Properties

Label 672.2.q.l.289.3
Level $672$
Weight $2$
Character 672.289
Analytic conductor $5.366$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.36594701583\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.3
Root \(0.500000 + 2.43956i\) of defining polynomial
Character \(\chi\) \(=\) 672.289
Dual form 672.2.q.l.193.3

$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 1.60074 2.77256i 0.715871 1.23992i −0.246752 0.969079i \(-0.579363\pi\)
0.962623 0.270846i \(-0.0873035\pi\)
\(6\) 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 \(-0.644070\pi\)
−0.437314 + 0.899309i \(0.644070\pi\)
\(14\) 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 −0.539872 0.841747i \(-0.681527\pi\)
0.998910 + 0.0466689i \(0.0148606\pi\)
\(24\) 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 \(-0.266877\pi\)
0.668640 + 0.743586i \(0.266877\pi\)
\(30\) 0 0
\(31\) 1.02398 + 1.77358i 0.183912 + 0.318544i 0.943209 0.332199i \(-0.107791\pi\)
−0.759298 + 0.650744i \(0.774457\pi\)
\(32\) 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 \(-0.541632\pi\)
0.923838 0.382784i \(-0.125035\pi\)
\(38\) 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 −0.940249 0.340488i \(-0.889408\pi\)
0.764996 + 0.644035i \(0.222741\pi\)
\(48\) 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 0.956758 0.290885i \(-0.0939498\pi\)
−0.730293 + 0.683134i \(0.760616\pi\)
\(54\) 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 \(-0.659903\pi\)
0.999774 0.0212466i \(-0.00676352\pi\)
\(62\) 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 \(-0.624057\pi\)
−0.379945 + 0.925009i \(0.624057\pi\)
\(72\) 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 \(0.542967\pi\)
−0.790860 + 0.611998i \(0.790366\pi\)
\(80\) 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 0.752414 0.658691i \(-0.228889\pi\)
−0.946650 + 0.322264i \(0.895556\pi\)
\(102\) 0 0
\(103\) 4.62471 8.01024i 0.455686 0.789272i −0.543041 0.839706i \(-0.682727\pi\)
0.998727 + 0.0504341i \(0.0160605\pi\)
\(104\) 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 \(-0.756459\pi\)
−0.239167 0.970979i \(-0.576874\pi\)
\(110\) 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 \(-0.686295\pi\)
−0.552419 + 0.833566i \(0.686295\pi\)
\(128\) 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 −0.996524 0.0833012i \(-0.973454\pi\)
0.570403 + 0.821365i \(0.306787\pi\)
\(150\) 0 0
\(151\) −10.0037 17.3269i −0.814088 1.41004i −0.909981 0.414650i \(-0.863904\pi\)
0.0958929 0.995392i \(-0.469429\pi\)
\(152\) 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 \(-0.970279\pi\)
0.417077 0.908871i \(-0.363055\pi\)
\(158\) 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 \(-0.733509\pi\)
−0.669540 + 0.742776i \(0.733509\pi\)
\(168\) 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 −0.782229 0.622991i \(-0.785917\pi\)
0.930640 + 0.365935i \(0.119251\pi\)
\(174\) 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 \(-0.663884\pi\)
−0.492411 + 0.870363i \(0.663884\pi\)
\(182\) 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 −0.780181 0.625553i \(-0.784873\pi\)
0.931836 + 0.362880i \(0.118207\pi\)
\(192\) 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 \(-0.360603\pi\)
0.424066 + 0.905631i \(0.360603\pi\)
\(198\) 0 0
\(199\) 0.402945 + 0.697921i 0.0285640 + 0.0494743i 0.879954 0.475059i \(-0.157573\pi\)
−0.851390 + 0.524533i \(0.824240\pi\)
\(200\) 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 \(-0.309856\pi\)
0.562456 + 0.826827i \(0.309856\pi\)
\(224\) 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 \(0.404309\pi\)
−0.975244 + 0.221133i \(0.929024\pi\)
\(230\) 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 \(-0.545482\pi\)
−0.142401 + 0.989809i \(0.545482\pi\)
\(240\) 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 0.840355 0.542036i \(-0.182346\pi\)
−0.889595 + 0.456751i \(0.849013\pi\)
\(264\) 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 \(-0.985241\pi\)
0.459321 0.888270i \(-0.348093\pi\)
\(270\) 0 0
\(271\) −1.19779 + 2.07464i −0.0727607 + 0.126025i −0.900110 0.435662i \(-0.856514\pi\)
0.827350 + 0.561687i \(0.189848\pi\)
\(272\) 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 0.934040 0.357168i \(-0.116258\pi\)
−0.776337 + 0.630319i \(0.782924\pi\)
\(278\) 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 \(-0.393895\pi\)
0.327199 + 0.944956i \(0.393895\pi\)
\(294\) 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 \(0.115158\pi\)
−0.161113 + 0.986936i \(0.551508\pi\)
\(312\) 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 −0.699070 0.715053i \(-0.746403\pi\)
0.968789 + 0.247886i \(0.0797359\pi\)
\(318\) 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 \(-0.661870\pi\)
−0.486893 + 0.873462i \(0.661870\pi\)
\(350\) 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 \(0.392552\pi\)
−0.982744 + 0.184971i \(0.940781\pi\)
\(360\) 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 0.779428 0.626492i \(-0.215510\pi\)
−0.932272 + 0.361758i \(0.882177\pi\)
\(368\) 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 −0.874132 0.485688i \(-0.838569\pi\)
0.857684 + 0.514177i \(0.171903\pi\)
\(374\) 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 −0.608341 0.793676i \(-0.708165\pi\)
0.991514 + 0.130000i \(0.0414979\pi\)
\(384\) 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 0.776493 0.630126i \(-0.216997\pi\)
−0.933952 + 0.357400i \(0.883663\pi\)
\(390\) 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 −0.881276 0.472601i \(-0.843315\pi\)
0.849923 + 0.526907i \(0.176648\pi\)
\(398\) 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 \(-0.461419\pi\)
0.120909 + 0.992664i \(0.461419\pi\)
\(422\) 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 \(-0.999598\pi\)
0.498907 0.866656i \(-0.333735\pi\)
\(432\) 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 −0.991986 0.126348i \(-0.959674\pi\)
0.605414 + 0.795911i \(0.293008\pi\)
\(440\) 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 \(-0.397446\pi\)
0.316639 + 0.948546i \(0.397446\pi\)
\(462\) 0 0
\(463\) −2.55876 −0.118916 −0.0594579 0.998231i \(-0.518937\pi\)
−0.0594579 + 0.998231i \(0.518937\pi\)
\(464\) 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 0.998914 0.0465970i \(-0.0148377\pi\)
−0.539811 + 0.841786i \(0.681504\pi\)
\(480\) 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 \(0.0109701\pi\)
−0.469863 + 0.882740i \(0.655697\pi\)
\(488\) 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 \(-0.554173\pi\)
−0.169368 + 0.985553i \(0.554173\pi\)
\(504\) 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 −0.805414 0.592712i \(-0.798057\pi\)
0.916011 + 0.401153i \(0.131391\pi\)
\(510\) 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 \(0.355114\pi\)
−0.997660 + 0.0683711i \(0.978220\pi\)
\(542\) 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 0.926678 0.375856i \(-0.122651\pi\)
−0.788840 + 0.614599i \(0.789318\pi\)
\(558\) 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 0.663113 0.748519i \(-0.269235\pi\)
−0.979793 + 0.200013i \(0.935901\pi\)
\(600\) 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 −0.799288 0.600949i \(-0.794790\pi\)
0.920081 + 0.391729i \(0.128123\pi\)
\(608\) 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 \(0.0277839\pi\)
−0.422601 + 0.906316i \(0.638883\pi\)
\(614\) 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 \(-0.810758\pi\)
−0.828416 + 0.560113i \(0.810758\pi\)
\(632\) 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 \(0.0622785\pi\)
−0.322098 + 0.946706i \(0.604388\pi\)
\(648\) 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 \(-0.469442\pi\)
0.814111 0.580709i \(-0.197225\pi\)
\(654\) 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 \(-0.942726\pi\)
0.336943 0.941525i \(-0.390607\pi\)
\(662\) 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 \(0.353340\pi\)
−0.998025 + 0.0628110i \(0.979993\pi\)
\(678\) 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 \(-0.512674\pi\)
−0.0398065 + 0.999207i \(0.512674\pi\)
\(702\) 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 −0.690160 0.723657i \(-0.742460\pi\)
0.971785 + 0.235868i \(0.0757932\pi\)
\(710\) 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 −0.571186 0.820820i \(-0.693517\pi\)
0.996444 + 0.0842518i \(0.0268500\pi\)
\(720\) 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 \(-0.601895\pi\)
−0.314674 + 0.949200i \(0.601895\pi\)
\(728\) 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 −0.878181 0.478329i \(-0.841243\pi\)
0.853335 + 0.521362i \(0.174576\pi\)
\(734\) 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 \(-0.329643\pi\)
0.510007 + 0.860170i \(0.329643\pi\)
\(744\) 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 \(-0.648532\pi\)
0.998378 0.0569412i \(-0.0181348\pi\)
\(752\) 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 \(-0.601946\pi\)
−0.314827 + 0.949149i \(0.601946\pi\)
\(758\) 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 0.868601 0.495512i \(-0.165020\pi\)
−0.863427 + 0.504474i \(0.831686\pi\)
\(774\) 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 \(-0.607440\pi\)
−0.331159 + 0.943575i \(0.607440\pi\)