Properties

Label 140.2.q.b.109.1
Level $140$
Weight $2$
Character 140.109
Analytic conductor $1.118$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \(x^{4} - x^{3} - 4 x^{2} - 5 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.1
Root \(2.13746 - 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 140.109
Dual form 140.2.q.b.9.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(2.63746 + 0.209313i) q^{7} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(2.63746 + 0.209313i) q^{7} +(-1.13746 + 1.97014i) q^{11} +6.09095i q^{13} +(1.13746 - 3.70219i) q^{15} +(-4.13746 - 2.38876i) q^{17} +(-2.13746 - 3.70219i) q^{19} +(3.77492 + 2.59808i) q^{21} +(-0.774917 + 0.447399i) q^{23} +(-4.50000 + 2.17945i) q^{25} -5.19615i q^{27} +3.27492 q^{29} +(2.13746 - 3.70219i) q^{31} +(-3.41238 + 1.97014i) q^{33} +(-0.862541 - 5.85286i) q^{35} +(-4.86254 + 2.80739i) q^{37} +(-5.27492 + 9.13642i) q^{39} -11.2749 q^{41} +6.50958i q^{43} +(1.86254 - 1.07534i) q^{47} +(6.91238 + 1.10411i) q^{49} +(-4.13746 - 7.16629i) q^{51} +(6.41238 + 3.70219i) q^{53} +(4.86254 + 1.49397i) q^{55} -7.40437i q^{57} +(2.13746 - 3.70219i) q^{59} +(-0.774917 - 1.34220i) q^{61} +(13.2749 - 3.04547i) q^{65} +(12.0498 + 6.95698i) q^{67} -1.54983 q^{69} +10.5498 q^{71} +(1.86254 + 1.07534i) q^{73} +(-8.63746 - 0.627940i) q^{75} +(-3.41238 + 4.95807i) q^{77} +(-0.137459 - 0.238085i) q^{79} +(4.50000 - 7.79423i) q^{81} -5.67232i q^{83} +(-3.13746 + 10.2118i) q^{85} +(4.91238 + 2.83616i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(-1.27492 + 16.0646i) q^{91} +(6.41238 - 3.70219i) q^{93} +(-7.00000 + 6.50958i) q^{95} -6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + O(q^{10}) \) \( 4 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 3 q^{11} - 3 q^{15} - 9 q^{17} - q^{19} + 12 q^{23} - 18 q^{25} - 2 q^{29} + q^{31} + 9 q^{33} - 11 q^{35} - 27 q^{37} - 6 q^{39} - 30 q^{41} + 15 q^{47} + 5 q^{49} - 9 q^{51} + 3 q^{53} + 27 q^{55} + q^{59} + 12 q^{61} + 38 q^{65} + 18 q^{67} + 24 q^{69} + 12 q^{71} + 15 q^{73} - 27 q^{75} + 9 q^{77} + 7 q^{79} + 18 q^{81} - 5 q^{85} - 3 q^{87} - 14 q^{89} + 10 q^{91} + 3 q^{93} - 28 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −0.500000 2.17945i −0.223607 0.974679i
\(6\) 0 0
\(7\) 2.63746 + 0.209313i 0.996866 + 0.0791130i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.13746 + 1.97014i −0.342957 + 0.594018i −0.984980 0.172666i \(-0.944762\pi\)
0.642024 + 0.766685i \(0.278095\pi\)
\(12\) 0 0
\(13\) 6.09095i 1.68933i 0.535299 + 0.844663i \(0.320199\pi\)
−0.535299 + 0.844663i \(0.679801\pi\)
\(14\) 0 0
\(15\) 1.13746 3.70219i 0.293691 0.955901i
\(16\) 0 0
\(17\) −4.13746 2.38876i −1.00348 0.579360i −0.0942047 0.995553i \(-0.530031\pi\)
−0.909276 + 0.416193i \(0.863364\pi\)
\(18\) 0 0
\(19\) −2.13746 3.70219i −0.490367 0.849340i 0.509572 0.860428i \(-0.329804\pi\)
−0.999939 + 0.0110882i \(0.996470\pi\)
\(20\) 0 0
\(21\) 3.77492 + 2.59808i 0.823754 + 0.566947i
\(22\) 0 0
\(23\) −0.774917 + 0.447399i −0.161581 + 0.0932891i −0.578610 0.815604i \(-0.696405\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −4.50000 + 2.17945i −0.900000 + 0.435890i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 3.27492 0.608137 0.304068 0.952650i \(-0.401655\pi\)
0.304068 + 0.952650i \(0.401655\pi\)
\(30\) 0 0
\(31\) 2.13746 3.70219i 0.383899 0.664932i −0.607717 0.794154i \(-0.707914\pi\)
0.991616 + 0.129221i \(0.0412478\pi\)
\(32\) 0 0
\(33\) −3.41238 + 1.97014i −0.594018 + 0.342957i
\(34\) 0 0
\(35\) −0.862541 5.85286i −0.145796 0.989315i
\(36\) 0 0
\(37\) −4.86254 + 2.80739i −0.799397 + 0.461532i −0.843260 0.537506i \(-0.819367\pi\)
0.0438633 + 0.999038i \(0.486033\pi\)
\(38\) 0 0
\(39\) −5.27492 + 9.13642i −0.844663 + 1.46300i
\(40\) 0 0
\(41\) −11.2749 −1.76085 −0.880423 0.474189i \(-0.842741\pi\)
−0.880423 + 0.474189i \(0.842741\pi\)
\(42\) 0 0
\(43\) 6.50958i 0.992701i 0.868122 + 0.496351i \(0.165327\pi\)
−0.868122 + 0.496351i \(0.834673\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.86254 1.07534i 0.271680 0.156854i −0.357971 0.933733i \(-0.616531\pi\)
0.629651 + 0.776878i \(0.283198\pi\)
\(48\) 0 0
\(49\) 6.91238 + 1.10411i 0.987482 + 0.157730i
\(50\) 0 0
\(51\) −4.13746 7.16629i −0.579360 1.00348i
\(52\) 0 0
\(53\) 6.41238 + 3.70219i 0.880808 + 0.508534i 0.870925 0.491417i \(-0.163521\pi\)
0.00988297 + 0.999951i \(0.496854\pi\)
\(54\) 0 0
\(55\) 4.86254 + 1.49397i 0.655665 + 0.201446i
\(56\) 0 0
\(57\) 7.40437i 0.980733i
\(58\) 0 0
\(59\) 2.13746 3.70219i 0.278273 0.481984i −0.692682 0.721243i \(-0.743571\pi\)
0.970956 + 0.239259i \(0.0769045\pi\)
\(60\) 0 0
\(61\) −0.774917 1.34220i −0.0992180 0.171851i 0.812143 0.583458i \(-0.198301\pi\)
−0.911361 + 0.411608i \(0.864967\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 13.2749 3.04547i 1.64655 0.377745i
\(66\) 0 0
\(67\) 12.0498 + 6.95698i 1.47212 + 0.849930i 0.999509 0.0313404i \(-0.00997759\pi\)
0.472613 + 0.881270i \(0.343311\pi\)
\(68\) 0 0
\(69\) −1.54983 −0.186578
\(70\) 0 0
\(71\) 10.5498 1.25204 0.626018 0.779809i \(-0.284684\pi\)
0.626018 + 0.779809i \(0.284684\pi\)
\(72\) 0 0
\(73\) 1.86254 + 1.07534i 0.217994 + 0.125859i 0.605021 0.796209i \(-0.293165\pi\)
−0.387027 + 0.922068i \(0.626498\pi\)
\(74\) 0 0
\(75\) −8.63746 0.627940i −0.997368 0.0725083i
\(76\) 0 0
\(77\) −3.41238 + 4.95807i −0.388876 + 0.565024i
\(78\) 0 0
\(79\) −0.137459 0.238085i −0.0154653 0.0267867i 0.858189 0.513334i \(-0.171590\pi\)
−0.873654 + 0.486547i \(0.838256\pi\)
\(80\) 0 0
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) 0 0
\(83\) 5.67232i 0.622618i −0.950309 0.311309i \(-0.899233\pi\)
0.950309 0.311309i \(-0.100767\pi\)
\(84\) 0 0
\(85\) −3.13746 + 10.2118i −0.340305 + 1.10762i
\(86\) 0 0
\(87\) 4.91238 + 2.83616i 0.526662 + 0.304068i
\(88\) 0 0
\(89\) −3.50000 6.06218i −0.370999 0.642590i 0.618720 0.785611i \(-0.287651\pi\)
−0.989720 + 0.143022i \(0.954318\pi\)
\(90\) 0 0
\(91\) −1.27492 + 16.0646i −0.133648 + 1.68403i
\(92\) 0 0
\(93\) 6.41238 3.70219i 0.664932 0.383899i
\(94\) 0 0
\(95\) −7.00000 + 6.50958i −0.718185 + 0.667868i
\(96\) 0 0
\(97\) 6.92820i 0.703452i −0.936103 0.351726i \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −0.774917 + 1.34220i −0.0771071 + 0.133553i −0.902001 0.431735i \(-0.857902\pi\)
0.824894 + 0.565288i \(0.191235\pi\)
\(102\) 0 0
\(103\) −2.22508 + 1.28465i −0.219244 + 0.126581i −0.605600 0.795769i \(-0.707067\pi\)
0.386356 + 0.922350i \(0.373734\pi\)
\(104\) 0 0
\(105\) 3.77492 9.52628i 0.368394 0.929670i
\(106\) 0 0
\(107\) −12.0498 + 6.95698i −1.16490 + 0.672556i −0.952474 0.304621i \(-0.901470\pi\)
−0.212428 + 0.977177i \(0.568137\pi\)
\(108\) 0 0
\(109\) 1.77492 3.07425i 0.170006 0.294459i −0.768416 0.639951i \(-0.778955\pi\)
0.938422 + 0.345492i \(0.112288\pi\)
\(110\) 0 0
\(111\) −9.72508 −0.923064
\(112\) 0 0
\(113\) 13.0192i 1.22474i −0.790572 0.612369i \(-0.790217\pi\)
0.790572 0.612369i \(-0.209783\pi\)
\(114\) 0 0
\(115\) 1.36254 + 1.46519i 0.127058 + 0.136630i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.4124 7.16629i −0.954501 0.656933i
\(120\) 0 0
\(121\) 2.91238 + 5.04438i 0.264761 + 0.458580i
\(122\) 0 0
\(123\) −16.9124 9.76436i −1.52494 0.880423i
\(124\) 0 0
\(125\) 7.00000 + 8.71780i 0.626099 + 0.779744i
\(126\) 0 0
\(127\) 1.78959i 0.158801i 0.996843 + 0.0794004i \(0.0253006\pi\)
−0.996843 + 0.0794004i \(0.974699\pi\)
\(128\) 0 0
\(129\) −5.63746 + 9.76436i −0.496351 + 0.859704i
\(130\) 0 0
\(131\) 9.13746 + 15.8265i 0.798343 + 1.38277i 0.920694 + 0.390285i \(0.127623\pi\)
−0.122351 + 0.992487i \(0.539043\pi\)
\(132\) 0 0
\(133\) −4.86254 10.2118i −0.421636 0.885472i
\(134\) 0 0
\(135\) −11.3248 + 2.59808i −0.974679 + 0.223607i
\(136\) 0 0
\(137\) −7.96221 4.59698i −0.680258 0.392747i 0.119695 0.992811i \(-0.461808\pi\)
−0.799952 + 0.600064i \(0.795142\pi\)
\(138\) 0 0
\(139\) 17.0997 1.45037 0.725187 0.688551i \(-0.241753\pi\)
0.725187 + 0.688551i \(0.241753\pi\)
\(140\) 0 0
\(141\) 3.72508 0.313709
\(142\) 0 0
\(143\) −12.0000 6.92820i −1.00349 0.579365i
\(144\) 0 0
\(145\) −1.63746 7.13752i −0.135984 0.592738i
\(146\) 0 0
\(147\) 9.41238 + 7.64246i 0.776320 + 0.630339i
\(148\) 0 0
\(149\) 3.77492 + 6.53835i 0.309253 + 0.535642i 0.978199 0.207669i \(-0.0665876\pi\)
−0.668946 + 0.743311i \(0.733254\pi\)
\(150\) 0 0
\(151\) 10.1375 17.5586i 0.824975 1.42890i −0.0769640 0.997034i \(-0.524523\pi\)
0.901939 0.431864i \(-0.142144\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.13746 2.80739i −0.733938 0.225495i
\(156\) 0 0
\(157\) −9.41238 5.43424i −0.751189 0.433699i 0.0749341 0.997188i \(-0.476125\pi\)
−0.826123 + 0.563489i \(0.809459\pi\)
\(158\) 0 0
\(159\) 6.41238 + 11.1066i 0.508534 + 0.880808i
\(160\) 0 0
\(161\) −2.13746 + 1.01779i −0.168455 + 0.0802135i
\(162\) 0 0
\(163\) 6.41238 3.70219i 0.502256 0.289978i −0.227389 0.973804i \(-0.573019\pi\)
0.729645 + 0.683826i \(0.239685\pi\)
\(164\) 0 0
\(165\) 6.00000 + 6.45203i 0.467099 + 0.502290i
\(166\) 0 0
\(167\) 12.6005i 0.975058i 0.873107 + 0.487529i \(0.162102\pi\)
−0.873107 + 0.487529i \(0.837898\pi\)
\(168\) 0 0
\(169\) −24.0997 −1.85382
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16.2371 9.37451i 1.23449 0.712731i 0.266524 0.963828i \(-0.414125\pi\)
0.967962 + 0.251097i \(0.0807915\pi\)
\(174\) 0 0
\(175\) −12.3248 + 4.80630i −0.931664 + 0.363322i
\(176\) 0 0
\(177\) 6.41238 3.70219i 0.481984 0.278273i
\(178\) 0 0
\(179\) 0.137459 0.238085i 0.0102741 0.0177953i −0.860843 0.508871i \(-0.830063\pi\)
0.871117 + 0.491076i \(0.163396\pi\)
\(180\) 0 0
\(181\) −16.7251 −1.24317 −0.621583 0.783348i \(-0.713510\pi\)
−0.621583 + 0.783348i \(0.713510\pi\)
\(182\) 0 0
\(183\) 2.68439i 0.198436i
\(184\) 0 0
\(185\) 8.54983 + 9.19397i 0.628596 + 0.675954i
\(186\) 0 0
\(187\) 9.41238 5.43424i 0.688301 0.397391i
\(188\) 0 0
\(189\) 1.08762 13.7046i 0.0791130 0.996866i
\(190\) 0 0
\(191\) −11.4124 19.7668i −0.825771 1.43028i −0.901329 0.433135i \(-0.857407\pi\)
0.0755585 0.997141i \(-0.475926\pi\)
\(192\) 0 0
\(193\) −7.96221 4.59698i −0.573132 0.330898i 0.185267 0.982688i \(-0.440685\pi\)
−0.758399 + 0.651790i \(0.774018\pi\)
\(194\) 0 0
\(195\) 22.5498 + 6.92820i 1.61483 + 0.496139i
\(196\) 0 0
\(197\) 26.0383i 1.85515i 0.373634 + 0.927576i \(0.378112\pi\)
−0.373634 + 0.927576i \(0.621888\pi\)
\(198\) 0 0
\(199\) 4.86254 8.42217i 0.344696 0.597032i −0.640602 0.767873i \(-0.721315\pi\)
0.985299 + 0.170841i \(0.0546485\pi\)
\(200\) 0 0
\(201\) 12.0498 + 20.8709i 0.849930 + 1.47212i
\(202\) 0 0
\(203\) 8.63746 + 0.685484i 0.606231 + 0.0481115i
\(204\) 0 0
\(205\) 5.63746 + 24.5731i 0.393737 + 1.71626i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 9.72508 0.672698
\(210\) 0 0
\(211\) −19.6495 −1.35273 −0.676364 0.736568i \(-0.736445\pi\)
−0.676364 + 0.736568i \(0.736445\pi\)
\(212\) 0 0
\(213\) 15.8248 + 9.13642i 1.08429 + 0.626018i
\(214\) 0 0
\(215\) 14.1873 3.25479i 0.967565 0.221975i
\(216\) 0 0
\(217\) 6.41238 9.31697i 0.435300 0.632477i
\(218\) 0 0
\(219\) 1.86254 + 3.22602i 0.125859 + 0.217994i
\(220\) 0 0
\(221\) 14.5498 25.2011i 0.978728 1.69521i
\(222\) 0 0
\(223\) 8.71780i 0.583787i −0.956451 0.291893i \(-0.905715\pi\)
0.956451 0.291893i \(-0.0942853\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.58762 + 3.22602i 0.370864 + 0.214118i 0.673836 0.738881i \(-0.264646\pi\)
−0.302972 + 0.952999i \(0.597979\pi\)
\(228\) 0 0
\(229\) −2.13746 3.70219i −0.141247 0.244647i 0.786719 0.617311i \(-0.211778\pi\)
−0.927967 + 0.372663i \(0.878445\pi\)
\(230\) 0 0
\(231\) −9.41238 + 4.48190i −0.619289 + 0.294887i
\(232\) 0 0
\(233\) −16.1375 + 9.31697i −1.05720 + 0.610375i −0.924656 0.380802i \(-0.875648\pi\)
−0.132544 + 0.991177i \(0.542314\pi\)
\(234\) 0 0
\(235\) −3.27492 3.52165i −0.213632 0.229727i
\(236\) 0 0
\(237\) 0.476171i 0.0309306i
\(238\) 0 0
\(239\) 14.5498 0.941151 0.470575 0.882360i \(-0.344046\pi\)
0.470575 + 0.882360i \(0.344046\pi\)
\(240\) 0 0
\(241\) 6.41238 11.1066i 0.413057 0.715436i −0.582165 0.813071i \(-0.697794\pi\)
0.995222 + 0.0976343i \(0.0311275\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.04983 15.6172i −0.0670715 0.997748i
\(246\) 0 0
\(247\) 22.5498 13.0192i 1.43481 0.828389i
\(248\) 0 0
\(249\) 4.91238 8.50848i 0.311309 0.539203i
\(250\) 0 0
\(251\) −5.45017 −0.344011 −0.172006 0.985096i \(-0.555025\pi\)
−0.172006 + 0.985096i \(0.555025\pi\)
\(252\) 0 0
\(253\) 2.03559i 0.127976i
\(254\) 0 0
\(255\) −13.5498 + 12.6005i −0.848524 + 0.789076i
\(256\) 0 0
\(257\) −21.4124 + 12.3624i −1.33567 + 0.771148i −0.986162 0.165786i \(-0.946984\pi\)
−0.349506 + 0.936934i \(0.613650\pi\)
\(258\) 0 0
\(259\) −13.4124 + 6.38658i −0.833404 + 0.396843i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 23.3248 + 13.4666i 1.43827 + 0.830383i 0.997729 0.0673516i \(-0.0214549\pi\)
0.440536 + 0.897735i \(0.354788\pi\)
\(264\) 0 0
\(265\) 4.86254 15.8265i 0.298704 0.972217i
\(266\) 0 0
\(267\) 12.1244i 0.741999i
\(268\) 0 0
\(269\) −14.7749 + 25.5909i −0.900843 + 1.56031i −0.0744400 + 0.997225i \(0.523717\pi\)
−0.826403 + 0.563080i \(0.809616\pi\)
\(270\) 0 0
\(271\) 6.41238 + 11.1066i 0.389524 + 0.674676i 0.992386 0.123170i \(-0.0393062\pi\)
−0.602861 + 0.797846i \(0.705973\pi\)
\(272\) 0 0
\(273\) −15.8248 + 22.9928i −0.957758 + 1.39159i
\(274\) 0 0
\(275\) 0.824752 11.3446i 0.0497344 0.684108i
\(276\) 0 0
\(277\) −16.1375 9.31697i −0.969606 0.559802i −0.0704898 0.997512i \(-0.522456\pi\)
−0.899116 + 0.437710i \(0.855790\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −16.9622 9.79314i −1.00830 0.582142i −0.0976056 0.995225i \(-0.531118\pi\)
−0.910693 + 0.413084i \(0.864452\pi\)
\(284\) 0 0
\(285\) −16.1375 + 3.70219i −0.955901 + 0.219299i
\(286\) 0 0
\(287\) −29.7371 2.35999i −1.75533 0.139306i
\(288\) 0 0
\(289\) 2.91238 + 5.04438i 0.171316 + 0.296728i
\(290\) 0 0
\(291\) 6.00000 10.3923i 0.351726 0.609208i
\(292\) 0 0
\(293\) 6.92820i 0.404750i −0.979308 0.202375i \(-0.935134\pi\)
0.979308 0.202375i \(-0.0648660\pi\)
\(294\) 0 0
\(295\) −9.13746 2.80739i −0.532003 0.163453i
\(296\) 0 0
\(297\) 10.2371 + 5.91041i 0.594018 + 0.342957i
\(298\) 0 0
\(299\) −2.72508 4.71998i −0.157596 0.272964i
\(300\) 0 0
\(301\) −1.36254 + 17.1687i −0.0785356 + 0.989590i
\(302\) 0 0
\(303\) −2.32475 + 1.34220i −0.133553 + 0.0771071i
\(304\) 0 0
\(305\) −2.53779 + 2.35999i −0.145313 + 0.135133i
\(306\) 0 0
\(307\) 3.99782i 0.228167i −0.993471 0.114084i \(-0.963607\pi\)
0.993471 0.114084i \(-0.0363932\pi\)
\(308\) 0 0
\(309\) −4.45017 −0.253161
\(310\) 0 0
\(311\) −6.41238 + 11.1066i −0.363612 + 0.629795i −0.988552 0.150878i \(-0.951790\pi\)
0.624940 + 0.780673i \(0.285123\pi\)
\(312\) 0 0
\(313\) −12.5120 + 7.22383i −0.707223 + 0.408315i −0.810032 0.586386i \(-0.800550\pi\)
0.102809 + 0.994701i \(0.467217\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.31271 1.91259i 0.186060 0.107422i −0.404077 0.914725i \(-0.632407\pi\)
0.590137 + 0.807303i \(0.299074\pi\)
\(318\) 0 0
\(319\) −3.72508 + 6.45203i −0.208565 + 0.361244i
\(320\) 0 0
\(321\) −24.0997 −1.34511
\(322\) 0 0
\(323\) 20.4235i 1.13640i
\(324\) 0 0
\(325\) −13.2749 27.4093i −0.736360 1.52039i
\(326\) 0 0
\(327\) 5.32475 3.07425i 0.294459 0.170006i
\(328\) 0 0
\(329\) 5.13746 2.44631i 0.283237 0.134869i
\(330\) 0 0
\(331\) 2.41238 + 4.17836i 0.132596 + 0.229663i 0.924677 0.380753i \(-0.124335\pi\)
−0.792080 + 0.610417i \(0.791002\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.13746 29.7405i 0.499233 1.62490i
\(336\) 0 0
\(337\) 13.0192i 0.709198i −0.935018 0.354599i \(-0.884617\pi\)
0.935018 0.354599i \(-0.115383\pi\)
\(338\) 0 0
\(339\) 11.2749 19.5287i 0.612369 1.06065i
\(340\) 0 0
\(341\) 4.86254 + 8.42217i 0.263321 + 0.456086i
\(342\) 0 0
\(343\) 18.0000 + 4.35890i 0.971909 + 0.235358i
\(344\) 0 0
\(345\) 0.774917 + 3.37779i 0.0417201 + 0.181854i
\(346\) 0 0
\(347\) −10.5000 6.06218i −0.563670 0.325435i 0.190947 0.981600i \(-0.438844\pi\)
−0.754617 + 0.656165i \(0.772177\pi\)
\(348\) 0 0
\(349\) 11.2749 0.603532 0.301766 0.953382i \(-0.402424\pi\)
0.301766 + 0.953382i \(0.402424\pi\)
\(350\) 0 0
\(351\) 31.6495 1.68933
\(352\) 0 0
\(353\) 18.4124 + 10.6304i 0.979992 + 0.565799i 0.902268 0.431176i \(-0.141901\pi\)
0.0777242 + 0.996975i \(0.475235\pi\)
\(354\) 0 0
\(355\) −5.27492 22.9928i −0.279964 1.22033i
\(356\) 0 0
\(357\) −9.41238 19.7668i −0.498156 1.04617i
\(358\) 0 0
\(359\) −0.687293 1.19043i −0.0362739 0.0628283i 0.847318 0.531085i \(-0.178216\pi\)
−0.883592 + 0.468257i \(0.844882\pi\)
\(360\) 0 0
\(361\) 0.362541 0.627940i 0.0190811 0.0330495i
\(362\) 0 0
\(363\) 10.0888i 0.529523i
\(364\) 0 0
\(365\) 1.41238 4.59698i 0.0739271 0.240617i
\(366\) 0 0
\(367\) 12.7749 + 7.37560i 0.666845 + 0.385003i 0.794880 0.606766i \(-0.207534\pi\)
−0.128035 + 0.991770i \(0.540867\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 16.1375 + 11.1066i 0.837815 + 0.576624i
\(372\) 0 0
\(373\) −4.86254 + 2.80739i −0.251773 + 0.145361i −0.620576 0.784146i \(-0.713101\pi\)
0.368803 + 0.929508i \(0.379768\pi\)
\(374\) 0 0
\(375\) 2.95017 + 19.1389i 0.152346 + 0.988327i
\(376\) 0 0
\(377\) 19.9474i 1.02734i
\(378\) 0 0
\(379\) −23.6495 −1.21479 −0.607397 0.794399i \(-0.707786\pi\)
−0.607397 + 0.794399i \(0.707786\pi\)
\(380\) 0 0
\(381\) −1.54983 + 2.68439i −0.0794004 + 0.137526i
\(382\) 0 0
\(383\) −17.3248 + 10.0025i −0.885253 + 0.511101i −0.872387 0.488816i \(-0.837429\pi\)
−0.0128665 + 0.999917i \(0.504096\pi\)
\(384\) 0 0
\(385\) 12.5120 + 4.95807i 0.637673 + 0.252686i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.68729 + 4.65453i −0.136251 + 0.235994i −0.926075 0.377340i \(-0.876839\pi\)
0.789824 + 0.613334i \(0.210172\pi\)
\(390\) 0 0
\(391\) 4.27492 0.216192
\(392\) 0 0
\(393\) 31.6531i 1.59669i
\(394\) 0 0
\(395\) −0.450166 + 0.418627i −0.0226503 + 0.0210634i
\(396\) 0 0
\(397\) 13.1375 7.58492i 0.659350 0.380676i −0.132679 0.991159i \(-0.542358\pi\)
0.792029 + 0.610483i \(0.209025\pi\)
\(398\) 0 0
\(399\) 1.54983 19.5287i 0.0775888 0.977659i
\(400\) 0 0
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) 22.5498 + 13.0192i 1.12329 + 0.648530i
\(404\) 0 0
\(405\) −19.2371 5.91041i −0.955901 0.293691i
\(406\) 0 0
\(407\) 12.7732i 0.633142i
\(408\) 0 0
\(409\) 5.04983 8.74657i 0.249698 0.432490i −0.713744 0.700407i \(-0.753002\pi\)
0.963442 + 0.267917i \(0.0863352\pi\)
\(410\) 0 0
\(411\) −7.96221 13.7910i −0.392747 0.680258i
\(412\) 0 0
\(413\) 6.41238 9.31697i 0.315532 0.458458i
\(414\) 0 0
\(415\) −12.3625 + 2.83616i −0.606853 + 0.139222i
\(416\) 0 0
\(417\) 25.6495 + 14.8087i 1.25606 + 0.725187i
\(418\) 0 0
\(419\) −17.0997 −0.835373 −0.417687 0.908591i \(-0.637159\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(420\) 0 0
\(421\) 3.27492 0.159610 0.0798048 0.996811i \(-0.474570\pi\)
0.0798048 + 0.996811i \(0.474570\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 23.8248 + 1.73205i 1.15567 + 0.0840168i
\(426\) 0 0
\(427\) −1.76287 3.70219i −0.0853114 0.179161i
\(428\) 0 0
\(429\) −12.0000 20.7846i −0.579365 1.00349i
\(430\) 0 0
\(431\) −9.68729 + 16.7789i −0.466620 + 0.808210i −0.999273 0.0381236i \(-0.987862\pi\)
0.532653 + 0.846334i \(0.321195\pi\)
\(432\) 0 0
\(433\) 26.8756i 1.29156i 0.763525 + 0.645778i \(0.223467\pi\)
−0.763525 + 0.645778i \(0.776533\pi\)
\(434\) 0 0
\(435\) 3.72508 12.1244i 0.178604 0.581318i
\(436\) 0 0
\(437\) 3.31271 + 1.91259i 0.158468 + 0.0914917i
\(438\) 0 0
\(439\) 0.587624 + 1.01779i 0.0280458 + 0.0485767i 0.879708 0.475515i \(-0.157738\pi\)
−0.851662 + 0.524092i \(0.824405\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.5000 6.06218i 0.498870 0.288023i −0.229377 0.973338i \(-0.573669\pi\)
0.728247 + 0.685315i \(0.240335\pi\)
\(444\) 0 0
\(445\) −11.4622 + 10.6592i −0.543361 + 0.505293i
\(446\) 0 0
\(447\) 13.0767i 0.618507i
\(448\) 0 0
\(449\) 25.8248 1.21875 0.609373 0.792884i \(-0.291421\pi\)
0.609373 + 0.792884i \(0.291421\pi\)
\(450\) 0 0
\(451\) 12.8248 22.2131i 0.603894 1.04598i
\(452\) 0 0
\(453\) 30.4124 17.5586i 1.42890 0.824975i
\(454\) 0 0
\(455\) 35.6495 5.25370i 1.67127 0.246297i
\(456\) 0 0
\(457\) 17.6873 10.2118i 0.827377 0.477686i −0.0255769 0.999673i \(-0.508142\pi\)
0.852954 + 0.521987i \(0.174809\pi\)
\(458\) 0 0
\(459\) −12.4124 + 21.4989i −0.579360 + 1.00348i
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) 6.50958i 0.302526i −0.988494 0.151263i \(-0.951666\pi\)
0.988494 0.151263i \(-0.0483340\pi\)
\(464\) 0 0
\(465\) −11.2749 12.1244i −0.522862 0.562254i
\(466\) 0 0
\(467\) −16.5997 + 9.58382i −0.768141 + 0.443486i −0.832211 0.554459i \(-0.812925\pi\)
0.0640700 + 0.997945i \(0.479592\pi\)
\(468\) 0 0
\(469\) 30.3248 + 20.8709i 1.40027 + 0.963730i
\(470\) 0 0
\(471\) −9.41238 16.3027i −0.433699 0.751189i
\(472\) 0 0
\(473\) −12.8248 7.40437i −0.589683 0.340453i
\(474\) 0 0
\(475\) 17.6873 + 12.0014i 0.811549 + 0.550660i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.41238 + 11.1066i −0.292989 + 0.507472i −0.974515 0.224322i \(-0.927983\pi\)
0.681526 + 0.731794i \(0.261317\pi\)
\(480\) 0 0
\(481\) −17.0997 29.6175i −0.779678 1.35044i
\(482\) 0 0
\(483\) −4.08762 0.324401i −0.185993 0.0147608i
\(484\) 0 0
\(485\) −15.0997 + 3.46410i −0.685641 + 0.157297i
\(486\) 0 0
\(487\) −28.9622 16.7213i −1.31240 0.757716i −0.329909 0.944013i \(-0.607018\pi\)
−0.982494 + 0.186296i \(0.940352\pi\)
\(488\) 0 0
\(489\) 12.8248 0.579955
\(490\) 0 0
\(491\) −13.4502 −0.606997 −0.303499 0.952832i \(-0.598155\pi\)
−0.303499 + 0.952832i \(0.598155\pi\)
\(492\) 0 0
\(493\) −13.5498 7.82300i −0.610254 0.352330i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 27.8248 + 2.20822i 1.24811 + 0.0990523i
\(498\) 0 0
\(499\) 19.6873 + 34.0994i 0.881324 + 1.52650i 0.849869 + 0.526993i \(0.176681\pi\)
0.0314548 + 0.999505i \(0.489986\pi\)
\(500\) 0 0
\(501\) −10.9124 + 18.9008i −0.487529 + 0.844425i
\(502\) 0 0
\(503\) 16.1797i 0.721418i 0.932678 + 0.360709i \(0.117465\pi\)
−0.932678 + 0.360709i \(0.882535\pi\)
\(504\) 0 0
\(505\) 3.31271 + 1.01779i 0.147414 + 0.0452913i
\(506\) 0 0
\(507\) −36.1495 20.8709i −1.60546 0.926910i
\(508\) 0 0
\(509\) −14.7749 25.5909i −0.654887 1.13430i −0.981922 0.189285i \(-0.939383\pi\)
0.327036 0.945012i \(-0.393950\pi\)
\(510\) 0 0
\(511\) 4.68729 + 3.22602i 0.207354 + 0.142711i
\(512\) 0 0
\(513\) −19.2371 + 11.1066i −0.849340 + 0.490367i
\(514\) 0 0
\(515\) 3.91238 + 4.20713i 0.172400 + 0.185388i
\(516\) 0 0
\(517\) 4.89261i 0.215177i
\(518\) 0 0
\(519\) 32.4743 1.42546
\(520\) 0 0
\(521\) 6.41238 11.1066i 0.280931 0.486587i −0.690683 0.723158i \(-0.742690\pi\)
0.971614 + 0.236570i \(0.0760234\pi\)
\(522\) 0 0
\(523\) −10.1375 + 5.85286i −0.443280 + 0.255928i −0.704988 0.709219i \(-0.749048\pi\)
0.261708 + 0.965147i \(0.415714\pi\)
\(524\) 0 0
\(525\) −22.6495 3.46410i −0.988505 0.151186i
\(526\) 0 0
\(527\) −17.6873 + 10.2118i −0.770471 + 0.444831i
\(528\) 0 0
\(529\) −11.0997 + 19.2252i −0.482594 + 0.835878i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 68.6750i 2.97464i
\(534\) 0 0
\(535\) 21.1873 + 22.7835i 0.916007 + 0.985017i
\(536\) 0 0
\(537\) 0.412376 0.238085i 0.0177953 0.0102741i
\(538\) 0 0
\(539\) −10.0378 + 12.3624i −0.432358 + 0.532488i
\(540\) 0 0
\(541\) 1.22508 + 2.12191i 0.0526704 + 0.0912278i 0.891159 0.453692i \(-0.149893\pi\)
−0.838488 + 0.544920i \(0.816560\pi\)
\(542\) 0 0
\(543\) −25.0876 14.4843i −1.07661 0.621583i
\(544\) 0 0
\(545\) −7.58762 2.33122i −0.325018 0.0998585i
\(546\) 0 0
\(547\) 36.1271i 1.54468i 0.635208 + 0.772341i \(0.280914\pi\)
−0.635208 + 0.772341i \(0.719086\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.00000 12.1244i −0.298210 0.516515i
\(552\) 0 0
\(553\) −0.312707 0.656712i −0.0132977 0.0279262i
\(554\) 0 0
\(555\) 4.86254 + 21.1953i 0.206403 + 0.899692i
\(556\) 0 0
\(557\) −4.86254 2.80739i −0.206032 0.118953i 0.393434 0.919353i \(-0.371287\pi\)
−0.599466 + 0.800400i \(0.704620\pi\)
\(558\) 0 0
\(559\) −39.6495 −1.67700
\(560\) 0 0
\(561\) 18.8248 0.794782
\(562\) 0 0
\(563\) 10.5997 + 6.11972i 0.446723 + 0.257916i 0.706445 0.707768i \(-0.250298\pi\)
−0.259722 + 0.965683i \(0.583631\pi\)
\(564\) 0 0
\(565\) −28.3746 + 6.50958i −1.19373 + 0.273860i
\(566\) 0 0
\(567\) 13.5000 19.6150i 0.566947 0.823754i
\(568\) 0 0
\(569\) −14.6873 25.4391i −0.615723 1.06646i −0.990257 0.139251i \(-0.955531\pi\)
0.374534 0.927213i \(-0.377803\pi\)
\(570\) 0 0
\(571\) 0.137459 0.238085i 0.00575246 0.00996356i −0.863135 0.504974i \(-0.831502\pi\)
0.868887 + 0.495010i \(0.164836\pi\)
\(572\) 0 0
\(573\) 39.5336i 1.65154i
\(574\) 0 0
\(575\) 2.51204 3.70219i 0.104760 0.154392i
\(576\) 0 0
\(577\) 7.13746 + 4.12081i 0.297136 + 0.171552i 0.641156 0.767411i \(-0.278455\pi\)
−0.344019 + 0.938963i \(0.611789\pi\)
\(578\) 0 0
\(579\) −7.96221 13.7910i −0.330898 0.573132i
\(580\) 0 0
\(581\) 1.18729 14.9605i 0.0492572 0.620667i
\(582\) 0 0
\(583\) −14.5876 + 8.42217i −0.604158 + 0.348811i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13.9715i 0.576665i −0.957530 0.288333i \(-0.906899\pi\)
0.957530 0.288333i \(-0.0931009\pi\)
\(588\) 0 0
\(589\) −18.2749 −0.753005
\(590\) 0 0
\(591\) −22.5498 + 39.0575i −0.927576 + 1.60661i
\(592\) 0 0
\(593\) −17.5876 + 10.1542i −0.722237 + 0.416984i −0.815576 0.578651i \(-0.803579\pi\)
0.0933384 + 0.995634i \(0.470246\pi\)
\(594\) 0 0
\(595\) −10.4124 + 26.2764i −0.426866 + 1.07723i
\(596\) 0 0
\(597\) 14.5876 8.42217i 0.597032 0.344696i
\(598\) 0 0
\(599\) −1.13746 + 1.97014i −0.0464753 + 0.0804976i −0.888327 0.459211i \(-0.848132\pi\)
0.841852 + 0.539709i \(0.181466\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.53779 8.86957i 0.387766 0.360599i
\(606\) 0 0
\(607\) −27.8746 + 16.0934i −1.13139 + 0.653211i −0.944285 0.329128i \(-0.893245\pi\)
−0.187109 + 0.982339i \(0.559912\pi\)
\(608\) 0 0
\(609\) 12.3625 + 8.50848i 0.500955 + 0.344781i
\(610\) 0 0
\(611\) 6.54983 + 11.3446i 0.264978 + 0.458955i
\(612\) 0 0
\(613\) 32.0619 + 18.5109i 1.29497 + 0.747650i 0.979530 0.201297i \(-0.0645156\pi\)
0.315437 + 0.948947i \(0.397849\pi\)
\(614\) 0 0
\(615\) −12.8248 + 41.7419i −0.517144 + 1.68319i
\(616\) 0 0
\(617\) 3.57919i 0.144093i 0.997401 + 0.0720464i \(0.0229530\pi\)
−0.997401 + 0.0720464i \(0.977047\pi\)
\(618\) 0 0
\(619\) 21.9622 38.0397i 0.882736 1.52894i 0.0344487 0.999406i \(-0.489032\pi\)
0.848287 0.529537i \(-0.177634\pi\)
\(620\) 0 0
\(621\) 2.32475 + 4.02659i 0.0932891 + 0.161581i
\(622\) 0 0
\(623\) −7.96221 16.7213i −0.318999 0.669926i
\(624\) 0 0
\(625\) 15.5000 19.6150i 0.620000 0.784602i
\(626\) 0 0
\(627\) 14.5876 + 8.42217i 0.582574 + 0.336349i
\(628\) 0 0
\(629\) 26.8248 1.06957
\(630\) 0 0
\(631\) 2.90033 0.115460 0.0577302 0.998332i \(-0.481614\pi\)
0.0577302 + 0.998332i \(0.481614\pi\)
\(632\) 0 0
\(633\) −29.4743 17.0170i −1.17150 0.676364i
\(634\) 0 0
\(635\) 3.90033 0.894797i 0.154780 0.0355089i
\(636\) 0 0
\(637\) −6.72508 + 42.1029i −0.266457 + 1.66818i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −14.0498 + 24.3350i −0.554935 + 0.961176i 0.442973 + 0.896535i \(0.353924\pi\)
−0.997909 + 0.0646411i \(0.979410\pi\)
\(642\) 0 0
\(643\) 38.3353i 1.51180i −0.654689 0.755898i \(-0.727200\pi\)
0.654689 0.755898i \(-0.272800\pi\)
\(644\) 0 0
\(645\) 24.0997 + 7.40437i 0.948924 + 0.291547i
\(646\) 0 0
\(647\) −0.675248 0.389855i −0.0265468 0.0153268i 0.486668 0.873587i \(-0.338212\pi\)
−0.513215 + 0.858260i \(0.671546\pi\)
\(648\) 0 0
\(649\) 4.86254 + 8.42217i 0.190871 + 0.330599i
\(650\) 0 0
\(651\) 17.6873 8.42217i 0.693220 0.330091i
\(652\) 0 0
\(653\) 32.0619 18.5109i 1.25468 0.724389i 0.282643 0.959225i \(-0.408789\pi\)
0.972035 + 0.234836i \(0.0754554\pi\)
\(654\) 0 0
\(655\) 29.9244 27.8279i 1.16924 1.08733i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 25.4502 0.991398 0.495699 0.868494i \(-0.334912\pi\)
0.495699 + 0.868494i \(0.334912\pi\)
\(660\) 0 0
\(661\) 7.77492 13.4666i 0.302409 0.523788i −0.674272 0.738483i \(-0.735542\pi\)
0.976681 + 0.214695i \(0.0688758\pi\)
\(662\) 0 0
\(663\) 43.6495 25.2011i 1.69521 0.978728i
\(664\) 0 0
\(665\) −19.8248 + 15.7035i −0.768771 + 0.608957i
\(666\) 0 0
\(667\) −2.53779 + 1.46519i −0.0982636 + 0.0567325i
\(668\) 0 0
\(669\) 7.54983 13.0767i 0.291893 0.505574i
\(670\) 0 0
\(671\) 3.52575 0.136110
\(672\) 0 0
\(673\) 3.57919i 0.137968i −0.997618 0.0689838i \(-0.978024\pi\)
0.997618 0.0689838i \(-0.0219757\pi\)
\(674\) 0 0
\(675\) 11.3248 + 23.3827i 0.435890 + 0.900000i
\(676\) 0 0
\(677\) 21.3127 12.3049i 0.819114 0.472916i −0.0309969 0.999519i \(-0.509868\pi\)
0.850111 + 0.526604i \(0.176535\pi\)
\(678\) 0 0
\(679\) 1.45017 18.2728i 0.0556522 0.701248i
\(680\) 0 0
\(681\) 5.58762 + 9.67805i 0.214118 + 0.370864i
\(682\) 0 0
\(683\) −13.5997 7.85177i −0.520377 0.300440i 0.216712 0.976236i \(-0.430467\pi\)
−0.737089 + 0.675796i \(0.763800\pi\)
\(684\) 0 0
\(685\) −6.03779 + 19.6517i −0.230692 + 0.750854i
\(686\) 0 0
\(687\) 7.40437i 0.282494i
\(688\) 0 0
\(689\) −22.5498 + 39.0575i −0.859080 + 1.48797i
\(690\) 0 0
\(691\) 3.68729 + 6.38658i 0.140271 + 0.242957i 0.927599 0.373578i \(-0.121869\pi\)
−0.787327 + 0.616535i \(0.788536\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.54983 37.2679i −0.324314 1.41365i
\(696\) 0 0
\(697\) 46.6495 + 26.9331i 1.76698 + 1.02016i
\(698\) 0 0
\(699\) −32.2749 −1.22075
\(700\) 0 0
\(701\) −13.8248 −0.522154 −0.261077 0.965318i \(-0.584078\pi\)
−0.261077 + 0.965318i \(0.584078\pi\)
\(702\) 0 0
\(703\) 20.7870 + 12.0014i 0.783995 + 0.452640i
\(704\) 0 0
\(705\) −1.86254 8.11863i −0.0701474 0.305765i
\(706\) 0 0
\(707\) −2.32475 + 3.37779i −0.0874313 + 0.127035i
\(708\) 0 0
\(709\) −12.7749 22.1268i −0.479772 0.830990i 0.519959 0.854191i \(-0.325947\pi\)
−0.999731 + 0.0232018i \(0.992614\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.82518i 0.143254i
\(714\) 0 0
\(715\) −9.09967 + 29.6175i −0.340308 + 1.10763i
\(716\) 0 0
\(717\) 21.8248 + 12.6005i 0.815060 + 0.470575i
\(718\) 0 0
\(719\) 3.68729 + 6.38658i 0.137513 + 0.238179i 0.926555 0.376160i \(-0.122756\pi\)
−0.789042 + 0.614340i \(0.789423\pi\)
\(720\) 0 0
\(721\) −6.13746 + 2.92248i −0.228571 + 0.108839i
\(722\) 0 0
\(723\) 19.2371 11.1066i 0.715436 0.413057i
\(724\) 0 0
\(725\) −14.7371 + 7.13752i −0.547323 + 0.265081i
\(726\) 0 0
\(727\) 18.6915i 0.693228i −0.938008 0.346614i \(-0.887331\pi\)
0.938008 0.346614i \(-0.112669\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 15.5498 26.9331i 0.575131 0.996157i
\(732\) 0 0
\(733\) −28.8625 + 16.6638i −1.06606 + 0.615491i −0.927103 0.374807i \(-0.877709\pi\)
−0.138959 + 0.990298i \(0.544376\pi\)
\(734\) 0 0
\(735\) 11.9502 24.3350i 0.440788 0.897611i
\(736\) 0 0
\(737\) −27.4124 + 15.8265i −1.00975 + 0.582978i
\(738\) 0 0
\(739\) 15.9622 27.6474i 0.587179 1.01702i −0.407420 0.913241i \(-0.633572\pi\)
0.994600 0.103784i \(-0.0330950\pi\)
\(740\) 0 0
\(741\) 45.0997 1.65678
\(742\) 0 0
\(743\) 19.5287i 0.716440i 0.933637 + 0.358220i \(0.116616\pi\)
−0.933637 + 0.358220i \(0.883384\pi\)
\(744\) 0 0
\(745\) 12.3625 11.4964i 0.452928 0.421196i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −33.2371 + 15.8265i −1.21446 + 0.578289i
\(750\) 0 0
\(751\) 11.1375 + 19.2906i 0.406412 + 0.703926i 0.994485 0.104882i \(-0.0334466\pi\)
−0.588073 + 0.808808i \(0.700113\pi\)
\(752\) 0 0
\(753\) −8.17525 4.71998i −0.297923 0.172006i
\(754\) 0 0
\(755\) −43.3368 13.3148i −1.57719 0.484575i
\(756\) 0 0
\(757\) 9.43996i 0.343101i 0.985175 + 0.171551i \(0.0548777\pi\)
−0.985175 + 0.171551i \(0.945122\pi\)
\(758\) 0 0
\(759\) 1.76287 3.05338i 0.0639882 0.110831i
\(760\) 0 0
\(761\) 14.9622 + 25.9153i 0.542380 + 0.939429i 0.998767 + 0.0496479i \(0.0158099\pi\)
−0.456387 + 0.889781i \(0.650857\pi\)
\(762\) 0 0
\(763\) 5.32475 7.73668i 0.192769 0.280087i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 22.5498 + 13.0192i 0.814227 + 0.470094i
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −42.8248 −1.54230
\(772\) 0 0
\(773\) −23.5876 13.6183i −0.848388 0.489817i 0.0117187 0.999931i \(-0.496270\pi\)
−0.860107 + 0.510114i \(0.829603\pi\)
\(774\) 0 0
\(775\) −1.54983 + 21.3183i −0.0556717 + 0.765777i
\(776\) 0 0
\(777\) −25.6495 2.03559i −0.920171 0.0730264i
\(778\) 0 0
\(779\) 24.0997 + 41.7419i 0.863460 + 1.49556i
\(780\) 0 0
\(781\) −12.0000 + 20.7846i −0.429394 + 0.743732i
\(782\) 0 0
\(783\) 17.0170i 0.608137i
\(784\) 0 0
\(785\) −7.13746 + 23.2309i −0.254747 + 0.829147i
\(786\) 0 0
\(787\) 1.50000 + 0.866025i 0.0534692 + 0.0308705i 0.526496 0.850177i \(-0.323505\pi\)
−0.473027 + 0.881048i \(0.656839\pi\)
\(788\) 0 0
\(789\) 23.3248 + 40.3997i 0.830383 + 1.43827i
\(790\) 0 0
\(791\) 2.72508 34.3375i 0.0968928 1.22090i
\(792\) 0 0
\(793\) 8.17525 4.71998i 0.290312 0.167611i
\(794\) 0 0
\(795\) 21.0000 19.5287i 0.744793 0.692613i
\(796\) 0 0