Properties

Label 512.2.g.d.449.1
Level $512$
Weight $2$
Character 512.449
Analytic conductor $4.088$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 512 = 2^{9} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 512.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.08834058349\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 449.1
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 512.449
Dual form 512.2.g.d.65.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.292893 + 0.707107i) q^{3} +(2.70711 + 1.12132i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(1.70711 - 1.70711i) q^{9} +O(q^{10})\) \(q+(0.292893 + 0.707107i) q^{3} +(2.70711 + 1.12132i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(1.70711 - 1.70711i) q^{9} +(1.70711 - 4.12132i) q^{11} +(0.707107 - 0.292893i) q^{13} +2.24264i q^{15} +2.82843i q^{17} +(3.70711 - 1.53553i) q^{19} +(0.414214 - 1.00000i) q^{21} +(-5.82843 + 5.82843i) q^{23} +(2.53553 + 2.53553i) q^{25} +(3.82843 + 1.58579i) q^{27} +(1.29289 + 3.12132i) q^{29} -4.00000 q^{31} +3.41421 q^{33} +(-1.58579 - 3.82843i) q^{35} +(0.707107 + 0.292893i) q^{37} +(0.414214 + 0.414214i) q^{39} +(0.171573 - 0.171573i) q^{41} +(-1.94975 + 4.70711i) q^{43} +(6.53553 - 2.70711i) q^{45} +0.343146i q^{47} -5.00000i q^{49} +(-2.00000 + 0.828427i) q^{51} +(0.464466 - 1.12132i) q^{53} +(9.24264 - 9.24264i) q^{55} +(2.17157 + 2.17157i) q^{57} +(-4.53553 - 1.87868i) q^{59} +(-0.707107 - 1.70711i) q^{61} -3.41421 q^{63} +2.24264 q^{65} +(2.29289 + 5.53553i) q^{67} +(-5.82843 - 2.41421i) q^{69} +(5.82843 + 5.82843i) q^{71} +(-7.00000 + 7.00000i) q^{73} +(-1.05025 + 2.53553i) q^{75} +(-5.82843 + 2.41421i) q^{77} -6.00000i q^{79} -4.07107i q^{81} +(4.53553 - 1.87868i) q^{83} +(-3.17157 + 7.65685i) q^{85} +(-1.82843 + 1.82843i) q^{87} +(-8.65685 - 8.65685i) q^{89} +(-1.00000 - 0.414214i) q^{91} +(-1.17157 - 2.82843i) q^{93} +11.7574 q^{95} -18.4853 q^{97} +(-4.12132 - 9.94975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} + 8q^{5} - 4q^{7} + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} + 8q^{5} - 4q^{7} + 4q^{9} + 4q^{11} + 12q^{19} - 4q^{21} - 12q^{23} - 4q^{25} + 4q^{27} + 8q^{29} - 16q^{31} + 8q^{33} - 12q^{35} - 4q^{39} + 12q^{41} + 12q^{43} + 12q^{45} - 8q^{51} + 16q^{53} + 20q^{55} + 20q^{57} - 4q^{59} - 8q^{63} - 8q^{65} + 12q^{67} - 12q^{69} + 12q^{71} - 28q^{73} - 24q^{75} - 12q^{77} + 4q^{83} - 24q^{85} + 4q^{87} - 12q^{89} - 4q^{91} - 16q^{93} + 64q^{95} - 40q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(1\)

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
\(3\) 0.292893 + 0.707107i 0.169102 + 0.408248i 0.985599 0.169102i \(-0.0540867\pi\)
−0.816497 + 0.577350i \(0.804087\pi\)
\(4\) 0 0
\(5\) 2.70711 + 1.12132i 1.21065 + 0.501470i 0.894427 0.447214i \(-0.147584\pi\)
0.316228 + 0.948683i \(0.397584\pi\)
\(6\) 0 0
\(7\) −1.00000 1.00000i −0.377964 0.377964i 0.492403 0.870367i \(-0.336119\pi\)
−0.870367 + 0.492403i \(0.836119\pi\)
\(8\) 0 0
\(9\) 1.70711 1.70711i 0.569036 0.569036i
\(10\) 0 0
\(11\) 1.70711 4.12132i 0.514712 1.24262i −0.426401 0.904534i \(-0.640219\pi\)
0.941113 0.338091i \(-0.109781\pi\)
\(12\) 0 0
\(13\) 0.707107 0.292893i 0.196116 0.0812340i −0.282464 0.959278i \(-0.591152\pi\)
0.478580 + 0.878044i \(0.341152\pi\)
\(14\) 0 0
\(15\) 2.24264i 0.579047i
\(16\) 0 0
\(17\) 2.82843i 0.685994i 0.939336 + 0.342997i \(0.111442\pi\)
−0.939336 + 0.342997i \(0.888558\pi\)
\(18\) 0 0
\(19\) 3.70711 1.53553i 0.850469 0.352276i 0.0854961 0.996339i \(-0.472752\pi\)
0.764973 + 0.644063i \(0.222752\pi\)
\(20\) 0 0
\(21\) 0.414214 1.00000i 0.0903888 0.218218i
\(22\) 0 0
\(23\) −5.82843 + 5.82843i −1.21531 + 1.21531i −0.246055 + 0.969256i \(0.579134\pi\)
−0.969256 + 0.246055i \(0.920866\pi\)
\(24\) 0 0
\(25\) 2.53553 + 2.53553i 0.507107 + 0.507107i
\(26\) 0 0
\(27\) 3.82843 + 1.58579i 0.736781 + 0.305185i
\(28\) 0 0
\(29\) 1.29289 + 3.12132i 0.240084 + 0.579615i 0.997291 0.0735609i \(-0.0234363\pi\)
−0.757206 + 0.653176i \(0.773436\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 3.41421 0.594338
\(34\) 0 0
\(35\) −1.58579 3.82843i −0.268047 0.647122i
\(36\) 0 0
\(37\) 0.707107 + 0.292893i 0.116248 + 0.0481513i 0.440049 0.897974i \(-0.354961\pi\)
−0.323802 + 0.946125i \(0.604961\pi\)
\(38\) 0 0
\(39\) 0.414214 + 0.414214i 0.0663273 + 0.0663273i
\(40\) 0 0
\(41\) 0.171573 0.171573i 0.0267952 0.0267952i −0.693582 0.720377i \(-0.743969\pi\)
0.720377 + 0.693582i \(0.243969\pi\)
\(42\) 0 0
\(43\) −1.94975 + 4.70711i −0.297334 + 0.717827i 0.702647 + 0.711539i \(0.252002\pi\)
−0.999980 + 0.00628798i \(0.997998\pi\)
\(44\) 0 0
\(45\) 6.53553 2.70711i 0.974260 0.403552i
\(46\) 0 0
\(47\) 0.343146i 0.0500530i 0.999687 + 0.0250265i \(0.00796701\pi\)
−0.999687 + 0.0250265i \(0.992033\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) −2.00000 + 0.828427i −0.280056 + 0.116003i
\(52\) 0 0
\(53\) 0.464466 1.12132i 0.0637993 0.154025i −0.888764 0.458364i \(-0.848436\pi\)
0.952564 + 0.304339i \(0.0984356\pi\)
\(54\) 0 0
\(55\) 9.24264 9.24264i 1.24628 1.24628i
\(56\) 0 0
\(57\) 2.17157 + 2.17157i 0.287632 + 0.287632i
\(58\) 0 0
\(59\) −4.53553 1.87868i −0.590476 0.244583i 0.0673793 0.997727i \(-0.478536\pi\)
−0.657855 + 0.753144i \(0.728536\pi\)
\(60\) 0 0
\(61\) −0.707107 1.70711i −0.0905357 0.218573i 0.872125 0.489283i \(-0.162741\pi\)
−0.962661 + 0.270710i \(0.912741\pi\)
\(62\) 0 0
\(63\) −3.41421 −0.430150
\(64\) 0 0
\(65\) 2.24264 0.278165
\(66\) 0 0
\(67\) 2.29289 + 5.53553i 0.280121 + 0.676273i 0.999838 0.0179949i \(-0.00572826\pi\)
−0.719717 + 0.694268i \(0.755728\pi\)
\(68\) 0 0
\(69\) −5.82843 2.41421i −0.701660 0.290637i
\(70\) 0 0
\(71\) 5.82843 + 5.82843i 0.691707 + 0.691707i 0.962607 0.270900i \(-0.0873214\pi\)
−0.270900 + 0.962607i \(0.587321\pi\)
\(72\) 0 0
\(73\) −7.00000 + 7.00000i −0.819288 + 0.819288i −0.986005 0.166717i \(-0.946683\pi\)
0.166717 + 0.986005i \(0.446683\pi\)
\(74\) 0 0
\(75\) −1.05025 + 2.53553i −0.121273 + 0.292778i
\(76\) 0 0
\(77\) −5.82843 + 2.41421i −0.664211 + 0.275125i
\(78\) 0 0
\(79\) 6.00000i 0.675053i −0.941316 0.337526i \(-0.890410\pi\)
0.941316 0.337526i \(-0.109590\pi\)
\(80\) 0 0
\(81\) 4.07107i 0.452341i
\(82\) 0 0
\(83\) 4.53553 1.87868i 0.497840 0.206212i −0.119612 0.992821i \(-0.538165\pi\)
0.617452 + 0.786609i \(0.288165\pi\)
\(84\) 0 0
\(85\) −3.17157 + 7.65685i −0.344005 + 0.830502i
\(86\) 0 0
\(87\) −1.82843 + 1.82843i −0.196028 + 0.196028i
\(88\) 0 0
\(89\) −8.65685 8.65685i −0.917625 0.917625i 0.0792315 0.996856i \(-0.474753\pi\)
−0.996856 + 0.0792315i \(0.974753\pi\)
\(90\) 0 0
\(91\) −1.00000 0.414214i −0.104828 0.0434214i
\(92\) 0 0
\(93\) −1.17157 2.82843i −0.121486 0.293294i
\(94\) 0 0
\(95\) 11.7574 1.20628
\(96\) 0 0
\(97\) −18.4853 −1.87690 −0.938448 0.345421i \(-0.887736\pi\)
−0.938448 + 0.345421i \(0.887736\pi\)
\(98\) 0 0
\(99\) −4.12132 9.94975i −0.414208 0.999987i
\(100\) 0 0
\(101\) −3.29289 1.36396i −0.327655 0.135719i 0.212791 0.977098i \(-0.431745\pi\)
−0.540446 + 0.841379i \(0.681745\pi\)
\(102\) 0 0
\(103\) −9.48528 9.48528i −0.934613 0.934613i 0.0633771 0.997990i \(-0.479813\pi\)
−0.997990 + 0.0633771i \(0.979813\pi\)
\(104\) 0 0
\(105\) 2.24264 2.24264i 0.218859 0.218859i
\(106\) 0 0
\(107\) 1.70711 4.12132i 0.165032 0.398423i −0.819630 0.572893i \(-0.805821\pi\)
0.984663 + 0.174470i \(0.0558211\pi\)
\(108\) 0 0
\(109\) −13.7782 + 5.70711i −1.31971 + 0.546642i −0.927702 0.373320i \(-0.878219\pi\)
−0.392007 + 0.919962i \(0.628219\pi\)
\(110\) 0 0
\(111\) 0.585786i 0.0556004i
\(112\) 0 0
\(113\) 6.34315i 0.596713i 0.954455 + 0.298356i \(0.0964384\pi\)
−0.954455 + 0.298356i \(0.903562\pi\)
\(114\) 0 0
\(115\) −22.3137 + 9.24264i −2.08076 + 0.861881i
\(116\) 0 0
\(117\) 0.707107 1.70711i 0.0653720 0.157822i
\(118\) 0 0
\(119\) 2.82843 2.82843i 0.259281 0.259281i
\(120\) 0 0
\(121\) −6.29289 6.29289i −0.572081 0.572081i
\(122\) 0 0
\(123\) 0.171573 + 0.0710678i 0.0154702 + 0.00640797i
\(124\) 0 0
\(125\) −1.58579 3.82843i −0.141837 0.342425i
\(126\) 0 0
\(127\) 12.9706 1.15095 0.575476 0.817819i \(-0.304817\pi\)
0.575476 + 0.817819i \(0.304817\pi\)
\(128\) 0 0
\(129\) −3.89949 −0.343331
\(130\) 0 0
\(131\) 6.77817 + 16.3640i 0.592212 + 1.42973i 0.881362 + 0.472442i \(0.156627\pi\)
−0.289150 + 0.957284i \(0.593373\pi\)
\(132\) 0 0
\(133\) −5.24264 2.17157i −0.454595 0.188299i
\(134\) 0 0
\(135\) 8.58579 + 8.58579i 0.738947 + 0.738947i
\(136\) 0 0
\(137\) 8.65685 8.65685i 0.739605 0.739605i −0.232897 0.972502i \(-0.574820\pi\)
0.972502 + 0.232897i \(0.0748204\pi\)
\(138\) 0 0
\(139\) −5.46447 + 13.1924i −0.463490 + 1.11896i 0.503465 + 0.864016i \(0.332058\pi\)
−0.966955 + 0.254948i \(0.917942\pi\)
\(140\) 0 0
\(141\) −0.242641 + 0.100505i −0.0204340 + 0.00846405i
\(142\) 0 0
\(143\) 3.41421i 0.285511i
\(144\) 0 0
\(145\) 9.89949i 0.822108i
\(146\) 0 0
\(147\) 3.53553 1.46447i 0.291606 0.120787i
\(148\) 0 0
\(149\) 6.46447 15.6066i 0.529590 1.27854i −0.402203 0.915551i \(-0.631755\pi\)
0.931792 0.362992i \(-0.118245\pi\)
\(150\) 0 0
\(151\) 1.48528 1.48528i 0.120870 0.120870i −0.644084 0.764955i \(-0.722761\pi\)
0.764955 + 0.644084i \(0.222761\pi\)
\(152\) 0 0
\(153\) 4.82843 + 4.82843i 0.390355 + 0.390355i
\(154\) 0 0
\(155\) −10.8284 4.48528i −0.869760 0.360266i
\(156\) 0 0
\(157\) −0.707107 1.70711i −0.0564333 0.136242i 0.893148 0.449763i \(-0.148491\pi\)
−0.949581 + 0.313521i \(0.898491\pi\)
\(158\) 0 0
\(159\) 0.928932 0.0736691
\(160\) 0 0
\(161\) 11.6569 0.918689
\(162\) 0 0
\(163\) −0.192388 0.464466i −0.0150690 0.0363798i 0.916166 0.400799i \(-0.131267\pi\)
−0.931235 + 0.364419i \(0.881267\pi\)
\(164\) 0 0
\(165\) 9.24264 + 3.82843i 0.719539 + 0.298043i
\(166\) 0 0
\(167\) −14.6569 14.6569i −1.13418 1.13418i −0.989475 0.144707i \(-0.953776\pi\)
−0.144707 0.989475i \(-0.546224\pi\)
\(168\) 0 0
\(169\) −8.77817 + 8.77817i −0.675244 + 0.675244i
\(170\) 0 0
\(171\) 3.70711 8.94975i 0.283490 0.684404i
\(172\) 0 0
\(173\) 7.53553 3.12132i 0.572916 0.237310i −0.0773656 0.997003i \(-0.524651\pi\)
0.650282 + 0.759693i \(0.274651\pi\)
\(174\) 0 0
\(175\) 5.07107i 0.383337i
\(176\) 0 0
\(177\) 3.75736i 0.282420i
\(178\) 0 0
\(179\) −3.94975 + 1.63604i −0.295218 + 0.122283i −0.525377 0.850870i \(-0.676076\pi\)
0.230159 + 0.973153i \(0.426076\pi\)
\(180\) 0 0
\(181\) −6.70711 + 16.1924i −0.498535 + 1.20357i 0.451737 + 0.892151i \(0.350804\pi\)
−0.950272 + 0.311420i \(0.899196\pi\)
\(182\) 0 0
\(183\) 1.00000 1.00000i 0.0739221 0.0739221i
\(184\) 0 0
\(185\) 1.58579 + 1.58579i 0.116589 + 0.116589i
\(186\) 0 0
\(187\) 11.6569 + 4.82843i 0.852434 + 0.353090i
\(188\) 0 0
\(189\) −2.24264 5.41421i −0.163128 0.393826i
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) −1.51472 −0.109032 −0.0545159 0.998513i \(-0.517362\pi\)
−0.0545159 + 0.998513i \(0.517362\pi\)
\(194\) 0 0
\(195\) 0.656854 + 1.58579i 0.0470383 + 0.113561i
\(196\) 0 0
\(197\) 11.1924 + 4.63604i 0.797425 + 0.330304i 0.743924 0.668264i \(-0.232962\pi\)
0.0535002 + 0.998568i \(0.482962\pi\)
\(198\) 0 0
\(199\) 15.9706 + 15.9706i 1.13212 + 1.13212i 0.989824 + 0.142300i \(0.0454496\pi\)
0.142300 + 0.989824i \(0.454550\pi\)
\(200\) 0 0
\(201\) −3.24264 + 3.24264i −0.228718 + 0.228718i
\(202\) 0 0
\(203\) 1.82843 4.41421i 0.128330 0.309817i
\(204\) 0 0
\(205\) 0.656854 0.272078i 0.0458767 0.0190027i
\(206\) 0 0
\(207\) 19.8995i 1.38311i
\(208\) 0 0
\(209\) 17.8995i 1.23813i
\(210\) 0 0
\(211\) 18.1924 7.53553i 1.25242 0.518768i 0.344842 0.938661i \(-0.387932\pi\)
0.907574 + 0.419893i \(0.137932\pi\)
\(212\) 0 0
\(213\) −2.41421 + 5.82843i −0.165419 + 0.399357i
\(214\) 0 0
\(215\) −10.5563 + 10.5563i −0.719937 + 0.719937i
\(216\) 0 0
\(217\) 4.00000 + 4.00000i 0.271538 + 0.271538i
\(218\) 0 0
\(219\) −7.00000 2.89949i −0.473016 0.195930i
\(220\) 0 0
\(221\) 0.828427 + 2.00000i 0.0557260 + 0.134535i
\(222\) 0 0
\(223\) −20.9706 −1.40429 −0.702146 0.712033i \(-0.747775\pi\)
−0.702146 + 0.712033i \(0.747775\pi\)
\(224\) 0 0
\(225\) 8.65685 0.577124
\(226\) 0 0
\(227\) −7.70711 18.6066i −0.511539 1.23496i −0.942988 0.332826i \(-0.891998\pi\)
0.431449 0.902137i \(-0.358002\pi\)
\(228\) 0 0
\(229\) −22.2635 9.22183i −1.47121 0.609395i −0.504076 0.863659i \(-0.668167\pi\)
−0.967135 + 0.254264i \(0.918167\pi\)
\(230\) 0 0
\(231\) −3.41421 3.41421i −0.224639 0.224639i
\(232\) 0 0
\(233\) 2.65685 2.65685i 0.174056 0.174056i −0.614703 0.788759i \(-0.710724\pi\)
0.788759 + 0.614703i \(0.210724\pi\)
\(234\) 0 0
\(235\) −0.384776 + 0.928932i −0.0251000 + 0.0605969i
\(236\) 0 0
\(237\) 4.24264 1.75736i 0.275589 0.114153i
\(238\) 0 0
\(239\) 5.31371i 0.343715i 0.985122 + 0.171858i \(0.0549769\pi\)
−0.985122 + 0.171858i \(0.945023\pi\)
\(240\) 0 0
\(241\) 8.48528i 0.546585i 0.961931 + 0.273293i \(0.0881127\pi\)
−0.961931 + 0.273293i \(0.911887\pi\)
\(242\) 0 0
\(243\) 14.3640 5.94975i 0.921449 0.381676i
\(244\) 0 0
\(245\) 5.60660 13.5355i 0.358193 0.864754i
\(246\) 0 0
\(247\) 2.17157 2.17157i 0.138174 0.138174i
\(248\) 0 0
\(249\) 2.65685 + 2.65685i 0.168371 + 0.168371i
\(250\) 0 0
\(251\) 15.9497 + 6.60660i 1.00674 + 0.417005i 0.824264 0.566205i \(-0.191589\pi\)
0.182475 + 0.983210i \(0.441589\pi\)
\(252\) 0 0
\(253\) 14.0711 + 33.9706i 0.884640 + 2.13571i
\(254\) 0 0
\(255\) −6.34315 −0.397223
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) −0.414214 1.00000i −0.0257380 0.0621370i
\(260\) 0 0
\(261\) 7.53553 + 3.12132i 0.466438 + 0.193205i
\(262\) 0 0
\(263\) 5.82843 + 5.82843i 0.359396 + 0.359396i 0.863590 0.504194i \(-0.168210\pi\)
−0.504194 + 0.863590i \(0.668210\pi\)
\(264\) 0 0
\(265\) 2.51472 2.51472i 0.154478 0.154478i
\(266\) 0 0
\(267\) 3.58579 8.65685i 0.219447 0.529791i
\(268\) 0 0
\(269\) 22.0208 9.12132i 1.34263 0.556137i 0.408401 0.912803i \(-0.366087\pi\)
0.934232 + 0.356666i \(0.116087\pi\)
\(270\) 0 0
\(271\) 18.0000i 1.09342i −0.837321 0.546711i \(-0.815880\pi\)
0.837321 0.546711i \(-0.184120\pi\)
\(272\) 0 0
\(273\) 0.828427i 0.0501387i
\(274\) 0 0
\(275\) 14.7782 6.12132i 0.891157 0.369130i
\(276\) 0 0
\(277\) −0.707107 + 1.70711i −0.0424859 + 0.102570i −0.943698 0.330808i \(-0.892679\pi\)
0.901212 + 0.433378i \(0.142679\pi\)
\(278\) 0 0
\(279\) −6.82843 + 6.82843i −0.408807 + 0.408807i
\(280\) 0 0
\(281\) 11.8284 + 11.8284i 0.705625 + 0.705625i 0.965612 0.259987i \(-0.0837184\pi\)
−0.259987 + 0.965612i \(0.583718\pi\)
\(282\) 0 0
\(283\) 13.9497 + 5.77817i 0.829226 + 0.343477i 0.756596 0.653882i \(-0.226861\pi\)
0.0726300 + 0.997359i \(0.476861\pi\)
\(284\) 0 0
\(285\) 3.44365 + 8.31371i 0.203984 + 0.492462i
\(286\) 0 0
\(287\) −0.343146 −0.0202553
\(288\) 0 0
\(289\) 9.00000 0.529412
\(290\) 0 0
\(291\) −5.41421 13.0711i −0.317387 0.766240i
\(292\) 0 0
\(293\) 23.1924 + 9.60660i 1.35491 + 0.561224i 0.937656 0.347565i \(-0.112991\pi\)
0.417258 + 0.908788i \(0.362991\pi\)
\(294\) 0 0
\(295\) −10.1716 10.1716i −0.592212 0.592212i
\(296\) 0 0
\(297\) 13.0711 13.0711i 0.758460 0.758460i
\(298\) 0 0
\(299\) −2.41421 + 5.82843i −0.139618 + 0.337067i
\(300\) 0 0
\(301\) 6.65685 2.75736i 0.383695 0.158932i
\(302\) 0 0
\(303\) 2.72792i 0.156715i
\(304\) 0 0
\(305\) 5.41421i 0.310017i
\(306\) 0 0
\(307\) −16.7782 + 6.94975i −0.957581 + 0.396643i −0.806075 0.591813i \(-0.798412\pi\)
−0.151506 + 0.988456i \(0.548412\pi\)
\(308\) 0 0
\(309\) 3.92893 9.48528i 0.223509 0.539599i
\(310\) 0 0
\(311\) 2.65685 2.65685i 0.150656 0.150656i −0.627755 0.778411i \(-0.716026\pi\)
0.778411 + 0.627755i \(0.216026\pi\)
\(312\) 0 0
\(313\) 7.48528 + 7.48528i 0.423093 + 0.423093i 0.886267 0.463174i \(-0.153290\pi\)
−0.463174 + 0.886267i \(0.653290\pi\)
\(314\) 0 0
\(315\) −9.24264 3.82843i −0.520764 0.215707i
\(316\) 0 0
\(317\) −7.19239 17.3640i −0.403965 0.975257i −0.986694 0.162591i \(-0.948015\pi\)
0.582729 0.812667i \(-0.301985\pi\)
\(318\) 0 0
\(319\) 15.0711 0.843818
\(320\) 0 0
\(321\) 3.41421 0.190563
\(322\) 0 0
\(323\) 4.34315 + 10.4853i 0.241659 + 0.583417i
\(324\) 0 0
\(325\) 2.53553 + 1.05025i 0.140646 + 0.0582575i
\(326\) 0 0
\(327\) −8.07107 8.07107i −0.446331 0.446331i
\(328\) 0 0
\(329\) 0.343146 0.343146i 0.0189182 0.0189182i
\(330\) 0 0
\(331\) 0.535534 1.29289i 0.0294356 0.0710638i −0.908478 0.417932i \(-0.862755\pi\)
0.937914 + 0.346868i \(0.112755\pi\)
\(332\) 0 0
\(333\) 1.70711 0.707107i 0.0935489 0.0387492i
\(334\) 0 0
\(335\) 17.5563i 0.959206i
\(336\) 0 0
\(337\) 16.9706i 0.924445i 0.886764 + 0.462223i \(0.152948\pi\)
−0.886764 + 0.462223i \(0.847052\pi\)
\(338\) 0 0
\(339\) −4.48528 + 1.85786i −0.243607 + 0.100905i
\(340\) 0 0
\(341\) −6.82843 + 16.4853i −0.369780 + 0.892728i
\(342\) 0 0
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 0 0
\(345\) −13.0711 13.0711i −0.703723 0.703723i
\(346\) 0 0
\(347\) 3.94975 + 1.63604i 0.212034 + 0.0878272i 0.486172 0.873863i \(-0.338393\pi\)
−0.274139 + 0.961690i \(0.588393\pi\)
\(348\) 0 0
\(349\) −10.2218 24.6777i −0.547162 1.32097i −0.919581 0.392901i \(-0.871472\pi\)
0.372419 0.928065i \(-0.378528\pi\)
\(350\) 0 0
\(351\) 3.17157 0.169286
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 9.24264 + 22.3137i 0.490548 + 1.18429i
\(356\) 0 0
\(357\) 2.82843 + 1.17157i 0.149696 + 0.0620062i
\(358\) 0 0
\(359\) 17.8284 + 17.8284i 0.940948 + 0.940948i 0.998351 0.0574027i \(-0.0182819\pi\)
−0.0574027 + 0.998351i \(0.518282\pi\)
\(360\) 0 0
\(361\) −2.05025 + 2.05025i −0.107908 + 0.107908i
\(362\) 0 0
\(363\) 2.60660 6.29289i 0.136811 0.330291i
\(364\) 0 0
\(365\) −26.7990 + 11.1005i −1.40272 + 0.581027i
\(366\) 0 0
\(367\) 6.00000i 0.313197i 0.987662 + 0.156599i \(0.0500529\pi\)
−0.987662 + 0.156599i \(0.949947\pi\)
\(368\) 0 0
\(369\) 0.585786i 0.0304948i
\(370\) 0 0
\(371\) −1.58579 + 0.656854i −0.0823299 + 0.0341022i
\(372\) 0 0
\(373\) 4.26346 10.2929i 0.220753 0.532946i −0.774239 0.632893i \(-0.781867\pi\)
0.994993 + 0.0999471i \(0.0318673\pi\)
\(374\) 0 0
\(375\) 2.24264 2.24264i 0.115809 0.115809i
\(376\) 0 0
\(377\) 1.82843 + 1.82843i 0.0941688 + 0.0941688i
\(378\) 0 0
\(379\) −33.0208 13.6777i −1.69617 0.702575i −0.696281 0.717769i \(-0.745163\pi\)
−0.999885 + 0.0151948i \(0.995163\pi\)
\(380\) 0 0
\(381\) 3.79899 + 9.17157i 0.194628 + 0.469874i
\(382\) 0 0
\(383\) −16.9706 −0.867155 −0.433578 0.901116i \(-0.642749\pi\)
−0.433578 + 0.901116i \(0.642749\pi\)
\(384\) 0 0
\(385\) −18.4853 −0.942097
\(386\) 0 0
\(387\) 4.70711 + 11.3640i 0.239276 + 0.577663i
\(388\) 0 0
\(389\) −20.2635 8.39340i −1.02740 0.425562i −0.195625 0.980679i \(-0.562674\pi\)
−0.831773 + 0.555117i \(0.812674\pi\)
\(390\) 0 0
\(391\) −16.4853 16.4853i −0.833697 0.833697i
\(392\) 0 0
\(393\) −9.58579 + 9.58579i −0.483539 + 0.483539i
\(394\) 0 0
\(395\) 6.72792 16.2426i 0.338518 0.817256i
\(396\) 0 0
\(397\) −22.2635 + 9.22183i −1.11737 + 0.462830i −0.863470 0.504400i \(-0.831714\pi\)
−0.253901 + 0.967230i \(0.581714\pi\)
\(398\) 0 0
\(399\) 4.34315i 0.217429i
\(400\) 0 0
\(401\) 2.82843i 0.141245i 0.997503 + 0.0706225i \(0.0224986\pi\)
−0.997503 + 0.0706225i \(0.977501\pi\)
\(402\) 0 0
\(403\) −2.82843 + 1.17157i −0.140894 + 0.0583602i
\(404\) 0 0
\(405\) 4.56497 11.0208i 0.226835 0.547629i
\(406\) 0 0
\(407\) 2.41421 2.41421i 0.119668 0.119668i
\(408\) 0 0
\(409\) −21.4853 21.4853i −1.06238 1.06238i −0.997920 0.0644584i \(-0.979468\pi\)
−0.0644584 0.997920i \(-0.520532\pi\)
\(410\) 0 0
\(411\) 8.65685 + 3.58579i 0.427011 + 0.176874i
\(412\) 0 0
\(413\) 2.65685 + 6.41421i 0.130735 + 0.315623i
\(414\) 0 0
\(415\) 14.3848 0.706121
\(416\) 0 0
\(417\) −10.9289 −0.535192
\(418\) 0 0
\(419\) −5.22183 12.6066i −0.255103 0.615873i 0.743499 0.668737i \(-0.233165\pi\)
−0.998602 + 0.0528644i \(0.983165\pi\)
\(420\) 0 0
\(421\) 15.1924 + 6.29289i 0.740432 + 0.306697i 0.720831 0.693111i \(-0.243760\pi\)
0.0196009 + 0.999808i \(0.493760\pi\)
\(422\) 0 0
\(423\) 0.585786 + 0.585786i 0.0284819 + 0.0284819i
\(424\) 0 0
\(425\) −7.17157 + 7.17157i −0.347872 + 0.347872i
\(426\) 0 0
\(427\) −1.00000 + 2.41421i −0.0483934 + 0.116832i
\(428\) 0 0
\(429\) 2.41421 1.00000i 0.116559 0.0482805i
\(430\) 0 0
\(431\) 12.3431i 0.594548i 0.954792 + 0.297274i \(0.0960775\pi\)
−0.954792 + 0.297274i \(0.903922\pi\)
\(432\) 0 0
\(433\) 15.5147i 0.745590i 0.927914 + 0.372795i \(0.121600\pi\)
−0.927914 + 0.372795i \(0.878400\pi\)
\(434\) 0 0
\(435\) −7.00000 + 2.89949i −0.335624 + 0.139020i
\(436\) 0 0
\(437\) −12.6569 + 30.5563i −0.605459 + 1.46171i
\(438\) 0 0
\(439\) 17.0000 17.0000i 0.811366 0.811366i −0.173473 0.984839i \(-0.555499\pi\)
0.984839 + 0.173473i \(0.0554989\pi\)
\(440\) 0 0
\(441\) −8.53553 8.53553i −0.406454 0.406454i
\(442\) 0 0
\(443\) 1.46447 + 0.606602i 0.0695789 + 0.0288205i 0.417201 0.908814i \(-0.363011\pi\)
−0.347623 + 0.937635i \(0.613011\pi\)
\(444\) 0 0
\(445\) −13.7279 33.1421i −0.650766 1.57109i
\(446\) 0 0
\(447\) 12.9289 0.611518
\(448\) 0 0
\(449\) −19.4558 −0.918178 −0.459089 0.888390i \(-0.651824\pi\)
−0.459089 + 0.888390i \(0.651824\pi\)
\(450\) 0 0
\(451\) −0.414214 1.00000i −0.0195046 0.0470882i
\(452\) 0 0
\(453\) 1.48528 + 0.615224i 0.0697846 + 0.0289057i
\(454\) 0 0
\(455\) −2.24264 2.24264i −0.105137 0.105137i
\(456\) 0 0
\(457\) 7.48528 7.48528i 0.350147 0.350147i −0.510017 0.860164i \(-0.670361\pi\)
0.860164 + 0.510017i \(0.170361\pi\)
\(458\) 0 0
\(459\) −4.48528 + 10.8284i −0.209355 + 0.505428i
\(460\) 0 0
\(461\) 1.53553 0.636039i 0.0715169 0.0296233i −0.346638 0.937999i \(-0.612677\pi\)
0.418155 + 0.908376i \(0.362677\pi\)
\(462\) 0 0
\(463\) 22.9706i 1.06753i −0.845632 0.533766i \(-0.820776\pi\)
0.845632 0.533766i \(-0.179224\pi\)
\(464\) 0 0
\(465\) 8.97056i 0.416000i
\(466\) 0 0
\(467\) −21.9497 + 9.09188i −1.01571 + 0.420722i −0.827536 0.561413i \(-0.810258\pi\)
−0.188177 + 0.982135i \(0.560258\pi\)
\(468\) 0 0
\(469\) 3.24264 7.82843i 0.149731 0.361483i
\(470\) 0 0
\(471\) 1.00000 1.00000i 0.0460776 0.0460776i
\(472\) 0 0
\(473\) 16.0711 + 16.0711i 0.738948 + 0.738948i
\(474\) 0 0
\(475\) 13.2929 + 5.50610i 0.609920 + 0.252637i
\(476\) 0 0
\(477\) −1.12132 2.70711i −0.0513417 0.123950i
\(478\) 0 0
\(479\) 28.9706 1.32370 0.661849 0.749637i \(-0.269772\pi\)
0.661849 + 0.749637i \(0.269772\pi\)
\(480\) 0 0
\(481\) 0.585786 0.0267096
\(482\) 0 0
\(483\) 3.41421 + 8.24264i 0.155352 + 0.375053i
\(484\) 0 0
\(485\) −50.0416 20.7279i −2.27227 0.941206i
\(486\) 0 0
\(487\) 11.0000 + 11.0000i 0.498458 + 0.498458i 0.910958 0.412500i \(-0.135344\pi\)
−0.412500 + 0.910958i \(0.635344\pi\)
\(488\) 0 0
\(489\) 0.272078 0.272078i 0.0123038 0.0123038i
\(490\) 0 0
\(491\) −16.2929 + 39.3345i −0.735288 + 1.77514i −0.111186 + 0.993800i \(0.535465\pi\)
−0.624102 + 0.781343i \(0.714535\pi\)
\(492\) 0 0
\(493\) −8.82843 + 3.65685i −0.397612 + 0.164696i
\(494\) 0 0
\(495\) 31.5563i 1.41835i
\(496\) 0 0
\(497\) 11.6569i 0.522881i
\(498\) 0 0
\(499\) −2.29289 + 0.949747i −0.102644 + 0.0425165i −0.433415 0.901195i \(-0.642691\pi\)
0.330771 + 0.943711i \(0.392691\pi\)
\(500\) 0 0
\(501\) 6.07107 14.6569i 0.271235 0.654820i
\(502\) 0 0
\(503\) 11.1421 11.1421i 0.496803 0.496803i −0.413638 0.910441i \(-0.635742\pi\)
0.910441 + 0.413638i \(0.135742\pi\)
\(504\) 0 0
\(505\) −7.38478 7.38478i −0.328618 0.328618i
\(506\) 0 0
\(507\) −8.77817 3.63604i −0.389852 0.161482i
\(508\) 0 0
\(509\) 10.8076 + 26.0919i 0.479039 + 1.15650i 0.960060 + 0.279793i \(0.0902660\pi\)
−0.481021 + 0.876709i \(0.659734\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) 0 0
\(513\) 16.6274 0.734118
\(514\) 0 0
\(515\) −15.0416 36.3137i −0.662813 1.60017i
\(516\) 0 0
\(517\) 1.41421 + 0.585786i 0.0621970 + 0.0257629i
\(518\) 0 0
\(519\) 4.41421 + 4.41421i 0.193762 + 0.193762i
\(520\) 0 0
\(521\) −3.34315 + 3.34315i −0.146466 + 0.146466i −0.776537 0.630071i \(-0.783026\pi\)
0.630071 + 0.776537i \(0.283026\pi\)
\(522\) 0 0
\(523\) −7.94975 + 19.1924i −0.347618 + 0.839225i 0.649282 + 0.760548i \(0.275070\pi\)
−0.996900 + 0.0786768i \(0.974930\pi\)
\(524\) 0 0
\(525\) 3.58579 1.48528i 0.156497 0.0648230i
\(526\) 0 0
\(527\) 11.3137i 0.492833i
\(528\) 0 0
\(529\) 44.9411i 1.95396i
\(530\) 0 0
\(531\) −10.9497 + 4.53553i −0.475179 + 0.196825i
\(532\) 0 0
\(533\) 0.0710678 0.171573i 0.00307829 0.00743165i
\(534\) 0 0
\(535\) 9.24264 9.24264i 0.399594 0.399594i
\(536\) 0 0
\(537\) −2.31371 2.31371i −0.0998439 0.0998439i
\(538\) 0 0
\(539\) −20.6066 8.53553i −0.887589 0.367651i
\(540\) 0 0
\(541\) 11.2929 + 27.2635i 0.485519 + 1.17215i 0.956952 + 0.290246i \(0.0937370\pi\)
−0.471433 + 0.881902i \(0.656263\pi\)
\(542\) 0 0
\(543\) −13.4142 −0.575659
\(544\) 0 0
\(545\) −43.6985 −1.87184
\(546\) 0 0
\(547\) 7.26346 + 17.5355i 0.310563 + 0.749765i 0.999684 + 0.0251195i \(0.00799662\pi\)
−0.689122 + 0.724646i \(0.742003\pi\)
\(548\) 0 0
\(549\) −4.12132 1.70711i −0.175894 0.0728575i
\(550\) 0 0
\(551\) 9.58579 + 9.58579i 0.408368 + 0.408368i
\(552\) 0 0
\(553\) −6.00000 + 6.00000i −0.255146 + 0.255146i
\(554\) 0 0
\(555\) −0.656854 + 1.58579i −0.0278819 + 0.0673129i
\(556\) 0 0
\(557\) 36.5061 15.1213i 1.54681 0.640711i 0.564077 0.825722i \(-0.309232\pi\)
0.982736 + 0.185012i \(0.0592323\pi\)
\(558\) 0 0
\(559\) 3.89949i 0.164931i
\(560\) 0 0
\(561\) 9.65685i 0.407713i
\(562\) 0 0
\(563\) 19.0208 7.87868i 0.801632 0.332047i 0.0560220 0.998430i \(-0.482158\pi\)
0.745610 + 0.666383i \(0.232158\pi\)
\(564\) 0 0
\(565\) −7.11270 + 17.1716i −0.299233 + 0.722414i
\(566\) 0 0
\(567\) −4.07107 + 4.07107i −0.170969 + 0.170969i
\(568\) 0 0
\(569\) −14.6569 14.6569i −0.614447 0.614447i 0.329654 0.944102i \(-0.393068\pi\)
−0.944102 + 0.329654i \(0.893068\pi\)
\(570\) 0 0
\(571\) −6.53553 2.70711i −0.273504 0.113289i 0.241716 0.970347i \(-0.422290\pi\)
−0.515220 + 0.857058i \(0.672290\pi\)
\(572\) 0 0
\(573\) −3.51472 8.48528i −0.146829 0.354478i
\(574\) 0 0
\(575\) −29.5563 −1.23258
\(576\) 0 0
\(577\) 18.9706 0.789755 0.394877 0.918734i \(-0.370787\pi\)
0.394877 + 0.918734i \(0.370787\pi\)
\(578\) 0 0
\(579\) −0.443651 1.07107i −0.0184375 0.0445121i
\(580\) 0 0
\(581\) −6.41421 2.65685i −0.266106 0.110225i
\(582\) 0 0
\(583\) −3.82843 3.82843i −0.158557 0.158557i
\(584\) 0 0
\(585\) 3.82843 3.82843i 0.158286 0.158286i
\(586\) 0 0
\(587\) 5.22183 12.6066i 0.215528 0.520330i −0.778728 0.627362i \(-0.784135\pi\)
0.994256 + 0.107032i \(0.0341347\pi\)
\(588\) 0 0
\(589\) −14.8284 + 6.14214i −0.610995 + 0.253082i
\(590\) 0 0
\(591\) 9.27208i 0.381402i
\(592\) 0 0
\(593\) 28.2843i 1.16150i 0.814083 + 0.580748i \(0.197240\pi\)
−0.814083 + 0.580748i \(0.802760\pi\)
\(594\) 0 0
\(595\) 10.8284 4.48528i 0.443922 0.183879i
\(596\) 0 0
\(597\) −6.61522 + 15.9706i −0.270743 + 0.653632i
\(598\) 0 0
\(599\) 26.6569 26.6569i 1.08917 1.08917i 0.0935555 0.995614i \(-0.470177\pi\)
0.995614 0.0935555i \(-0.0298232\pi\)
\(600\) 0 0
\(601\) 21.9706 + 21.9706i 0.896198 + 0.896198i 0.995097 0.0988995i \(-0.0315322\pi\)
−0.0988995 + 0.995097i \(0.531532\pi\)
\(602\) 0 0
\(603\) 13.3640 + 5.53553i 0.544223 + 0.225424i
\(604\) 0 0
\(605\) −9.97918 24.0919i −0.405712 0.979474i
\(606\) 0 0
\(607\) −32.9706 −1.33823 −0.669117 0.743157i \(-0.733327\pi\)
−0.669117 + 0.743157i \(0.733327\pi\)
\(608\) 0 0
\(609\) 3.65685 0.148183
\(610\) 0 0
\(611\) 0.100505 + 0.242641i 0.00406600 + 0.00981619i
\(612\) 0 0
\(613\) 3.19239 + 1.32233i 0.128939 + 0.0534084i 0.446220 0.894923i \(-0.352770\pi\)
−0.317281 + 0.948332i \(0.602770\pi\)
\(614\) 0 0
\(615\) 0.384776 + 0.384776i 0.0155157 + 0.0155157i
\(616\) 0 0
\(617\) −22.7990 + 22.7990i −0.917853 + 0.917853i −0.996873 0.0790202i \(-0.974821\pi\)
0.0790202 + 0.996873i \(0.474821\pi\)
\(618\) 0 0
\(619\) 9.02082 21.7782i 0.362577 0.875339i −0.632345 0.774687i \(-0.717907\pi\)
0.994922 0.100651i \(-0.0320927\pi\)
\(620\) 0 0
\(621\) −31.5563 + 13.0711i −1.26631 + 0.524524i
\(622\) 0 0
\(623\) 17.3137i 0.693659i
\(624\) 0 0
\(625\) 30.0711i 1.20284i
\(626\) 0 0
\(627\) 12.6569 5.24264i 0.505466 0.209371i
\(628\) 0 0
\(629\) −0.828427 + 2.00000i −0.0330316 + 0.0797452i
\(630\) 0 0
\(631\) −32.4558 + 32.4558i −1.29205 + 1.29205i −0.358528 + 0.933519i \(0.616721\pi\)
−0.933519 + 0.358528i \(0.883279\pi\)
\(632\) 0 0
\(633\) 10.6569 + 10.6569i 0.423572 + 0.423572i
\(634\) 0 0
\(635\) 35.1127 + 14.5442i 1.39340 + 0.577167i
\(636\) 0 0
\(637\) −1.46447 3.53553i −0.0580243 0.140083i
\(638\) 0 0
\(639\) 19.8995 0.787212
\(640\) 0 0
\(641\) 7.45584 0.294488 0.147244 0.989100i \(-0.452960\pi\)
0.147244 + 0.989100i \(0.452960\pi\)
\(642\) 0 0
\(643\) −4.73654 11.4350i −0.186791 0.450954i 0.802547 0.596588i \(-0.203478\pi\)
−0.989338 + 0.145635i \(0.953478\pi\)
\(644\) 0 0
\(645\) −10.5563 4.37258i −0.415656 0.172170i
\(646\) 0 0
\(647\) −6.17157 6.17157i −0.242630 0.242630i 0.575308 0.817937i \(-0.304882\pi\)
−0.817937 + 0.575308i \(0.804882\pi\)
\(648\) 0 0
\(649\) −15.4853 + 15.4853i −0.607850 + 0.607850i
\(650\) 0 0
\(651\) −1.65685 + 4.00000i −0.0649372 + 0.156772i
\(652\) 0 0
\(653\) 5.05025 2.09188i 0.197632 0.0818617i −0.281672 0.959511i \(-0.590889\pi\)
0.479304 + 0.877649i \(0.340889\pi\)
\(654\) 0 0
\(655\) 51.8995i 2.02788i
\(656\) 0 0
\(657\) 23.8995i 0.932408i
\(658\) 0 0
\(659\) −24.4350 + 10.1213i −0.951854 + 0.394271i −0.803927 0.594728i \(-0.797260\pi\)
−0.147926 + 0.988998i \(0.547260\pi\)
\(660\) 0 0
\(661\) 17.2929 41.7487i 0.672616 1.62384i −0.104534 0.994521i \(-0.533335\pi\)
0.777149 0.629316i \(-0.216665\pi\)
\(662\) 0 0
\(663\) −1.17157 + 1.17157i −0.0455001 + 0.0455001i
\(664\) 0 0
\(665\) −11.7574 11.7574i −0.455931 0.455931i
\(666\) 0 0
\(667\) −25.7279 10.6569i −0.996189 0.412635i
\(668\) 0 0
\(669\) −6.14214 14.8284i −0.237469 0.573300i
\(670\) 0 0
\(671\) −8.24264 −0.318204
\(672\) 0 0
\(673\) 22.4853 0.866744 0.433372 0.901215i \(-0.357324\pi\)
0.433372 + 0.901215i \(0.357324\pi\)
\(674\) 0 0
\(675\) 5.68629 + 13.7279i 0.218865 + 0.528388i
\(676\) 0 0
\(677\) 37.6777 + 15.6066i 1.44807 + 0.599810i 0.961740 0.273964i \(-0.0883351\pi\)
0.486331 + 0.873775i \(0.338335\pi\)
\(678\) 0 0
\(679\) 18.4853 + 18.4853i 0.709400 + 0.709400i
\(680\) 0 0
\(681\) 10.8995 10.8995i 0.417670 0.417670i
\(682\) 0 0
\(683\) 4.19239 10.1213i 0.160417 0.387282i −0.823150 0.567824i \(-0.807785\pi\)
0.983567 + 0.180543i \(0.0577854\pi\)
\(684\) 0 0
\(685\) 33.1421 13.7279i 1.26630 0.524517i
\(686\) 0 0
\(687\) 18.4437i 0.703669i
\(688\) 0 0
\(689\) 0.928932i 0.0353895i
\(690\) 0 0
\(691\) 30.1924 12.5061i 1.14857 0.475754i 0.274518 0.961582i \(-0.411482\pi\)
0.874055 + 0.485828i \(0.161482\pi\)
\(692\) 0 0
\(693\) −5.82843 + 14.0711i −0.221404 + 0.534516i
\(694\) 0 0
\(695\) −29.5858 + 29.5858i −1.12225 + 1.12225i
\(696\) 0 0
\(697\) 0.485281 + 0.485281i 0.0183813 + 0.0183813i
\(698\) 0 0
\(699\) 2.65685 + 1.10051i 0.100491 + 0.0416249i
\(700\) 0 0
\(701\) −1.19239 2.87868i −0.0450359 0.108726i 0.899761 0.436383i \(-0.143741\pi\)
−0.944797 + 0.327657i \(0.893741\pi\)
\(702\) 0 0
\(703\) 3.07107 0.115828
\(704\) 0 0
\(705\) −0.769553 −0.0289830
\(706\) 0 0
\(707\) 1.92893 + 4.65685i 0.0725450 + 0.175139i
\(708\) 0 0
\(709\) 21.1924 + 8.77817i 0.795897 + 0.329671i 0.743312 0.668945i \(-0.233254\pi\)
0.0525851 + 0.998616i \(0.483254\pi\)
\(710\) 0 0
\(711\) −10.2426 10.2426i −0.384129 0.384129i
\(712\) 0 0
\(713\) 23.3137 23.3137i 0.873105 0.873105i
\(714\) 0 0
\(715\) 3.82843 9.24264i 0.143175 0.345655i
\(716\) 0 0
\(717\) −3.75736 + 1.55635i −0.140321 + 0.0581229i
\(718\) 0 0
\(719\) 35.6569i 1.32978i −0.746943 0.664888i \(-0.768479\pi\)
0.746943 0.664888i \(-0.231521\pi\)
\(720\) 0 0
\(721\) 18.9706i 0.706501i
\(722\) 0 0
\(723\) −6.00000 + 2.48528i −0.223142 + 0.0924286i
\(724\) 0 0
\(725\) −4.63604 + 11.1924i −0.172178 + 0.415675i
\(726\) 0 0
\(727\) 9.97056 9.97056i 0.369788 0.369788i −0.497612 0.867400i \(-0.665790\pi\)
0.867400 + 0.497612i \(0.165790\pi\)
\(728\) 0 0
\(729\) −0.221825 0.221825i −0.00821576 0.00821576i
\(730\) 0 0
\(731\) −13.3137 5.51472i −0.492425 0.203969i
\(732\) 0 0
\(733\) 13.7782 + 33.2635i 0.508908 + 1.22861i 0.944513 + 0.328475i \(0.106535\pi\)
−0.435604 + 0.900138i \(0.643465\pi\)
\(734\) 0 0
\(735\) 11.2132 0.413605
\(736\) 0 0
\(737\) 26.7279 0.984536
\(738\) 0 0
\(739\) −0.192388 0.464466i −0.00707711 0.0170857i 0.920301 0.391210i \(-0.127943\pi\)
−0.927379 + 0.374124i \(0.877943\pi\)
\(740\) 0 0
\(741\) 2.17157 + 0.899495i 0.0797747 + 0.0330438i
\(742\) 0 0
\(743\) −31.6274 31.6274i −1.16030 1.16030i −0.984410 0.175887i \(-0.943721\pi\)
−0.175887 0.984410i \(-0.556279\pi\)
\(744\) 0 0
\(745\) 35.0000 35.0000i 1.28230 1.28230i
\(746\) 0 0
\(747\) 4.53553 10.9497i 0.165947 0.400630i
\(748\) 0 0
\(749\) −5.82843 + 2.41421i −0.212966 + 0.0882134i
\(750\) 0 0
\(751\) 10.9706i 0.400322i 0.979763 + 0.200161i \(0.0641464\pi\)
−0.979763 + 0.200161i \(0.935854\pi\)
\(752\) 0 0
\(753\) 13.2132i 0.481516i
\(754\) 0 0
\(755\) 5.68629 2.35534i 0.206945 0.0857196i
\(756\) 0 0
\(757\) 13.7782 33.2635i 0.500776 1.20898i −0.448285 0.893890i \(-0.647965\pi\)
0.949062 0.315090i \(-0.102035\pi\)
\(758\) 0 0
\(759\) −19.8995 + 19.8995i −0.722306 + 0.722306i
\(760\) 0 0
\(761\) 29.8284 + 29.8284i 1.08128 + 1.08128i 0.996390 + 0.0848892i \(0.0270536\pi\)
0.0848892 + 0.996390i \(0.472946\pi\)
\(762\) 0 0
\(763\) 19.4853 + 8.07107i 0.705415 + 0.292192i
\(764\) 0 0
\(765\) 7.65685 + 18.4853i 0.276834 + 0.668337i
\(766\) 0 0
\(767\) −3.75736 −0.135670
\(768\) 0 0
\(769\) 5.51472 0.198866 0.0994329 0.995044i \(-0.468297\pi\)
0.0994329 + 0.995044i \(0.468297\pi\)
\(770\) 0 0
\(771\) 1.75736 + 4.24264i 0.0632897 + 0.152795i
\(772\) 0 0
\(773\) 29.1924 + 12.0919i 1.04998 + 0.434915i 0.839884 0.542766i \(-0.182623\pi\)
0.210094 + 0.977681i \(0.432623\pi\)
\(774\) 0 0
\(775\) −10.1421 10.1421i −0.364316 0.364316i
\(776\) 0 0
\(777\) 0.585786 0.585786i 0.0210150 0.0210150i
\(778\) 0 0
\(779\) 0.372583 0.899495i 0.0133492 0.0322278i
\(780\) 0 0
\(781\) 33.9706 14.0711i 1.21556 0.503502i
\(782\) 0 0
\(783\) 14.0000i 0.500319i
\(784\) 0 0
\(785\) 5.41421i 0.193242i
\(786\) 0 0
\(787\) −2.29289 + 0.949747i −0.0817328 + 0.0338548i −0.423175 0.906048i \(-0.639085\pi\)
0.341442 + 0.939903i \(0.389085\pi\)
\(788\) 0 0
\(789\) −2.41421 + 5.82843i −0.0859483 + 0.207498i
\(790\) 0 0
\(791\) 6.34315 6.34315i 0.225536 0.225536i
\(792\) 0 0
\(793\) −1.00000 1.00000i −0.0355110 0.0355110i
\(794\) 0 0
\(795\)