Properties

Label 1344.2.q.z.961.1
Level $1344$
Weight $2$
Character 1344.961
Analytic conductor $10.732$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.7318940317\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 672)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 2.43956i\) of defining polynomial
Character \(\chi\) \(=\) 1344.961
Dual form 1344.2.q.z.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.60074 + 2.77256i) q^{5} +(-1.02398 - 2.43956i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.60074 + 2.77256i) q^{5} +(-1.02398 - 2.43956i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.12471 + 3.68011i) q^{11} +3.15352 q^{13} -3.20147 q^{15} +(2.20147 + 3.81306i) q^{17} +(1.57676 - 2.73103i) q^{19} +(1.60074 - 2.10657i) q^{21} +(-2.20147 + 3.81306i) q^{23} +(-2.62471 - 4.54614i) q^{25} -1.00000 q^{27} -7.20147 q^{29} +(-1.02398 - 1.77358i) q^{31} +(-2.12471 + 3.68011i) q^{33} +(8.40294 + 1.06607i) q^{35} +(-4.82618 + 8.35920i) q^{37} +(1.57676 + 2.73103i) q^{39} -10.4989 q^{41} -0.750575 q^{43} +(-1.60074 - 2.77256i) q^{45} +(1.20147 - 2.08101i) q^{47} +(-4.90294 + 4.99611i) q^{49} +(-2.20147 + 3.81306i) q^{51} +(-1.64869 - 2.85561i) q^{53} -13.6044 q^{55} +3.15352 q^{57} +(4.12471 + 7.14421i) q^{59} +(-4.04795 + 7.01126i) q^{61} +(2.62471 + 0.332992i) q^{63} +(-5.04795 + 8.74331i) q^{65} +(2.57676 + 4.46308i) q^{67} -4.40294 q^{69} +6.40294 q^{71} +(-7.62471 - 13.2064i) q^{73} +(2.62471 - 4.54614i) q^{75} +(6.80221 - 8.95172i) q^{77} +(8.22545 - 14.2469i) q^{79} +(-0.500000 - 0.866025i) q^{81} -14.5565 q^{83} -14.0959 q^{85} +(-3.60074 - 6.23666i) q^{87} +(-1.20147 + 2.08101i) q^{89} +(-3.22913 - 7.69321i) q^{91} +(1.02398 - 1.77358i) q^{93} +(5.04795 + 8.74331i) q^{95} +4.24943 q^{97} -4.24943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{3} - 3q^{7} - 3q^{9} + O(q^{10}) \) \( 6q + 3q^{3} - 3q^{7} - 3q^{9} + 6q^{13} - 6q^{17} + 3q^{19} + 6q^{23} - 3q^{25} - 6q^{27} - 24q^{29} - 3q^{31} + 12q^{35} + 3q^{37} + 3q^{39} - 12q^{41} - 30q^{43} - 12q^{47} + 9q^{49} + 6q^{51} + 6q^{53} - 24q^{55} + 6q^{57} + 12q^{59} - 18q^{61} + 3q^{63} - 24q^{65} + 9q^{67} + 12q^{69} - 33q^{73} + 3q^{75} + 12q^{77} + 27q^{79} - 3q^{81} - 36q^{83} - 72q^{85} - 12q^{87} + 12q^{89} + 51q^{91} + 3q^{93} + 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(449\) \(577\) \(1093\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −1.60074 + 2.77256i −0.715871 + 1.23992i 0.246752 + 0.969079i \(0.420637\pi\)
−0.962623 + 0.270846i \(0.912697\pi\)
\(6\) 0 0
\(7\) −1.02398 2.43956i −0.387027 0.922069i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.12471 + 3.68011i 0.640625 + 1.10959i 0.985293 + 0.170871i \(0.0546580\pi\)
−0.344669 + 0.938724i \(0.612009\pi\)
\(12\) 0 0
\(13\) 3.15352 0.874629 0.437314 0.899309i \(-0.355930\pi\)
0.437314 + 0.899309i \(0.355930\pi\)
\(14\) 0 0
\(15\) −3.20147 −0.826617
\(16\) 0 0
\(17\) 2.20147 + 3.81306i 0.533935 + 0.924803i 0.999214 + 0.0396391i \(0.0126208\pi\)
−0.465279 + 0.885164i \(0.654046\pi\)
\(18\) 0 0
\(19\) 1.57676 2.73103i 0.361734 0.626541i −0.626513 0.779411i \(-0.715518\pi\)
0.988246 + 0.152870i \(0.0488517\pi\)
\(20\) 0 0
\(21\) 1.60074 2.10657i 0.349309 0.459692i
\(22\) 0 0
\(23\) −2.20147 + 3.81306i −0.459039 + 0.795078i −0.998910 0.0466689i \(-0.985139\pi\)
0.539872 + 0.841747i \(0.318473\pi\)
\(24\) 0 0
\(25\) −2.62471 4.54614i −0.524943 0.909227i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −7.20147 −1.33728 −0.668640 0.743586i \(-0.733123\pi\)
−0.668640 + 0.743586i \(0.733123\pi\)
\(30\) 0 0
\(31\) −1.02398 1.77358i −0.183912 0.318544i 0.759298 0.650744i \(-0.225543\pi\)
−0.943209 + 0.332199i \(0.892209\pi\)
\(32\) 0 0
\(33\) −2.12471 + 3.68011i −0.369865 + 0.640625i
\(34\) 0 0
\(35\) 8.40294 + 1.06607i 1.42036 + 0.180198i
\(36\) 0 0
\(37\) −4.82618 + 8.35920i −0.793420 + 1.37424i 0.130418 + 0.991459i \(0.458368\pi\)
−0.923838 + 0.382784i \(0.874965\pi\)
\(38\) 0 0
\(39\) 1.57676 + 2.73103i 0.252484 + 0.437314i
\(40\) 0 0
\(41\) −10.4989 −1.63964 −0.819822 0.572618i \(-0.805928\pi\)
−0.819822 + 0.572618i \(0.805928\pi\)
\(42\) 0 0
\(43\) −0.750575 −0.114462 −0.0572308 0.998361i \(-0.518227\pi\)
−0.0572308 + 0.998361i \(0.518227\pi\)
\(44\) 0 0
\(45\) −1.60074 2.77256i −0.238624 0.413308i
\(46\) 0 0
\(47\) 1.20147 2.08101i 0.175253 0.303547i −0.764996 0.644035i \(-0.777259\pi\)
0.940249 + 0.340488i \(0.110592\pi\)
\(48\) 0 0
\(49\) −4.90294 + 4.99611i −0.700421 + 0.713730i
\(50\) 0 0
\(51\) −2.20147 + 3.81306i −0.308268 + 0.533935i
\(52\) 0 0
\(53\) −1.64869 2.85561i −0.226465 0.392249i 0.730293 0.683134i \(-0.239384\pi\)
−0.956758 + 0.290885i \(0.906050\pi\)
\(54\) 0 0
\(55\) −13.6044 −1.83442
\(56\) 0 0
\(57\) 3.15352 0.417694
\(58\) 0 0
\(59\) 4.12471 + 7.14421i 0.536992 + 0.930097i 0.999064 + 0.0432549i \(0.0137727\pi\)
−0.462072 + 0.886842i \(0.652894\pi\)
\(60\) 0 0
\(61\) −4.04795 + 7.01126i −0.518287 + 0.897700i 0.481487 + 0.876453i \(0.340097\pi\)
−0.999774 + 0.0212466i \(0.993236\pi\)
\(62\) 0 0
\(63\) 2.62471 + 0.332992i 0.330683 + 0.0419531i
\(64\) 0 0
\(65\) −5.04795 + 8.74331i −0.626121 + 1.08447i
\(66\) 0 0
\(67\) 2.57676 + 4.46308i 0.314801 + 0.545252i 0.979395 0.201953i \(-0.0647288\pi\)
−0.664594 + 0.747205i \(0.731395\pi\)
\(68\) 0 0
\(69\) −4.40294 −0.530052
\(70\) 0 0
\(71\) 6.40294 0.759890 0.379945 0.925009i \(-0.375943\pi\)
0.379945 + 0.925009i \(0.375943\pi\)
\(72\) 0 0
\(73\) −7.62471 13.2064i −0.892405 1.54569i −0.836984 0.547228i \(-0.815683\pi\)
−0.0554215 0.998463i \(-0.517650\pi\)
\(74\) 0 0
\(75\) 2.62471 4.54614i 0.303076 0.524943i
\(76\) 0 0
\(77\) 6.80221 8.95172i 0.775184 1.02014i
\(78\) 0 0
\(79\) 8.22545 14.2469i 0.925435 1.60290i 0.134576 0.990903i \(-0.457033\pi\)
0.790860 0.611998i \(-0.209634\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −14.5565 −1.59778 −0.798890 0.601477i \(-0.794579\pi\)
−0.798890 + 0.601477i \(0.794579\pi\)
\(84\) 0 0
\(85\) −14.0959 −1.52892
\(86\) 0 0
\(87\) −3.60074 6.23666i −0.386039 0.668640i
\(88\) 0 0
\(89\) −1.20147 + 2.08101i −0.127356 + 0.220587i −0.922651 0.385635i \(-0.873982\pi\)
0.795296 + 0.606222i \(0.207316\pi\)
\(90\) 0 0
\(91\) −3.22913 7.69321i −0.338505 0.806468i
\(92\) 0 0
\(93\) 1.02398 1.77358i 0.106181 0.183912i
\(94\) 0 0
\(95\) 5.04795 + 8.74331i 0.517909 + 0.897045i
\(96\) 0 0
\(97\) 4.24943 0.431464 0.215732 0.976453i \(-0.430786\pi\)
0.215732 + 0.976453i \(0.430786\pi\)
\(98\) 0 0
\(99\) −4.24943 −0.427083
\(100\) 0 0
\(101\) 1.95205 + 3.38104i 0.194236 + 0.336427i 0.946650 0.322264i \(-0.104444\pi\)
−0.752414 + 0.658691i \(0.771111\pi\)
\(102\) 0 0
\(103\) −4.62471 + 8.01024i −0.455686 + 0.789272i −0.998727 0.0504341i \(-0.983940\pi\)
0.543041 + 0.839706i \(0.317273\pi\)
\(104\) 0 0
\(105\) 3.27823 + 7.81020i 0.319923 + 0.762197i
\(106\) 0 0
\(107\) 8.27823 14.3383i 0.800287 1.38614i −0.119140 0.992877i \(-0.538014\pi\)
0.919427 0.393260i \(-0.128653\pi\)
\(108\) 0 0
\(109\) 10.0277 + 17.3684i 0.960475 + 1.66359i 0.721309 + 0.692614i \(0.243541\pi\)
0.239167 + 0.970979i \(0.423126\pi\)
\(110\) 0 0
\(111\) −9.65237 −0.916162
\(112\) 0 0
\(113\) 8.00000 0.752577 0.376288 0.926503i \(-0.377200\pi\)
0.376288 + 0.926503i \(0.377200\pi\)
\(114\) 0 0
\(115\) −7.04795 12.2074i −0.657225 1.13835i
\(116\) 0 0
\(117\) −1.57676 + 2.73103i −0.145771 + 0.252484i
\(118\) 0 0
\(119\) 7.04795 9.27512i 0.646085 0.850249i
\(120\) 0 0
\(121\) −3.52881 + 6.11207i −0.320801 + 0.555643i
\(122\) 0 0
\(123\) −5.24943 9.09227i −0.473325 0.819822i
\(124\) 0 0
\(125\) 0.798528 0.0714225
\(126\) 0 0
\(127\) 12.4509 1.10484 0.552419 0.833566i \(-0.313705\pi\)
0.552419 + 0.833566i \(0.313705\pi\)
\(128\) 0 0
\(129\) −0.375287 0.650017i −0.0330422 0.0572308i
\(130\) 0 0
\(131\) 2.12471 3.68011i 0.185637 0.321533i −0.758154 0.652076i \(-0.773898\pi\)
0.943791 + 0.330543i \(0.107232\pi\)
\(132\) 0 0
\(133\) −8.27708 1.05010i −0.717714 0.0910551i
\(134\) 0 0
\(135\) 1.60074 2.77256i 0.137769 0.238624i
\(136\) 0 0
\(137\) 5.20147 + 9.00921i 0.444392 + 0.769709i 0.998010 0.0630617i \(-0.0200865\pi\)
−0.553618 + 0.832771i \(0.686753\pi\)
\(138\) 0 0
\(139\) −11.6524 −0.988341 −0.494171 0.869365i \(-0.664528\pi\)
−0.494171 + 0.869365i \(0.664528\pi\)
\(140\) 0 0
\(141\) 2.40294 0.202364
\(142\) 0 0
\(143\) 6.70032 + 11.6053i 0.560309 + 0.970484i
\(144\) 0 0
\(145\) 11.5277 19.9665i 0.957320 1.65813i
\(146\) 0 0
\(147\) −6.77823 1.74802i −0.559059 0.144174i
\(148\) 0 0
\(149\) 5.20147 9.00921i 0.426121 0.738064i −0.570403 0.821365i \(-0.693213\pi\)
0.996524 + 0.0833012i \(0.0265464\pi\)
\(150\) 0 0
\(151\) 10.0037 + 17.3269i 0.814088 + 1.41004i 0.909981 + 0.414650i \(0.136096\pi\)
−0.0958929 + 0.995392i \(0.530571\pi\)
\(152\) 0 0
\(153\) −4.40294 −0.355957
\(154\) 0 0
\(155\) 6.55646 0.526628
\(156\) 0 0
\(157\) 7.24943 + 12.5564i 0.578567 + 1.00211i 0.995644 + 0.0932364i \(0.0297212\pi\)
−0.417077 + 0.908871i \(0.636945\pi\)
\(158\) 0 0
\(159\) 1.64869 2.85561i 0.130750 0.226465i
\(160\) 0 0
\(161\) 11.5565 + 1.46615i 0.910777 + 0.115549i
\(162\) 0 0
\(163\) −5.35499 + 9.27512i −0.419435 + 0.726483i −0.995883 0.0906510i \(-0.971105\pi\)
0.576447 + 0.817134i \(0.304439\pi\)
\(164\) 0 0
\(165\) −6.80221 11.7818i −0.529551 0.917210i
\(166\) 0 0
\(167\) 17.3047 1.33908 0.669540 0.742776i \(-0.266491\pi\)
0.669540 + 0.742776i \(0.266491\pi\)
\(168\) 0 0
\(169\) −3.05531 −0.235024
\(170\) 0 0
\(171\) 1.57676 + 2.73103i 0.120578 + 0.208847i
\(172\) 0 0
\(173\) −1.95205 + 3.38104i −0.148411 + 0.257056i −0.930640 0.365935i \(-0.880749\pi\)
0.782229 + 0.622991i \(0.214083\pi\)
\(174\) 0 0
\(175\) −8.40294 + 11.0583i −0.635203 + 0.835928i
\(176\) 0 0
\(177\) −4.12471 + 7.14421i −0.310032 + 0.536992i
\(178\) 0 0
\(179\) 10.4029 + 18.0184i 0.777553 + 1.34676i 0.933349 + 0.358971i \(0.116872\pi\)
−0.155796 + 0.987789i \(0.549794\pi\)
\(180\) 0 0
\(181\) 13.2494 0.984822 0.492411 0.870363i \(-0.336116\pi\)
0.492411 + 0.870363i \(0.336116\pi\)
\(182\) 0 0
\(183\) −8.09591 −0.598467
\(184\) 0 0
\(185\) −15.4509 26.7617i −1.13597 1.96756i
\(186\) 0 0
\(187\) −9.35499 + 16.2033i −0.684105 + 1.18490i
\(188\) 0 0
\(189\) 1.02398 + 2.43956i 0.0744833 + 0.177452i
\(190\) 0 0
\(191\) −2.09591 + 3.63021i −0.151654 + 0.262673i −0.931836 0.362880i \(-0.881793\pi\)
0.780181 + 0.625553i \(0.215127\pi\)
\(192\) 0 0
\(193\) 9.15237 + 15.8524i 0.658802 + 1.14108i 0.980926 + 0.194381i \(0.0622698\pi\)
−0.322124 + 0.946697i \(0.604397\pi\)
\(194\) 0 0
\(195\) −10.0959 −0.722983
\(196\) 0 0
\(197\) −11.9041 −0.848132 −0.424066 0.905631i \(-0.639397\pi\)
−0.424066 + 0.905631i \(0.639397\pi\)
\(198\) 0 0
\(199\) −0.402945 0.697921i −0.0285640 0.0494743i 0.851390 0.524533i \(-0.175760\pi\)
−0.879954 + 0.475059i \(0.842427\pi\)
\(200\) 0 0
\(201\) −2.57676 + 4.46308i −0.181751 + 0.314801i
\(202\) 0 0
\(203\) 7.37414 + 17.5685i 0.517563 + 1.23306i
\(204\) 0 0
\(205\) 16.8059 29.1087i 1.17377 2.03304i
\(206\) 0 0
\(207\) −2.20147 3.81306i −0.153013 0.265026i
\(208\) 0 0
\(209\) 13.4006 0.926942
\(210\) 0 0
\(211\) −8.49885 −0.585085 −0.292542 0.956253i \(-0.594501\pi\)
−0.292542 + 0.956253i \(0.594501\pi\)
\(212\) 0 0
\(213\) 3.20147 + 5.54511i 0.219361 + 0.379945i
\(214\) 0 0
\(215\) 1.20147 2.08101i 0.0819397 0.141924i
\(216\) 0 0
\(217\) −3.27823 + 4.31416i −0.222541 + 0.292864i
\(218\) 0 0
\(219\) 7.62471 13.2064i 0.515230 0.892405i
\(220\) 0 0
\(221\) 6.94239 + 12.0246i 0.466995 + 0.808860i
\(222\) 0 0
\(223\) −16.7985 −1.12491 −0.562456 0.826827i \(-0.690144\pi\)
−0.562456 + 0.826827i \(0.690144\pi\)
\(224\) 0 0
\(225\) 5.24943 0.349962
\(226\) 0 0
\(227\) −8.43175 14.6042i −0.559635 0.969316i −0.997527 0.0702885i \(-0.977608\pi\)
0.437892 0.899028i \(-0.355725\pi\)
\(228\) 0 0
\(229\) 10.2771 17.8004i 0.679129 1.17629i −0.296115 0.955152i \(-0.595691\pi\)
0.975244 0.221133i \(-0.0709755\pi\)
\(230\) 0 0
\(231\) 11.1535 + 1.41503i 0.733848 + 0.0931019i
\(232\) 0 0
\(233\) −4.95205 + 8.57720i −0.324419 + 0.561911i −0.981395 0.192001i \(-0.938502\pi\)
0.656975 + 0.753912i \(0.271836\pi\)
\(234\) 0 0
\(235\) 3.84648 + 6.66230i 0.250917 + 0.434601i
\(236\) 0 0
\(237\) 16.4509 1.06860
\(238\) 0 0
\(239\) 4.40294 0.284803 0.142401 0.989809i \(-0.454518\pi\)
0.142401 + 0.989809i \(0.454518\pi\)
\(240\) 0 0
\(241\) −10.4318 18.0683i −0.671968 1.16388i −0.977345 0.211652i \(-0.932116\pi\)
0.305377 0.952232i \(-0.401218\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) −6.00368 21.5911i −0.383561 1.37941i
\(246\) 0 0
\(247\) 4.97234 8.61235i 0.316383 0.547991i
\(248\) 0 0
\(249\) −7.27823 12.6063i −0.461239 0.798890i
\(250\) 0 0
\(251\) −3.44354 −0.217354 −0.108677 0.994077i \(-0.534661\pi\)
−0.108677 + 0.994077i \(0.534661\pi\)
\(252\) 0 0
\(253\) −18.7100 −1.17629
\(254\) 0 0
\(255\) −7.04795 12.2074i −0.441360 0.764458i
\(256\) 0 0
\(257\) 2.79853 4.84719i 0.174567 0.302360i −0.765444 0.643502i \(-0.777481\pi\)
0.940011 + 0.341143i \(0.110814\pi\)
\(258\) 0 0
\(259\) 25.3347 + 3.21417i 1.57422 + 0.199719i
\(260\) 0 0
\(261\) 3.60074 6.23666i 0.222880 0.386039i
\(262\) 0 0
\(263\) 0.798528 + 1.38309i 0.0492393 + 0.0852850i 0.889595 0.456751i \(-0.150987\pi\)
−0.840355 + 0.542036i \(0.817654\pi\)
\(264\) 0 0
\(265\) 10.5565 0.648478
\(266\) 0 0
\(267\) −2.40294 −0.147058
\(268\) 0 0
\(269\) 8.85016 + 15.3289i 0.539604 + 0.934621i 0.998925 + 0.0463511i \(0.0147593\pi\)
−0.459321 + 0.888270i \(0.651907\pi\)
\(270\) 0 0
\(271\) 1.19779 2.07464i 0.0727607 0.126025i −0.827350 0.561687i \(-0.810152\pi\)
0.900110 + 0.435662i \(0.143486\pi\)
\(272\) 0 0
\(273\) 5.04795 6.64311i 0.305516 0.402060i
\(274\) 0 0
\(275\) 11.1535 19.3185i 0.672583 1.16495i
\(276\) 0 0
\(277\) −2.62471 4.54614i −0.157704 0.273151i 0.776337 0.630319i \(-0.217076\pi\)
−0.934040 + 0.357168i \(0.883742\pi\)
\(278\) 0 0
\(279\) 2.04795 0.122608
\(280\) 0 0
\(281\) 20.0959 1.19882 0.599411 0.800442i \(-0.295402\pi\)
0.599411 + 0.800442i \(0.295402\pi\)
\(282\) 0 0
\(283\) −11.6247 20.1346i −0.691017 1.19688i −0.971505 0.237020i \(-0.923829\pi\)
0.280487 0.959858i \(-0.409504\pi\)
\(284\) 0 0
\(285\) −5.04795 + 8.74331i −0.299015 + 0.517909i
\(286\) 0 0
\(287\) 10.7506 + 25.6126i 0.634586 + 1.51186i
\(288\) 0 0
\(289\) −1.19296 + 2.06627i −0.0701742 + 0.121545i
\(290\) 0 0
\(291\) 2.12471 + 3.68011i 0.124553 + 0.215732i
\(292\) 0 0
\(293\) −11.2015 −0.654397 −0.327199 0.944956i \(-0.606105\pi\)
−0.327199 + 0.944956i \(0.606105\pi\)
\(294\) 0 0
\(295\) −26.4103 −1.53767
\(296\) 0 0
\(297\) −2.12471 3.68011i −0.123288 0.213542i
\(298\) 0 0
\(299\) −6.94239 + 12.0246i −0.401489 + 0.695399i
\(300\) 0 0
\(301\) 0.768571 + 1.83108i 0.0442997 + 0.105541i
\(302\) 0 0
\(303\) −1.95205 + 3.38104i −0.112142 + 0.194236i
\(304\) 0 0
\(305\) −12.9594 22.4464i −0.742054 1.28527i
\(306\) 0 0
\(307\) 28.9571 1.65267 0.826335 0.563179i \(-0.190422\pi\)
0.826335 + 0.563179i \(0.190422\pi\)
\(308\) 0 0
\(309\) −9.24943 −0.526181
\(310\) 0 0
\(311\) −13.6524 23.6466i −0.774155 1.34088i −0.935268 0.353940i \(-0.884842\pi\)
0.161113 0.986936i \(-0.448492\pi\)
\(312\) 0 0
\(313\) 2.74943 4.76214i 0.155407 0.269172i −0.777800 0.628511i \(-0.783665\pi\)
0.933207 + 0.359339i \(0.116998\pi\)
\(314\) 0 0
\(315\) −5.12471 + 6.74413i −0.288745 + 0.379989i
\(316\) 0 0
\(317\) −4.80221 + 8.31767i −0.269719 + 0.467167i −0.968789 0.247886i \(-0.920264\pi\)
0.699070 + 0.715053i \(0.253597\pi\)
\(318\) 0 0
\(319\) −15.3011 26.5022i −0.856695 1.48384i
\(320\) 0 0
\(321\) 16.5565 0.924092
\(322\) 0 0
\(323\) 13.8848 0.772569
\(324\) 0 0
\(325\) −8.27708 14.3363i −0.459130 0.795236i
\(326\) 0 0
\(327\) −10.0277 + 17.3684i −0.554531 + 0.960475i
\(328\) 0 0
\(329\) −6.30704 0.800162i −0.347718 0.0441144i
\(330\) 0 0
\(331\) 7.77823 13.4723i 0.427530 0.740504i −0.569123 0.822253i \(-0.692717\pi\)
0.996653 + 0.0817484i \(0.0260504\pi\)
\(332\) 0 0
\(333\) −4.82618 8.35920i −0.264473 0.458081i
\(334\) 0 0
\(335\) −16.4989 −0.901428
\(336\) 0 0
\(337\) 17.9977 0.980397 0.490199 0.871611i \(-0.336924\pi\)
0.490199 + 0.871611i \(0.336924\pi\)
\(338\) 0 0
\(339\) 4.00000 + 6.92820i 0.217250 + 0.376288i
\(340\) 0 0
\(341\) 4.35131 7.53669i 0.235637 0.408135i
\(342\) 0 0
\(343\) 17.2088 + 6.84515i 0.929190 + 0.369603i
\(344\) 0 0
\(345\) 7.04795 12.2074i 0.379449 0.657225i
\(346\) 0 0
\(347\) 2.84648 + 4.93025i 0.152807 + 0.264670i 0.932258 0.361793i \(-0.117835\pi\)
−0.779451 + 0.626463i \(0.784502\pi\)
\(348\) 0 0
\(349\) 18.1918 0.973785 0.486893 0.873462i \(-0.338130\pi\)
0.486893 + 0.873462i \(0.338130\pi\)
\(350\) 0 0
\(351\) −3.15352 −0.168322
\(352\) 0 0
\(353\) 10.4989 + 18.1845i 0.558797 + 0.967866i 0.997597 + 0.0692807i \(0.0220704\pi\)
−0.438800 + 0.898585i \(0.644596\pi\)
\(354\) 0 0
\(355\) −10.2494 + 17.7525i −0.543983 + 0.942206i
\(356\) 0 0
\(357\) 11.5565 + 1.46615i 0.611633 + 0.0775967i
\(358\) 0 0
\(359\) 12.3453 21.3827i 0.651562 1.12854i −0.331182 0.943567i \(-0.607448\pi\)
0.982744 0.184971i \(-0.0592191\pi\)
\(360\) 0 0
\(361\) 4.52766 + 7.84213i 0.238298 + 0.412744i
\(362\) 0 0
\(363\) −7.05761 −0.370429
\(364\) 0 0
\(365\) 48.8206 2.55539
\(366\) 0 0
\(367\) 2.92807 + 5.07157i 0.152844 + 0.264734i 0.932272 0.361758i \(-0.117823\pi\)
−0.779428 + 0.626492i \(0.784490\pi\)
\(368\) 0 0
\(369\) 5.24943 9.09227i 0.273274 0.473325i
\(370\) 0 0
\(371\) −5.27823 + 6.94616i −0.274032 + 0.360627i
\(372\) 0 0
\(373\) 0.317673 0.550227i 0.0164485 0.0284897i −0.857684 0.514177i \(-0.828097\pi\)
0.874132 + 0.485688i \(0.161431\pi\)
\(374\) 0 0
\(375\) 0.399264 + 0.691545i 0.0206179 + 0.0357112i
\(376\) 0 0
\(377\) −22.7100 −1.16962
\(378\) 0 0
\(379\) −10.7506 −0.552220 −0.276110 0.961126i \(-0.589045\pi\)
−0.276110 + 0.961126i \(0.589045\pi\)
\(380\) 0 0
\(381\) 6.22545 + 10.7828i 0.318939 + 0.552419i
\(382\) 0 0
\(383\) −7.49885 + 12.9884i −0.383173 + 0.663676i −0.991514 0.130000i \(-0.958502\pi\)
0.608341 + 0.793676i \(0.291835\pi\)
\(384\) 0 0
\(385\) 13.9306 + 33.1888i 0.709969 + 1.69146i
\(386\) 0 0
\(387\) 0.375287 0.650017i 0.0190769 0.0330422i
\(388\) 0 0
\(389\) 3.10557 + 5.37900i 0.157458 + 0.272726i 0.933952 0.357400i \(-0.116337\pi\)
−0.776493 + 0.630126i \(0.783003\pi\)
\(390\) 0 0
\(391\) −19.3859 −0.980388
\(392\) 0 0
\(393\) 4.24943 0.214355
\(394\) 0 0
\(395\) 26.3335 + 45.6110i 1.32498 + 2.29494i
\(396\) 0 0
\(397\) 0.624713 1.08203i 0.0313534 0.0543057i −0.849923 0.526907i \(-0.823352\pi\)
0.881276 + 0.472601i \(0.156685\pi\)
\(398\) 0 0
\(399\) −3.22913 7.69321i −0.161659 0.385142i
\(400\) 0 0
\(401\) −1.05761 + 1.83184i −0.0528147 + 0.0914778i −0.891224 0.453563i \(-0.850153\pi\)
0.838409 + 0.545041i \(0.183486\pi\)
\(402\) 0 0
\(403\) −3.22913 5.59302i −0.160854 0.278608i
\(404\) 0 0
\(405\) 3.20147 0.159082
\(406\) 0 0
\(407\) −41.0170 −2.03314
\(408\) 0 0
\(409\) 8.05646 + 13.9542i 0.398367 + 0.689991i 0.993525 0.113618i \(-0.0362439\pi\)
−0.595158 + 0.803609i \(0.702911\pi\)
\(410\) 0 0
\(411\) −5.20147 + 9.00921i −0.256570 + 0.444392i
\(412\) 0 0
\(413\) 13.2052 17.3780i 0.649783 0.855116i
\(414\) 0 0
\(415\) 23.3011 40.3586i 1.14380 1.98113i
\(416\) 0 0
\(417\) −5.82618 10.0912i −0.285310 0.494171i
\(418\) 0 0
\(419\) 20.1106 0.982469 0.491234 0.871027i \(-0.336546\pi\)
0.491234 + 0.871027i \(0.336546\pi\)
\(420\) 0 0
\(421\) −4.96171 −0.241819 −0.120909 0.992664i \(-0.538581\pi\)
−0.120909 + 0.992664i \(0.538581\pi\)
\(422\) 0 0
\(423\) 1.20147 + 2.08101i 0.0584176 + 0.101182i
\(424\) 0 0
\(425\) 11.5565 20.0164i 0.560571 0.970937i
\(426\) 0 0
\(427\) 21.2494 + 2.69588i 1.02833 + 0.130463i
\(428\) 0 0
\(429\) −6.70032 + 11.6053i −0.323495 + 0.560309i
\(430\) 0 0
\(431\) 10.4029 + 18.0184i 0.501092 + 0.867917i 0.999999 + 0.00126164i \(0.000401592\pi\)
−0.498907 + 0.866656i \(0.666265\pi\)
\(432\) 0 0
\(433\) −8.05531 −0.387114 −0.193557 0.981089i \(-0.562002\pi\)
−0.193557 + 0.981089i \(0.562002\pi\)
\(434\) 0 0
\(435\) 23.0553 1.10542
\(436\) 0 0
\(437\) 6.94239 + 12.0246i 0.332099 + 0.575213i
\(438\) 0 0
\(439\) 8.09959 14.0289i 0.386572 0.669563i −0.605414 0.795911i \(-0.706992\pi\)
0.991986 + 0.126348i \(0.0403257\pi\)
\(440\) 0 0
\(441\) −1.87529 6.74413i −0.0892994 0.321149i
\(442\) 0 0
\(443\) 7.72177 13.3745i 0.366872 0.635441i −0.622202 0.782856i \(-0.713762\pi\)
0.989075 + 0.147415i \(0.0470953\pi\)
\(444\) 0 0
\(445\) −3.84648 6.66230i −0.182341 0.315823i
\(446\) 0 0
\(447\) 10.4029 0.492042
\(448\) 0 0
\(449\) 31.5159 1.48733 0.743663 0.668555i \(-0.233087\pi\)
0.743663 + 0.668555i \(0.233087\pi\)
\(450\) 0 0
\(451\) −22.3070 38.6369i −1.05040 1.81934i
\(452\) 0 0
\(453\) −10.0037 + 17.3269i −0.470014 + 0.814088i
\(454\) 0 0
\(455\) 26.4989 + 3.36186i 1.24229 + 0.157606i
\(456\) 0 0
\(457\) 5.55761 9.62607i 0.259974 0.450289i −0.706260 0.707952i \(-0.749619\pi\)
0.966235 + 0.257664i \(0.0829526\pi\)
\(458\) 0 0
\(459\) −2.20147 3.81306i −0.102756 0.177978i
\(460\) 0 0
\(461\) −13.5971 −0.633278 −0.316639 0.948546i \(-0.602554\pi\)
−0.316639 + 0.948546i \(0.602554\pi\)
\(462\) 0 0
\(463\) 2.55876 0.118916 0.0594579 0.998231i \(-0.481063\pi\)
0.0594579 + 0.998231i \(0.481063\pi\)
\(464\) 0 0
\(465\) 3.27823 + 5.67806i 0.152024 + 0.263314i
\(466\) 0 0
\(467\) −0.307039 + 0.531807i −0.0142081 + 0.0246091i −0.873042 0.487645i \(-0.837856\pi\)
0.858834 + 0.512254i \(0.171189\pi\)
\(468\) 0 0
\(469\) 8.24943 10.8563i 0.380923 0.501295i
\(470\) 0 0
\(471\) −7.24943 + 12.5564i −0.334036 + 0.578567i
\(472\) 0 0
\(473\) −1.59476 2.76220i −0.0733270 0.127006i
\(474\) 0 0
\(475\) −16.5542 −0.759557
\(476\) 0 0
\(477\) 3.29738 0.150977
\(478\) 0 0
\(479\) −10.0480 17.4036i −0.459103 0.795189i 0.539811 0.841786i \(-0.318496\pi\)
−0.998914 + 0.0465970i \(0.985162\pi\)
\(480\) 0 0
\(481\) −15.2195 + 26.3609i −0.693948 + 1.20195i
\(482\) 0 0
\(483\) 4.50851 + 10.7413i 0.205144 + 0.488744i
\(484\) 0 0
\(485\) −6.80221 + 11.7818i −0.308872 + 0.534983i
\(486\) 0 0
\(487\) −11.6860 20.2408i −0.529544 0.917196i −0.999406 0.0344568i \(-0.989030\pi\)
0.469863 0.882740i \(-0.344303\pi\)
\(488\) 0 0
\(489\) −10.7100 −0.484322
\(490\) 0 0
\(491\) −22.7483 −1.02662 −0.513308 0.858205i \(-0.671580\pi\)
−0.513308 + 0.858205i \(0.671580\pi\)
\(492\) 0 0
\(493\) −15.8538 27.4597i −0.714021 1.23672i
\(494\) 0 0
\(495\) 6.80221 11.7818i 0.305737 0.529551i
\(496\) 0 0
\(497\) −6.55646 15.6204i −0.294098 0.700670i
\(498\) 0 0
\(499\) −4.26972 + 7.39537i −0.191139 + 0.331062i −0.945628 0.325250i \(-0.894551\pi\)
0.754489 + 0.656313i \(0.227885\pi\)
\(500\) 0 0
\(501\) 8.65237 + 14.9863i 0.386559 + 0.669540i
\(502\) 0 0
\(503\) 7.59706 0.338736 0.169368 0.985553i \(-0.445827\pi\)
0.169368 + 0.985553i \(0.445827\pi\)
\(504\) 0 0
\(505\) −12.4989 −0.556192
\(506\) 0 0
\(507\) −1.52766 2.64598i −0.0678456 0.117512i
\(508\) 0 0
\(509\) −2.49517 + 4.32176i −0.110596 + 0.191559i −0.916011 0.401153i \(-0.868609\pi\)
0.805414 + 0.592712i \(0.201943\pi\)
\(510\) 0 0
\(511\) −24.4103 + 32.1240i −1.07985 + 1.42108i
\(512\) 0 0
\(513\) −1.57676 + 2.73103i −0.0696156 + 0.120578i
\(514\) 0 0
\(515\) −14.8059 25.6446i −0.652425 1.13003i
\(516\) 0 0
\(517\) 10.2111 0.449085
\(518\) 0 0
\(519\) −3.90409 −0.171371
\(520\) 0 0
\(521\) 6.24943 + 10.8243i 0.273792 + 0.474222i 0.969830 0.243783i \(-0.0783886\pi\)
−0.696037 + 0.718005i \(0.745055\pi\)
\(522\) 0 0
\(523\) 22.1309 38.3319i 0.967718 1.67614i 0.265589 0.964086i \(-0.414434\pi\)
0.702129 0.712050i \(-0.252233\pi\)
\(524\) 0 0
\(525\) −13.7782 1.74802i −0.601331 0.0762898i
\(526\) 0 0
\(527\) 4.50851 7.80897i 0.196394 0.340164i
\(528\) 0 0
\(529\) 1.80704 + 3.12988i 0.0785669 + 0.136082i
\(530\) 0 0
\(531\) −8.24943 −0.357995
\(532\) 0 0
\(533\) −33.1083 −1.43408
\(534\) 0 0
\(535\) 26.5025 + 45.9037i 1.14580 + 1.98459i
\(536\) 0 0
\(537\) −10.4029 + 18.0184i −0.448920 + 0.777553i
\(538\) 0 0
\(539\) −28.8036 7.42807i −1.24066 0.319950i
\(540\) 0 0
\(541\) 12.9797 22.4815i 0.558041 0.966556i −0.439619 0.898184i \(-0.644886\pi\)
0.997660 0.0683711i \(-0.0217802\pi\)
\(542\) 0 0
\(543\) 6.62471 + 11.4743i 0.284294 + 0.492411i
\(544\) 0 0
\(545\) −64.2065 −2.75031
\(546\) 0 0
\(547\) −22.9018 −0.979210 −0.489605 0.871944i \(-0.662859\pi\)
−0.489605 + 0.871944i \(0.662859\pi\)
\(548\) 0 0
\(549\) −4.04795 7.01126i −0.172762 0.299233i
\(550\) 0 0
\(551\) −11.3550 + 19.6674i −0.483739 + 0.837860i
\(552\) 0 0
\(553\) −43.1789 5.47802i −1.83615 0.232949i
\(554\) 0 0
\(555\) 15.4509 26.7617i 0.655854 1.13597i
\(556\) 0 0
\(557\) −3.25311 5.63454i −0.137839 0.238743i 0.788840 0.614599i \(-0.210682\pi\)
−0.926678 + 0.375856i \(0.877349\pi\)
\(558\) 0 0
\(559\) −2.36695 −0.100111
\(560\) 0 0
\(561\) −18.7100 −0.789936
\(562\) 0 0
\(563\) −22.1224 38.3171i −0.932349 1.61488i −0.779295 0.626657i \(-0.784423\pi\)
−0.153053 0.988218i \(-0.548911\pi\)
\(564\) 0 0
\(565\) −12.8059 + 22.1805i −0.538748 + 0.933139i
\(566\) 0 0
\(567\) −1.60074 + 2.10657i −0.0672246 + 0.0884677i
\(568\) 0 0
\(569\) 6.50851 11.2731i 0.272851 0.472592i −0.696740 0.717324i \(-0.745367\pi\)
0.969591 + 0.244732i \(0.0787001\pi\)
\(570\) 0 0
\(571\) 15.0853 + 26.1285i 0.631299 + 1.09344i 0.987286 + 0.158951i \(0.0508112\pi\)
−0.355987 + 0.934491i \(0.615855\pi\)
\(572\) 0 0
\(573\) −4.19181 −0.175115
\(574\) 0 0
\(575\) 23.1129 0.963876
\(576\) 0 0
\(577\) 14.9029 + 25.8127i 0.620418 + 1.07459i 0.989408 + 0.145162i \(0.0463702\pi\)
−0.368990 + 0.929433i \(0.620296\pi\)
\(578\) 0 0
\(579\) −9.15237 + 15.8524i −0.380360 + 0.658802i
\(580\) 0 0
\(581\) 14.9055 + 35.5114i 0.618383 + 1.47326i
\(582\) 0 0
\(583\) 7.00598 12.1347i 0.290158 0.502568i
\(584\) 0 0
\(585\) −5.04795 8.74331i −0.208707 0.361491i
\(586\) 0 0
\(587\) −18.2494 −0.753234 −0.376617 0.926369i \(-0.622913\pi\)
−0.376617 + 0.926369i \(0.622913\pi\)
\(588\) 0 0
\(589\) −6.45826 −0.266108
\(590\) 0 0
\(591\) −5.95205 10.3092i −0.244835 0.424066i
\(592\) 0 0
\(593\) 11.8944 20.6018i 0.488446 0.846013i −0.511466 0.859304i \(-0.670897\pi\)
0.999912 + 0.0132906i \(0.00423066\pi\)
\(594\) 0 0
\(595\) 14.4339 + 34.3879i 0.591731 + 1.40976i
\(596\) 0 0
\(597\) 0.402945 0.697921i 0.0164914 0.0285640i
\(598\) 0 0
\(599\) 7.75057 + 13.4244i 0.316680 + 0.548506i 0.979793 0.200013i \(-0.0640986\pi\)
−0.663113 + 0.748519i \(0.730765\pi\)
\(600\) 0 0
\(601\) 15.8059 0.644736 0.322368 0.946614i \(-0.395521\pi\)
0.322368 + 0.946614i \(0.395521\pi\)
\(602\) 0 0
\(603\) −5.15352 −0.209868
\(604\) 0 0
\(605\) −11.2974 19.5676i −0.459304 0.795537i
\(606\) 0 0
\(607\) −2.97602 + 5.15462i −0.120793 + 0.209220i −0.920081 0.391729i \(-0.871877\pi\)
0.799288 + 0.600949i \(0.205210\pi\)
\(608\) 0 0
\(609\) −11.5277 + 15.1704i −0.467124 + 0.614736i
\(610\) 0 0
\(611\) 3.78887 6.56251i 0.153281 0.265491i
\(612\) 0 0
\(613\) −14.2015 24.5977i −0.573592 0.993491i −0.996193 0.0871747i \(-0.972216\pi\)
0.422601 0.906316i \(-0.361117\pi\)
\(614\) 0 0
\(615\) 33.6118 1.35536
\(616\) 0 0
\(617\) −10.1918 −0.410307 −0.205153 0.978730i \(-0.565769\pi\)
−0.205153 + 0.978730i \(0.565769\pi\)
\(618\) 0 0
\(619\) 10.4306 + 18.0663i 0.419241 + 0.726147i 0.995863 0.0908638i \(-0.0289628\pi\)
−0.576622 + 0.817011i \(0.695629\pi\)
\(620\) 0 0
\(621\) 2.20147 3.81306i 0.0883420 0.153013i
\(622\) 0 0
\(623\) 6.30704 + 0.800162i 0.252686 + 0.0320578i
\(624\) 0 0
\(625\) 11.8453 20.5167i 0.473813 0.820669i
\(626\) 0 0
\(627\) 6.70032 + 11.6053i 0.267585 + 0.463471i
\(628\) 0 0
\(629\) −42.4989 −1.69454
\(630\) 0 0
\(631\) 41.6191 1.65683 0.828416 0.560113i \(-0.189242\pi\)
0.828416 + 0.560113i \(0.189242\pi\)
\(632\) 0 0
\(633\) −4.24943 7.36022i −0.168899 0.292542i
\(634\) 0 0
\(635\) −19.9306 + 34.5208i −0.790922 + 1.36992i
\(636\) 0 0
\(637\) −15.4615 + 15.7553i −0.612608 + 0.624249i
\(638\) 0 0
\(639\) −3.20147 + 5.54511i −0.126648 + 0.219361i
\(640\) 0 0
\(641\) 24.4006 + 42.2632i 0.963768 + 1.66929i 0.712890 + 0.701275i \(0.247386\pi\)
0.250877 + 0.968019i \(0.419281\pi\)
\(642\) 0 0
\(643\) −11.8442 −0.467089 −0.233544 0.972346i \(-0.575032\pi\)
−0.233544 + 0.972346i \(0.575032\pi\)
\(644\) 0 0
\(645\) 2.40294 0.0946159
\(646\) 0 0
\(647\) −16.7579 29.0256i −0.658822 1.14111i −0.980921 0.194408i \(-0.937722\pi\)
0.322098 0.946706i \(-0.395612\pi\)
\(648\) 0 0
\(649\) −17.5277 + 30.3588i −0.688021 + 1.19169i
\(650\) 0 0
\(651\) −5.37529 0.681953i −0.210674 0.0267278i
\(652\) 0 0
\(653\) −23.2531 + 40.2756i −0.909964 + 1.57610i −0.0958532 + 0.995395i \(0.530558\pi\)
−0.814111 + 0.580709i \(0.802775\pi\)
\(654\) 0 0
\(655\) 6.80221 + 11.7818i 0.265784 + 0.460352i
\(656\) 0 0
\(657\) 15.2494 0.594937
\(658\) 0 0
\(659\) 10.1152 0.394033 0.197017 0.980400i \(-0.436875\pi\)
0.197017 + 0.980400i \(0.436875\pi\)
\(660\) 0 0
\(661\) 16.6321 + 28.8076i 0.646913 + 1.12049i 0.983856 + 0.178961i \(0.0572735\pi\)
−0.336943 + 0.941525i \(0.609393\pi\)
\(662\) 0 0
\(663\) −6.94239 + 12.0246i −0.269620 + 0.466995i
\(664\) 0 0
\(665\) 16.1609 21.2677i 0.626692 0.824728i
\(666\) 0 0
\(667\) 15.8538 27.4597i 0.613863 1.06324i
\(668\) 0 0
\(669\) −8.39926 14.5480i −0.324734 0.562456i
\(670\) 0 0
\(671\) −34.4029 −1.32811
\(672\) 0 0
\(673\) −50.4966 −1.94650 −0.973249 0.229751i \(-0.926209\pi\)
−0.973249 + 0.229751i \(0.926209\pi\)
\(674\) 0 0
\(675\) 2.62471 + 4.54614i 0.101025 + 0.174981i
\(676\) 0 0
\(677\) 14.3993 24.9403i 0.553409 0.958532i −0.444617 0.895721i \(-0.646660\pi\)
0.998025 0.0628110i \(-0.0200065\pi\)
\(678\) 0 0
\(679\) −4.35131 10.3667i −0.166988 0.397839i
\(680\) 0 0
\(681\) 8.43175 14.6042i 0.323105 0.559635i
\(682\) 0 0
\(683\) −6.62356 11.4723i −0.253444 0.438977i 0.711028 0.703164i \(-0.248230\pi\)
−0.964472 + 0.264186i \(0.914897\pi\)
\(684\) 0 0
\(685\) −33.3047 −1.27251
\(686\) 0 0
\(687\) 20.5542 0.784190
\(688\) 0 0
\(689\) −5.19917 9.00523i −0.198073 0.343072i
\(690\) 0 0
\(691\) −19.8335 + 34.3527i −0.754504 + 1.30684i 0.191117 + 0.981567i \(0.438789\pi\)
−0.945621 + 0.325271i \(0.894544\pi\)
\(692\) 0 0
\(693\) 4.35131 + 10.3667i 0.165293 + 0.393800i
\(694\) 0 0
\(695\) 18.6524 32.3069i 0.707525 1.22547i
\(696\) 0 0
\(697\) −23.1129 40.0328i −0.875465 1.51635i
\(698\) 0 0
\(699\) −9.90409 −0.374607
\(700\) 0 0
\(701\) 2.10787 0.0796130 0.0398065 0.999207i \(-0.487326\pi\)
0.0398065 + 0.999207i \(0.487326\pi\)
\(702\) 0 0
\(703\) 15.2195 + 26.3609i 0.574013 + 0.994220i
\(704\) 0 0
\(705\) −3.84648 + 6.66230i −0.144867 + 0.250917i
\(706\) 0 0
\(707\) 6.24943 8.22425i 0.235034 0.309305i
\(708\) 0 0
\(709\) −7.49885 + 12.9884i −0.281625 + 0.487789i −0.971785 0.235868i \(-0.924207\pi\)
0.690160 + 0.723657i \(0.257540\pi\)
\(710\) 0 0
\(711\) 8.22545 + 14.2469i 0.308478 + 0.534300i
\(712\) 0 0
\(713\) 9.01702 0.337690
\(714\) 0 0
\(715\) −42.9018 −1.60444
\(716\) 0 0
\(717\) 2.20147 + 3.81306i 0.0822155 + 0.142401i
\(718\) 0 0
\(719\) −11.4029 + 19.7505i −0.425258 + 0.736569i −0.996444 0.0842518i \(-0.973150\pi\)
0.571186 + 0.820820i \(0.306483\pi\)
\(720\) 0 0
\(721\) 24.2771 + 3.07999i 0.904126 + 0.114705i
\(722\) 0 0
\(723\) 10.4318 18.0683i 0.387961 0.671968i
\(724\) 0 0
\(725\) 18.9018 + 32.7389i 0.701995 + 1.21589i
\(726\) 0 0
\(727\) 16.9691 0.629348 0.314674 0.949200i \(-0.398105\pi\)
0.314674 + 0.949200i \(0.398105\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −1.65237 2.86199i −0.0611151 0.105854i
\(732\) 0 0
\(733\) 0.672665 1.16509i 0.0248455 0.0430336i −0.853335 0.521362i \(-0.825424\pi\)
0.878181 + 0.478329i \(0.158757\pi\)
\(734\) 0 0
\(735\) 15.6966 15.9949i 0.578979 0.589981i
\(736\) 0 0
\(737\) −10.9497 + 18.9655i −0.403339 + 0.698604i
\(738\) 0 0
\(739\) 22.6321 + 39.1999i 0.832534 + 1.44199i 0.896022 + 0.444009i \(0.146444\pi\)
−0.0634880 + 0.997983i \(0.520222\pi\)
\(740\) 0 0
\(741\) 9.94469 0.365327
\(742\) 0 0
\(743\) −27.8036 −1.02001 −0.510007 0.860170i \(-0.670357\pi\)
−0.510007 + 0.860170i \(0.670357\pi\)
\(744\) 0 0
\(745\) 16.6524 + 28.8428i 0.610096 + 1.05672i
\(746\) 0 0
\(747\) 7.27823 12.6063i 0.266297 0.461239i
\(748\) 0 0
\(749\) −43.4560 5.51318i −1.58785 0.201447i
\(750\) 0 0
\(751\) −15.0313 + 26.0350i −0.548501 + 0.950032i 0.449876 + 0.893091i \(0.351468\pi\)
−0.998378 + 0.0569412i \(0.981865\pi\)
\(752\) 0 0
\(753\) −1.72177 2.98219i −0.0627447 0.108677i
\(754\) 0 0
\(755\) −64.0530 −2.33113
\(756\) 0 0
\(757\) 17.3241 0.629654 0.314827 0.949149i \(-0.398054\pi\)
0.314827 + 0.949149i \(0.398054\pi\)
\(758\) 0 0
\(759\) −9.35499 16.2033i −0.339565 0.588143i
\(760\) 0 0
\(761\) −6.10557 + 10.5752i −0.221327 + 0.383349i −0.955211 0.295925i \(-0.904372\pi\)
0.733884 + 0.679274i \(0.237705\pi\)
\(762\) 0 0
\(763\) 32.1033 42.2480i 1.16222 1.52948i
\(764\) 0 0
\(765\) 7.04795 12.2074i 0.254819 0.441360i
\(766\) 0 0
\(767\) 13.0074 + 22.5294i 0.469669 + 0.813490i
\(768\) 0 0
\(769\) 11.1152 0.400825 0.200413 0.979712i \(-0.435772\pi\)
0.200413 + 0.979712i \(0.435772\pi\)
\(770\) 0 0
\(771\) 5.59706 0.201573
\(772\) 0 0
\(773\) −0.143858 0.249170i −0.00517423 0.00896202i 0.863427 0.504474i \(-0.168314\pi\)
−0.868601 + 0.495512i \(0.834980\pi\)
\(774\) 0 0
\(775\) −5.37529 + 9.31027i −0.193086 + 0.334435i
\(776\) 0 0
\(777\) 9.88380 + 23.5476i 0.354579 + 0.844764i
\(778\) 0 0
\(779\) −16.5542 + 28.6727i −0.593115 + 1.02730i
\(780\) 0 0
\(781\) 13.6044 + 23.5635i 0.486804 + 0.843170i
\(782\) 0 0
\(783\) 7.20147 0.257360
\(784\) 0 0
\(785\) −46.4177 −1.65672
\(786\) 0 0
\(787\) −5.75057 9.96029i −0.204986 0.355046i 0.745142 0.666905i \(-0.232382\pi\)
−0.950128 + 0.311860i \(0.899048\pi\)
\(788\) 0 0
\(789\) −0.798528 + 1.38309i −0.0284283 + 0.0492393i
\(790\) 0 0
\(791\) −8.19181 19.5165i −0.291267 0.693927i
\(792\) 0 0
\(793\) −12.7653 + 22.1101i −0.453309 + 0.785154i
\(794\) 0 0
\(795\) 5.27823 + 9.14217i 0.187200 + 0.324239i
\(796\) 0 0
\(797\) 18.6980 0.662318 0.331159 0.943575i \(-0.392560\pi\)
0.331159 + 0.943575i \(0.392560\pi\)