0.999398i \(-0.511047\pi\)
−0.0346980 + 0.999398i \(0.511047\pi\)
\(402\) 0 0
\(403\) 23.3129 1.16130
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 1.25388 0.0621528
\(408\) 0 0
\(409\) −4.77429 8.26931i −0.236073 0.408891i 0.723511 0.690313i \(-0.242527\pi\)
−0.959584 + 0.281422i \(0.909194\pi\)
\(410\) 0 0
\(411\) −7.65782 −0.377732
\(412\) 0 0
\(413\) −0.506629 0.877508i −0.0249296 0.0431793i
\(414\) 0 0
\(415\) −3.21009 + 5.56004i −0.157577 + 0.272932i
\(416\) 0 0
\(417\) −13.0649 −0.639790
\(418\) 0 0
\(419\) 7.84344 13.5852i 0.383177 0.663683i −0.608337 0.793679i \(-0.708163\pi\)
0.991515 + 0.129996i \(0.0414965\pi\)
\(420\) 0 0
\(421\) −9.83514 + 17.0350i −0.479336 + 0.830233i −0.999719 0.0236991i \(-0.992456\pi\)
0.520384 + 0.853933i \(0.325789\pi\)
\(422\) 0 0
\(423\) 5.48732 + 9.50432i 0.266803 + 0.462116i
\(424\) 0 0
\(425\) 0.129720 0.224682i 0.00629236 0.0108987i
\(426\) 0 0
\(427\) 14.0780 0.681281
\(428\) 0 0
\(429\) 0.566798 0.0273653
\(430\) 0 0
\(431\) −16.2820 28.2012i −0.784275 1.35840i −0.929431 0.368996i \(-0.879702\pi\)
0.145156 0.989409i \(-0.453632\pi\)
\(432\) 0 0
\(433\) 12.6446 + 21.9010i 0.607659 + 1.05250i 0.991625 + 0.129149i \(0.0412246\pi\)
−0.383966 + 0.923347i \(0.625442\pi\)
\(434\) 0 0
\(435\) 0.920164 + 1.59377i 0.0441185 + 0.0764155i
\(436\) 0 0
\(437\) −19.8734 34.4217i −0.950673 1.64661i
\(438\) 0 0
\(439\) 1.23674 2.14209i 0.0590263 0.102237i −0.835002 0.550247i \(-0.814534\pi\)
0.894029 + 0.448010i \(0.147867\pi\)
\(440\) 0 0
\(441\) 0.301411 0.522059i 0.0143529 0.0248599i
\(442\) 0 0
\(443\) −11.3001 19.5724i −0.536885 0.929913i −0.999070 0.0431289i \(-0.986267\pi\)
0.462184 0.886784i \(-0.347066\pi\)
\(444\) 0 0
\(445\) −1.27157 −0.0602783
\(446\) 0 0
\(447\) 1.39911 0.0661755
\(448\) 0 0
\(449\) −4.22258 7.31373i −0.199276 0.345156i 0.749018 0.662550i \(-0.230526\pi\)
−0.948294 + 0.317394i \(0.897192\pi\)
\(450\) 0 0
\(451\) −0.0738058 + 0.127835i −0.00347538 + 0.00601954i
\(452\) 0 0
\(453\) 8.77578 15.2001i 0.412322 0.714163i
\(454\) 0 0
\(455\) −11.2566 −0.527717
\(456\) 0 0
\(457\) −12.9230 22.3833i −0.604512 1.04705i −0.992128 0.125225i \(-0.960035\pi\)
0.387616 0.921821i \(-0.373299\pi\)
\(458\) 0 0
\(459\) −0.129720 + 0.224682i −0.00605483 + 0.0104873i
\(460\) 0 0
\(461\) −18.0486 −0.840605 −0.420302 0.907384i \(-0.638076\pi\)
−0.420302 + 0.907384i \(0.638076\pi\)
\(462\) 0 0
\(463\) 4.34724 7.52964i 0.202033 0.349932i −0.747150 0.664655i \(-0.768578\pi\)
0.949183 + 0.314723i \(0.101912\pi\)
\(464\) 0 0
\(465\) 2.61911 + 4.53644i 0.121458 + 0.210372i
\(466\) 0 0
\(467\) 15.0554 26.0767i 0.696681 1.20669i −0.272929 0.962034i \(-0.587993\pi\)
0.969611 0.244653i \(-0.0786741\pi\)
\(468\) 0 0
\(469\) 4.16030 + 20.2806i 0.192105 + 0.936471i
\(470\) 0 0
\(471\) 2.24823 3.89404i 0.103593 0.179428i
\(472\) 0 0
\(473\) 0.149729 + 0.259338i 0.00688455 + 0.0119244i
\(474\) 0 0
\(475\) 3.21355 5.56603i 0.147448 0.255387i
\(476\) 0 0
\(477\) −2.37847 −0.108903
\(478\) 0 0
\(479\) −8.45632 + 14.6468i −0.386379 + 0.669228i −0.991959 0.126556i \(-0.959608\pi\)
0.605580 + 0.795784i \(0.292941\pi\)
\(480\) 0 0
\(481\) 21.9091 + 37.9477i 0.998970 + 1.73027i
\(482\) 0 0
\(483\) −15.6416 −0.711717
\(484\) 0 0
\(485\) −2.93224 + 5.07880i −0.133146 + 0.230616i
\(486\) 0 0
\(487\) −8.89964 + 15.4146i −0.403281 + 0.698503i −0.994120 0.108286i \(-0.965464\pi\)
0.590839 + 0.806790i \(0.298797\pi\)
\(488\) 0 0
\(489\) −10.4296 18.0645i −0.471641 0.816907i
\(490\) 0 0
\(491\) −30.3667 −1.37043 −0.685216 0.728340i \(-0.740292\pi\)
−0.685216 + 0.728340i \(0.740292\pi\)
\(492\) 0 0
\(493\) −0.477456 −0.0215036
\(494\) 0 0
\(495\) 0.0636774 + 0.110293i 0.00286209 + 0.00495728i
\(496\) 0 0
\(497\) −9.17399 + 15.8898i −0.411510 + 0.712756i
\(498\) 0 0
\(499\) 5.87126 10.1693i 0.262834 0.455242i −0.704160 0.710041i \(-0.748676\pi\)
0.966994 + 0.254800i \(0.0820096\pi\)
\(500\) 0 0
\(501\) 6.14610 + 10.6454i 0.274588 + 0.475600i
\(502\) 0 0
\(503\) 18.0945 + 31.3406i 0.806793 + 1.39741i 0.915074 + 0.403287i \(0.132132\pi\)
−0.108280 + 0.994120i \(0.534534\pi\)
\(504\) 0 0
\(505\) 1.52837 + 2.64722i 0.0680117 + 0.117800i
\(506\) 0 0
\(507\) 3.40366 + 5.89531i 0.151162 + 0.261820i
\(508\) 0 0
\(509\) −16.6125 −0.736335 −0.368167 0.929759i \(-0.620015\pi\)
−0.368167 + 0.929759i \(0.620015\pi\)
\(510\) 0 0
\(511\) 5.07873 0.224670
\(512\) 0 0
\(513\) −3.21355 + 5.56603i −0.141882 + 0.245746i
\(514\) 0 0
\(515\) 6.62209 + 11.4698i 0.291804 + 0.505420i
\(516\) 0 0
\(517\) −0.698837 + 1.21042i −0.0307348 + 0.0532342i
\(518\) 0 0
\(519\) −3.90299 + 6.76018i −0.171322 + 0.296739i
\(520\) 0 0
\(521\) 1.82684 0.0800353 0.0400176 0.999199i \(-0.487259\pi\)
0.0400176 + 0.999199i \(0.487259\pi\)
\(522\) 0 0
\(523\) 2.41000 4.17424i 0.105382 0.182527i −0.808512 0.588479i \(-0.799727\pi\)
0.913894 + 0.405953i \(0.133060\pi\)
\(524\) 0 0
\(525\) −1.26463 2.19041i −0.0551931 0.0955972i
\(526\) 0 0
\(527\) −1.35901 −0.0591994
\(528\) 0 0
\(529\) −7.62247 13.2025i −0.331412 0.574022i
\(530\) 0 0
\(531\) −0.400614 −0.0173852
\(532\) 0 0
\(533\) −5.15844 −0.223437
\(534\) 0 0
\(535\) 9.51097 0.411195
\(536\) 0 0
\(537\) −15.9995 −0.690429
\(538\) 0 0
\(539\) 0.0767722 0.00330681
\(540\) 0 0
\(541\) −13.4880 −0.579895 −0.289948 0.957043i \(-0.593638\pi\)
−0.289948 + 0.957043i \(0.593638\pi\)
\(542\) 0 0
\(543\) 10.8380 + 18.7720i 0.465104 + 0.805583i
\(544\) 0 0
\(545\) 6.74556 0.288948
\(546\) 0 0
\(547\) 9.28593 + 16.0837i 0.397038 + 0.687690i 0.993359 0.115056i \(-0.0367048\pi\)
−0.596321 + 0.802746i \(0.703372\pi\)
\(548\) 0 0
\(549\) 2.78302 4.82033i 0.118776 0.205727i
\(550\) 0 0
\(551\) −11.8280 −0.503889
\(552\) 0 0
\(553\) −1.90657 + 3.30227i −0.0810754 + 0.140427i
\(554\) 0 0
\(555\) −4.92280 + 8.52654i −0.208961 + 0.361931i
\(556\) 0 0
\(557\) 10.3068 + 17.8518i 0.436711 + 0.756406i 0.997434 0.0715977i \(-0.0228098\pi\)
−0.560722 + 0.828004i \(0.689476\pi\)
\(558\) 0 0
\(559\) −5.23243 + 9.06284i −0.221308 + 0.383317i
\(560\) 0 0
\(561\) −0.0330410 −0.00139499
\(562\) 0 0
\(563\) 22.6923 0.956365 0.478182 0.878261i \(-0.341296\pi\)
0.478182 + 0.878261i \(0.341296\pi\)
\(564\) 0 0
\(565\) −4.56883 7.91345i −0.192212 0.332921i
\(566\) 0 0
\(567\) 1.26463 + 2.19041i 0.0531096 + 0.0919885i
\(568\) 0 0
\(569\) −16.4285 28.4550i −0.688720 1.19290i −0.972252 0.233935i \(-0.924840\pi\)
0.283532 0.958963i \(-0.408494\pi\)
\(570\) 0 0
\(571\) −10.7995 18.7053i −0.451944 0.782791i 0.546562 0.837418i \(-0.315936\pi\)
−0.998507 + 0.0546277i \(0.982603\pi\)
\(572\) 0 0
\(573\) 12.8281 22.2189i 0.535901 0.928207i
\(574\) 0 0
\(575\) 3.09212 5.35572i 0.128951 0.223349i
\(576\) 0 0
\(577\) 1.03957 + 1.80059i 0.0432780 + 0.0749596i 0.886853 0.462052i \(-0.152887\pi\)
−0.843575 + 0.537011i \(0.819553\pi\)
\(578\) 0 0
\(579\) −17.9337 −0.745300
\(580\) 0 0
\(581\) −16.2383 −0.673680
\(582\) 0 0
\(583\) −0.151455 0.262327i −0.00627261 0.0108645i
\(584\) 0 0
\(585\) −2.22527 + 3.85428i −0.0920036 + 0.159355i
\(586\) 0 0
\(587\) −16.6645 + 28.8637i −0.687817 + 1.19133i 0.284726 + 0.958609i \(0.408097\pi\)
−0.972543 + 0.232725i \(0.925236\pi\)
\(588\) 0 0
\(589\) −33.6666 −1.38721
\(590\) 0 0
\(591\) 3.49225 + 6.04876i 0.143652 + 0.248813i
\(592\) 0 0
\(593\) −15.1056 + 26.1636i −0.620311 + 1.07441i 0.369117 + 0.929383i \(0.379660\pi\)
−0.989428 + 0.145027i \(0.953673\pi\)
\(594\) 0 0
\(595\) 0.656194 0.0269013
\(596\) 0 0
\(597\) 1.19684 2.07299i 0.0489834 0.0848417i
\(598\) 0 0
\(599\) 21.0034 + 36.3789i 0.858175 + 1.48640i 0.873668 + 0.486523i \(0.161735\pi\)
−0.0154922 + 0.999880i \(0.504932\pi\)
\(600\) 0 0
\(601\) −6.98941 + 12.1060i −0.285104 + 0.493815i −0.972634 0.232341i \(-0.925361\pi\)
0.687530 + 0.726156i \(0.258695\pi\)
\(602\) 0 0
\(603\) 7.76655 + 2.58469i 0.316279 + 0.105257i
\(604\) 0 0
\(605\) 5.49189 9.51223i 0.223277 0.386727i
\(606\) 0 0
\(607\) 4.38323 + 7.59197i 0.177910 + 0.308149i 0.941164 0.337949i \(-0.109733\pi\)
−0.763255 + 0.646098i \(0.776400\pi\)
\(608\) 0 0
\(609\) −2.32734 + 4.03107i −0.0943085 + 0.163347i
\(610\) 0 0
\(611\) −48.8431 −1.97598
\(612\) 0 0
\(613\) 10.8529 18.7977i 0.438343 0.759233i −0.559219 0.829020i \(-0.688899\pi\)
0.997562 + 0.0697873i \(0.0222321\pi\)
\(614\) 0 0
\(615\) −0.579529 1.00377i −0.0233689 0.0404761i
\(616\) 0 0
\(617\) −13.0856 −0.526805 −0.263403 0.964686i \(-0.584845\pi\)
−0.263403 + 0.964686i \(0.584845\pi\)
\(618\) 0 0
\(619\) 2.59657 4.49739i 0.104365 0.180766i −0.809114 0.587652i \(-0.800052\pi\)
0.913479 + 0.406887i \(0.133386\pi\)
\(620\) 0 0
\(621\) −3.09212 + 5.35572i −0.124083 + 0.214918i
\(622\) 0 0
\(623\) −1.60807 2.78526i −0.0644261 0.111589i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.818522 −0.0326886
\(628\) 0 0
\(629\) −1.27718 2.21213i −0.0509243 0.0882035i
\(630\) 0 0
\(631\) 19.6639 34.0589i 0.782807 1.35586i −0.147493 0.989063i \(-0.547120\pi\)
0.930300 0.366799i \(-0.119546\pi\)
\(632\) 0 0
\(633\) −1.40604 + 2.43533i −0.0558851 + 0.0967959i
\(634\) 0 0
\(635\) −1.10991 1.92242i −0.0440455 0.0762890i
\(636\) 0 0
\(637\) 1.34144 + 2.32344i 0.0531498 + 0.0920582i
\(638\) 0 0
\(639\) 3.62714 + 6.28239i 0.143487 + 0.248527i
\(640\) 0 0
\(641\) −10.2916 17.8256i −0.406495 0.704071i 0.587999 0.808862i \(-0.299916\pi\)
−0.994494 + 0.104791i \(0.966583\pi\)
\(642\) 0 0
\(643\) 13.1661 0.519221 0.259611 0.965713i \(-0.416406\pi\)
0.259611 + 0.965713i \(0.416406\pi\)
\(644\) 0 0
\(645\) −2.35137 −0.0925851
\(646\) 0 0
\(647\) −21.8290 + 37.8089i −0.858185 + 1.48642i 0.0154731 + 0.999880i \(0.495075\pi\)
−0.873658 + 0.486540i \(0.838259\pi\)
\(648\) 0 0
\(649\) −0.0255101 0.0441847i −0.00100136 0.00173440i
\(650\) 0 0
\(651\) −6.62443 + 11.4738i −0.259632 + 0.449695i
\(652\) 0 0
\(653\) −6.06309 + 10.5016i −0.237267 + 0.410959i −0.959929 0.280243i \(-0.909585\pi\)
0.722662 + 0.691202i \(0.242918\pi\)
\(654\) 0 0
\(655\) −21.0542 −0.822656
\(656\) 0 0
\(657\) 1.00399 1.73897i 0.0391695 0.0678436i
\(658\) 0 0
\(659\) −5.16250 8.94172i −0.201103 0.348320i 0.747781 0.663945i \(-0.231119\pi\)
−0.948884 + 0.315625i \(0.897786\pi\)
\(660\) 0 0
\(661\) −7.49081 −0.291359 −0.145679 0.989332i \(-0.546537\pi\)
−0.145679 + 0.989332i \(0.546537\pi\)
\(662\) 0 0
\(663\) −0.577326 0.999958i −0.0224215 0.0388352i
\(664\) 0 0
\(665\) 16.2558 0.630374
\(666\) 0 0
\(667\) −11.3810 −0.440676
\(668\) 0 0
\(669\) 12.8891 0.498321
\(670\) 0 0
\(671\) 0.708862 0.0273653
\(672\) 0 0
\(673\) 36.6286 1.41193 0.705964 0.708248i \(-0.250514\pi\)
0.705964 + 0.708248i \(0.250514\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 0.846703 + 1.46653i 0.0325415 + 0.0563634i 0.881837 0.471553i \(-0.156307\pi\)
−0.849296 + 0.527917i \(0.822973\pi\)
\(678\) 0 0
\(679\) −14.8328 −0.569232
\(680\) 0 0
\(681\) −4.67253 8.09306i −0.179052 0.310127i
\(682\) 0 0
\(683\) 1.70767 2.95778i 0.0653423 0.113176i −0.831503 0.555520i \(-0.812519\pi\)
0.896846 + 0.442343i \(0.145853\pi\)
\(684\) 0 0
\(685\) 7.65782 0.292590
\(686\) 0 0
\(687\) −1.60442 + 2.77893i −0.0612123 + 0.106023i
\(688\) 0 0
\(689\) 5.29274 9.16729i 0.201637 0.349246i
\(690\) 0 0
\(691\) −0.242076 0.419288i −0.00920901 0.0159505i 0.861384 0.507954i \(-0.169598\pi\)
−0.870593 + 0.492004i \(0.836265\pi\)
\(692\) 0 0
\(693\) −0.161057 + 0.278959i −0.00611805 + 0.0105968i
\(694\) 0 0
\(695\) 13.0649 0.495579
\(696\) 0 0
\(697\) 0.300707 0.0113901
\(698\) 0 0
\(699\) −5.73530 9.93383i −0.216929 0.375732i
\(700\) 0 0
\(701\) −20.4531 35.4258i −0.772503 1.33801i −0.936187 0.351502i \(-0.885671\pi\)
0.163684 0.986513i \(-0.447662\pi\)
\(702\) 0 0
\(703\) −31.6393 54.8009i −1.19330 2.06686i
\(704\) 0 0
\(705\) −5.48732 9.50432i −0.206664 0.357953i
\(706\) 0 0
\(707\) −3.86566 + 6.69552i −0.145383 + 0.251811i
\(708\) 0 0
\(709\) −10.0717 + 17.4447i −0.378250 + 0.655148i −0.990808 0.135278i \(-0.956807\pi\)
0.612558 + 0.790426i \(0.290141\pi\)
\(710\) 0 0
\(711\) 0.753802 + 1.30562i 0.0282698 + 0.0489647i
\(712\) 0 0
\(713\) −32.3945 −1.21318
\(714\) 0 0
\(715\) −0.566798 −0.0211970
\(716\) 0 0
\(717\) 2.95082 + 5.11096i 0.110200 + 0.190872i
\(718\) 0 0
\(719\) −14.2608 + 24.7005i −0.531839 + 0.921173i 0.467470 + 0.884009i \(0.345166\pi\)
−0.999309 + 0.0371636i \(0.988168\pi\)
\(720\) 0 0
\(721\) −16.7490 + 29.0102i −0.623766 + 1.08040i
\(722\) 0 0
\(723\) −9.02817 −0.335761
\(724\) 0 0
\(725\) −0.920164 1.59377i −0.0341740 0.0591912i
\(726\) 0 0
\(727\) 3.10936 5.38557i 0.115320 0.199740i −0.802588 0.596534i \(-0.796544\pi\)
0.917908 + 0.396794i \(0.129877\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.305021 0.528311i 0.0112816 0.0195403i
\(732\) 0 0
\(733\) 3.23190 + 5.59782i 0.119373 + 0.206760i 0.919519 0.393045i \(-0.128578\pi\)
−0.800146 + 0.599805i \(0.795245\pi\)
\(734\) 0 0
\(735\) −0.301411 + 0.522059i −0.0111177 + 0.0192564i
\(736\) 0 0
\(737\) 0.209482 + 1.02118i 0.00771636 + 0.0376156i
\(738\) 0 0
\(739\) −16.6691 + 28.8717i −0.613183 + 1.06206i 0.377518 + 0.926002i \(0.376778\pi\)
−0.990700 + 0.136061i \(0.956556\pi\)
\(740\) 0 0
\(741\) −14.3020 24.7719i −0.525398 0.910017i
\(742\) 0 0
\(743\) 4.72772 8.18865i 0.173443 0.300412i −0.766178 0.642628i \(-0.777844\pi\)
0.939621 + 0.342216i \(0.111177\pi\)
\(744\) 0 0
\(745\) −1.39911 −0.0512593
\(746\) 0 0
\(747\) −3.21009 + 5.56004i −0.117451 + 0.203431i
\(748\) 0 0
\(749\) 12.0279 + 20.8329i 0.439489 + 0.761217i
\(750\) 0 0
\(751\) 3.14643 0.114815 0.0574074 0.998351i \(-0.481717\pi\)
0.0574074 + 0.998351i \(0.481717\pi\)
\(752\) 0 0
\(753\) 2.88177 4.99137i 0.105017 0.181896i
\(754\) 0 0
\(755\) −8.77578 + 15.2001i −0.319383 + 0.553188i
\(756\) 0 0
\(757\) −9.64743 16.7098i −0.350642 0.607329i 0.635720 0.771919i \(-0.280703\pi\)
−0.986362 + 0.164590i \(0.947370\pi\)
\(758\) 0 0
\(759\) −0.787594 −0.0285879
\(760\) 0 0
\(761\) −40.2180 −1.45790 −0.728951 0.684566i \(-0.759992\pi\)
−0.728951 + 0.684566i \(0.759992\pi\)
\(762\) 0 0
\(763\) 8.53065 + 14.7755i 0.308830 + 0.534910i
\(764\) 0 0
\(765\) 0.129720 0.224682i 0.00469005 0.00812341i
\(766\) 0 0
\(767\) 0.891474 1.54408i 0.0321893 0.0557535i
\(768\) 0 0
\(769\) 3.67851 + 6.37137i 0.132650 + 0.229757i 0.924697 0.380703i \(-0.124318\pi\)
−0.792047 + 0.610460i \(0.790985\pi\)
\(770\) 0 0
\(771\) 14.0716 + 24.3727i 0.506775 + 0.877761i
\(772\) 0 0
\(773\) −23.8282 41.2717i −0.857042 1.48444i −0.874738 0.484597i \(-0.838966\pi\)
0.0176957 0.999843i \(-0.494367\pi\)
\(774\) 0 0
\(775\) −2.61911 4.53644i −0.0940813 0.162954i
\(776\) 0 0
\(777\) −24.9021 −0.893359
\(778\) 0 0
\(779\) 7.44938 0.266902
\(780\) 0 0
\(781\) −0.461933 + 0.800092i −0.0165293 + 0.0286296i
\(782\) 0 0
\(783\) 0.920164 + 1.59377i 0.0328840 + 0.0569567i
\(784\) 0 0
\(785\) −2.24823 + 3.89404i −0.0802427 + 0.138984i
\(786\) 0 0
\(787\) 24.3590 42.1911i 0.868305 1.50395i 0.00457767 0.999990i \(-0.498543\pi\)
0.863727 0.503959i \(-0.168124\pi\)
\(788\) 0 0
\(789\) −14.3621 −0.511305
\(790\) 0 0
\(791\) 11.5558 20.0152i 0.410876 0.711659i
\(792\) 0 0
\(793\) 12.3859 + 21.4531i 0.439838 +