Properties

Label 256.2.g.a.161.1
Level $256$
Weight $2$
Character 256.161
Analytic conductor $2.044$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 256.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.04417029174\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 161.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 256.161
Dual form 256.2.g.a.97.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(255\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\)

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
\(3\) −0.707107 0.292893i −0.408248 0.169102i 0.169102 0.985599i \(-0.445913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 0 0
\(5\) −1.12132 2.70711i −0.501470 1.21065i −0.948683 0.316228i \(-0.897584\pi\)
0.447214 0.894427i \(-0.352416\pi\)
\(6\) 0 0
\(7\) −1.00000 + 1.00000i −0.377964 + 0.377964i −0.870367 0.492403i \(-0.836119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 0 0
\(9\) −1.70711 1.70711i −0.569036 0.569036i
\(10\) 0 0
\(11\) −4.12132 + 1.70711i −1.24262 + 0.514712i −0.904534 0.426401i \(-0.859781\pi\)
−0.338091 + 0.941113i \(0.609781\pi\)
\(12\) 0 0
\(13\) −0.292893 + 0.707107i −0.0812340 + 0.196116i −0.959278 0.282464i \(-0.908848\pi\)
0.878044 + 0.478580i \(0.158848\pi\)
\(14\) 0 0
\(15\) 2.24264i 0.579047i
\(16\) 0 0
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) 0 0
\(19\) 1.53553 3.70711i 0.352276 0.850469i −0.644063 0.764973i \(-0.722752\pi\)
0.996339 0.0854961i \(-0.0272475\pi\)
\(20\) 0 0
\(21\) 1.00000 0.414214i 0.218218 0.0903888i
\(22\) 0 0
\(23\) −5.82843 5.82843i −1.21531 1.21531i −0.969256 0.246055i \(-0.920866\pi\)
−0.246055 0.969256i \(-0.579134\pi\)
\(24\) 0 0
\(25\) −2.53553 + 2.53553i −0.507107 + 0.507107i
\(26\) 0 0
\(27\) 1.58579 + 3.82843i 0.305185 + 0.736781i
\(28\) 0 0
\(29\) 3.12132 + 1.29289i 0.579615 + 0.240084i 0.653176 0.757206i \(-0.273436\pi\)
−0.0735609 + 0.997291i \(0.523436\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 3.41421 0.594338
\(34\) 0 0
\(35\) 3.82843 + 1.58579i 0.647122 + 0.268047i
\(36\) 0 0
\(37\) −0.292893 0.707107i −0.0481513 0.116248i 0.897974 0.440049i \(-0.145039\pi\)
−0.946125 + 0.323802i \(0.895039\pi\)
\(38\) 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 \(-0.256031\pi\)
−0.720377 + 0.693582i \(0.756031\pi\)
\(42\) 0 0
\(43\) 4.70711 1.94975i 0.717827 0.297334i 0.00628798 0.999980i \(-0.497998\pi\)
0.711539 + 0.702647i \(0.247998\pi\)
\(44\) 0 0
\(45\) −2.70711 + 6.53553i −0.403552 + 0.974260i
\(46\) 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
\(51\) −0.828427 + 2.00000i −0.116003 + 0.280056i
\(52\) 0 0
\(53\) 1.12132 0.464466i 0.154025 0.0637993i −0.304339 0.952564i \(-0.598436\pi\)
0.458364 + 0.888764i \(0.348436\pi\)
\(54\) 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
\(59\) −1.87868 4.53553i −0.244583 0.590476i 0.753144 0.657855i \(-0.228536\pi\)
−0.997727 + 0.0673793i \(0.978536\pi\)
\(60\) 0 0
\(61\) −1.70711 0.707107i −0.218573 0.0905357i 0.270710 0.962661i \(-0.412741\pi\)
−0.489283 + 0.872125i \(0.662741\pi\)
\(62\) 0 0
\(63\) 3.41421 0.430150
\(64\) 0 0
\(65\) 2.24264 0.278165
\(66\) 0 0
\(67\) −5.53553 2.29289i −0.676273 0.280121i 0.0179949 0.999838i \(-0.494272\pi\)
−0.694268 + 0.719717i \(0.744272\pi\)
\(68\) 0 0
\(69\) 2.41421 + 5.82843i 0.290637 + 0.701660i
\(70\) 0 0
\(71\) 5.82843 5.82843i 0.691707 0.691707i −0.270900 0.962607i \(-0.587321\pi\)
0.962607 + 0.270900i \(0.0873214\pi\)
\(72\) 0 0
\(73\) 7.00000 + 7.00000i 0.819288 + 0.819288i 0.986005 0.166717i \(-0.0533166\pi\)
−0.166717 + 0.986005i \(0.553317\pi\)
\(74\) 0 0
\(75\) 2.53553 1.05025i 0.292778 0.121273i
\(76\) 0 0
\(77\) 2.41421 5.82843i 0.275125 0.664211i
\(78\) 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
\(83\) 1.87868 4.53553i 0.206212 0.497840i −0.786609 0.617452i \(-0.788165\pi\)
0.992821 + 0.119612i \(0.0381651\pi\)
\(84\) 0 0
\(85\) −7.65685 + 3.17157i −0.830502 + 0.344005i
\(86\) 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 \(-0.525247\pi\)
0.996856 + 0.0792315i \(0.0252466\pi\)
\(90\) 0 0
\(91\) −0.414214 1.00000i −0.0434214 0.104828i
\(92\) 0 0
\(93\) −2.82843 1.17157i −0.293294 0.121486i
\(94\) 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
\(99\) 9.94975 + 4.12132i 0.999987 + 0.414208i
\(100\) 0 0
\(101\) 1.36396 + 3.29289i 0.135719 + 0.327655i 0.977098 0.212791i \(-0.0682554\pi\)
−0.841379 + 0.540446i \(0.818255\pi\)
\(102\) 0 0
\(103\) −9.48528 + 9.48528i −0.934613 + 0.934613i −0.997990 0.0633771i \(-0.979813\pi\)
0.0633771 + 0.997990i \(0.479813\pi\)
\(104\) 0 0
\(105\) −2.24264 2.24264i −0.218859 0.218859i
\(106\) 0 0
\(107\) −4.12132 + 1.70711i −0.398423 + 0.165032i −0.572893 0.819630i \(-0.694179\pi\)
0.174470 + 0.984663i \(0.444179\pi\)
\(108\) 0 0
\(109\) 5.70711 13.7782i 0.546642 1.31971i −0.373320 0.927702i \(-0.621781\pi\)
0.919962 0.392007i \(-0.128219\pi\)
\(110\) 0 0
\(111\) 0.585786i 0.0556004i
\(112\) 0 0
\(113\) 6.34315i 0.596713i −0.954455 0.298356i \(-0.903562\pi\)
0.954455 0.298356i \(-0.0964384\pi\)
\(114\) 0 0
\(115\) −9.24264 + 22.3137i −0.861881 + 2.08076i
\(116\) 0 0
\(117\) 1.70711 0.707107i 0.157822 0.0653720i
\(118\) 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
\(123\) 0.0710678 + 0.171573i 0.00640797 + 0.0154702i
\(124\) 0 0
\(125\) −3.82843 1.58579i −0.342425 0.141837i
\(126\) 0 0
\(127\) −12.9706 −1.15095 −0.575476 0.817819i \(-0.695183\pi\)
−0.575476 + 0.817819i \(0.695183\pi\)
\(128\) 0 0
\(129\) −3.89949 −0.343331
\(130\) 0 0
\(131\) −16.3640 6.77817i −1.42973 0.592212i −0.472442 0.881362i \(-0.656627\pi\)
−0.957284 + 0.289150i \(0.906627\pi\)
\(132\) 0 0
\(133\) 2.17157 + 5.24264i 0.188299 + 0.454595i
\(134\) 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 \(-0.425180\pi\)
−0.972502 + 0.232897i \(0.925180\pi\)
\(138\) 0 0
\(139\) 13.1924 5.46447i 1.11896 0.463490i 0.254948 0.966955i \(-0.417942\pi\)
0.864016 + 0.503465i \(0.167942\pi\)
\(140\) 0 0
\(141\) 0.100505 0.242641i 0.00846405 0.0204340i
\(142\) 0 0
\(143\) 3.41421i 0.285511i
\(144\) 0 0
\(145\) 9.89949i 0.822108i
\(146\) 0 0
\(147\) 1.46447 3.53553i 0.120787 0.291606i
\(148\) 0 0
\(149\) 15.6066 6.46447i 1.27854 0.529590i 0.362992 0.931792i \(-0.381755\pi\)
0.915551 + 0.402203i \(0.131755\pi\)
\(150\) 0 0
\(151\) 1.48528 + 1.48528i 0.120870 + 0.120870i 0.764955 0.644084i \(-0.222761\pi\)
−0.644084 + 0.764955i \(0.722761\pi\)
\(152\) 0 0
\(153\) −4.82843 + 4.82843i −0.390355 + 0.390355i
\(154\) 0 0
\(155\) −4.48528 10.8284i −0.360266 0.869760i
\(156\) 0 0
\(157\) −1.70711 0.707107i −0.136242 0.0564333i 0.313521 0.949581i \(-0.398491\pi\)
−0.449763 + 0.893148i \(0.648491\pi\)
\(158\) 0 0
\(159\) −0.928932 −0.0736691
\(160\) 0 0
\(161\) 11.6569 0.918689
\(162\) 0 0
\(163\) 0.464466 + 0.192388i 0.0363798 + 0.0150690i 0.400799 0.916166i \(-0.368733\pi\)
−0.364419 + 0.931235i \(0.618733\pi\)
\(164\) 0 0
\(165\) −3.82843 9.24264i −0.298043 0.719539i
\(166\) 0 0
\(167\) −14.6569 + 14.6569i −1.13418 + 1.13418i −0.144707 + 0.989475i \(0.546224\pi\)
−0.989475 + 0.144707i \(0.953776\pi\)
\(168\) 0 0
\(169\) 8.77817 + 8.77817i 0.675244 + 0.675244i
\(170\) 0 0
\(171\) −8.94975 + 3.70711i −0.684404 + 0.283490i
\(172\) 0 0
\(173\) −3.12132 + 7.53553i −0.237310 + 0.572916i −0.997003 0.0773656i \(-0.975349\pi\)
0.759693 + 0.650282i \(0.225349\pi\)
\(174\) 0 0
\(175\) 5.07107i 0.383337i
\(176\) 0 0
\(177\) 3.75736i 0.282420i
\(178\) 0 0
\(179\) −1.63604 + 3.94975i −0.122283 + 0.295218i −0.973153 0.230159i \(-0.926076\pi\)
0.850870 + 0.525377i \(0.176076\pi\)
\(180\) 0 0
\(181\) −16.1924 + 6.70711i −1.20357 + 0.498535i −0.892151 0.451737i \(-0.850804\pi\)
−0.311420 + 0.950272i \(0.600804\pi\)
\(182\) 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
\(187\) 4.82843 + 11.6569i 0.353090 + 0.852434i
\(188\) 0 0
\(189\) −5.41421 2.24264i −0.393826 0.163128i
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −1.51472 −0.109032 −0.0545159 0.998513i \(-0.517362\pi\)
−0.0545159 + 0.998513i \(0.517362\pi\)
\(194\) 0 0
\(195\) −1.58579 0.656854i −0.113561 0.0470383i
\(196\) 0 0
\(197\) −4.63604 11.1924i −0.330304 0.797425i −0.998568 0.0535002i \(-0.982962\pi\)
0.668264 0.743924i \(-0.267038\pi\)
\(198\) 0 0
\(199\) 15.9706 15.9706i 1.13212 1.13212i 0.142300 0.989824i \(-0.454550\pi\)
0.989824 0.142300i \(-0.0454496\pi\)
\(200\) 0 0
\(201\) 3.24264 + 3.24264i 0.228718 + 0.228718i
\(202\) 0 0
\(203\) −4.41421 + 1.82843i −0.309817 + 0.128330i
\(204\) 0 0
\(205\) −0.272078 + 0.656854i −0.0190027 + 0.0458767i
\(206\) 0 0
\(207\) 19.8995i 1.38311i
\(208\) 0 0
\(209\) 17.8995i 1.23813i
\(210\) 0 0
\(211\) 7.53553 18.1924i 0.518768 1.25242i −0.419893 0.907574i \(-0.637932\pi\)
0.938661 0.344842i \(-0.112068\pi\)
\(212\) 0 0
\(213\) −5.82843 + 2.41421i −0.399357 + 0.165419i
\(214\) 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
\(219\) −2.89949 7.00000i −0.195930 0.473016i
\(220\) 0 0
\(221\) 2.00000 + 0.828427i 0.134535 + 0.0557260i
\(222\) 0 0
\(223\) 20.9706 1.40429 0.702146 0.712033i \(-0.252225\pi\)
0.702146 + 0.712033i \(0.252225\pi\)
\(224\) 0 0
\(225\) 8.65685 0.577124
\(226\) 0 0
\(227\) 18.6066 + 7.70711i 1.23496 + 0.511539i 0.902137 0.431449i \(-0.141998\pi\)
0.332826 + 0.942988i \(0.391998\pi\)
\(228\) 0 0
\(229\) 9.22183 + 22.2635i 0.609395 + 1.47121i 0.863659 + 0.504076i \(0.168167\pi\)
−0.254264 + 0.967135i \(0.581833\pi\)
\(230\) 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 \(-0.289276\pi\)
−0.788759 + 0.614703i \(0.789276\pi\)
\(234\) 0 0
\(235\) 0.928932 0.384776i 0.0605969 0.0251000i
\(236\) 0 0
\(237\) −1.75736 + 4.24264i −0.114153 + 0.275589i
\(238\) 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 \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) 0 0
\(243\) 5.94975 14.3640i 0.381676 0.921449i
\(244\) 0 0
\(245\) 13.5355 5.60660i 0.864754 0.358193i
\(246\) 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
\(251\) 6.60660 + 15.9497i 0.417005 + 1.00674i 0.983210 + 0.182475i \(0.0584109\pi\)
−0.566205 + 0.824264i \(0.691589\pi\)
\(252\) 0 0
\(253\) 33.9706 + 14.0711i 2.13571 + 0.884640i
\(254\) 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
\(259\) 1.00000 + 0.414214i 0.0621370 + 0.0257380i
\(260\) 0 0
\(261\) −3.12132 7.53553i −0.193205 0.466438i
\(262\) 0 0
\(263\) 5.82843 5.82843i 0.359396 0.359396i −0.504194 0.863590i \(-0.668210\pi\)
0.863590 + 0.504194i \(0.168210\pi\)
\(264\) 0 0
\(265\) −2.51472 2.51472i −0.154478 0.154478i
\(266\) 0 0
\(267\) −8.65685 + 3.58579i −0.529791 + 0.219447i
\(268\) 0 0
\(269\) −9.12132 + 22.0208i −0.556137 + 1.34263i 0.356666 + 0.934232i \(0.383913\pi\)
−0.912803 + 0.408401i \(0.866087\pi\)
\(270\) 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
\(275\) 6.12132 14.7782i 0.369130 0.891157i
\(276\) 0 0
\(277\) −1.70711 + 0.707107i −0.102570 + 0.0424859i −0.433378 0.901212i \(-0.642679\pi\)
0.330808 + 0.943698i \(0.392679\pi\)
\(278\) 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 \(-0.916282\pi\)
0.259987 + 0.965612i \(0.416282\pi\)
\(282\) 0 0
\(283\) 5.77817 + 13.9497i 0.343477 + 0.829226i 0.997359 + 0.0726300i \(0.0231392\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 0 0
\(285\) 8.31371 + 3.44365i 0.492462 + 0.203984i
\(286\) 0 0
\(287\) 0.343146 0.0202553
\(288\) 0 0
\(289\) 9.00000 0.529412
\(290\) 0 0
\(291\) 13.0711 + 5.41421i 0.766240 + 0.317387i
\(292\) 0 0
\(293\) −9.60660 23.1924i −0.561224 1.35491i −0.908788 0.417258i \(-0.862991\pi\)
0.347565 0.937656i \(-0.387009\pi\)
\(294\) 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
\(299\) 5.82843 2.41421i 0.337067 0.139618i
\(300\) 0 0
\(301\) −2.75736 + 6.65685i −0.158932 + 0.383695i
\(302\) 0 0
\(303\) 2.72792i 0.156715i
\(304\) 0 0
\(305\) 5.41421i 0.310017i
\(306\) 0 0
\(307\) −6.94975 + 16.7782i −0.396643 + 0.957581i 0.591813 + 0.806075i \(0.298412\pi\)
−0.988456 + 0.151506i \(0.951588\pi\)
\(308\) 0 0
\(309\) 9.48528 3.92893i 0.539599 0.223509i
\(310\) 0 0
\(311\) 2.65685 + 2.65685i 0.150656 + 0.150656i 0.778411 0.627755i \(-0.216026\pi\)
−0.627755 + 0.778411i \(0.716026\pi\)
\(312\) 0 0
\(313\) −7.48528 + 7.48528i −0.423093 + 0.423093i −0.886267 0.463174i \(-0.846710\pi\)
0.463174 + 0.886267i \(0.346710\pi\)
\(314\) 0 0
\(315\) −3.82843 9.24264i −0.215707 0.520764i
\(316\) 0 0
\(317\) −17.3640 7.19239i −0.975257 0.403965i −0.162591 0.986694i \(-0.551985\pi\)
−0.812667 + 0.582729i \(0.801985\pi\)
\(318\) 0 0
\(319\) −15.0711 −0.843818
\(320\) 0 0
\(321\) 3.41421 0.190563
\(322\) 0 0
\(323\) −10.4853 4.34315i −0.583417 0.241659i
\(324\) 0 0
\(325\) −1.05025 2.53553i −0.0582575 0.140646i
\(326\) 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
\(331\) −1.29289 + 0.535534i −0.0710638 + 0.0294356i −0.417932 0.908478i \(-0.637245\pi\)
0.346868 + 0.937914i \(0.387245\pi\)
\(332\) 0 0
\(333\) −0.707107 + 1.70711i −0.0387492 + 0.0935489i
\(334\) 0 0
\(335\) 17.5563i 0.959206i
\(336\) 0 0
\(337\) 16.9706i 0.924445i −0.886764 0.462223i \(-0.847052\pi\)
0.886764 0.462223i \(-0.152948\pi\)
\(338\) 0 0
\(339\) −1.85786 + 4.48528i −0.100905 + 0.243607i
\(340\) 0 0
\(341\) −16.4853 + 6.82843i −0.892728 + 0.369780i
\(342\) 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
\(347\) 1.63604 + 3.94975i 0.0878272 + 0.212034i 0.961690 0.274139i \(-0.0883927\pi\)
−0.873863 + 0.486172i \(0.838393\pi\)
\(348\) 0 0
\(349\) −24.6777 10.2218i −1.32097 0.547162i −0.392901 0.919581i \(-0.628528\pi\)
−0.928065 + 0.372419i \(0.878528\pi\)
\(350\) 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
\(355\) −22.3137 9.24264i −1.18429 0.490548i
\(356\) 0 0
\(357\) −1.17157 2.82843i −0.0620062 0.149696i
\(358\) 0 0
\(359\) 17.8284 17.8284i 0.940948 0.940948i −0.0574027 0.998351i \(-0.518282\pi\)
0.998351 + 0.0574027i \(0.0182819\pi\)
\(360\) 0 0
\(361\) 2.05025 + 2.05025i 0.107908 + 0.107908i
\(362\) 0 0
\(363\) −6.29289 + 2.60660i −0.330291 + 0.136811i
\(364\) 0 0
\(365\) 11.1005 26.7990i 0.581027 1.40272i
\(366\) 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
\(371\) −0.656854 + 1.58579i −0.0341022 + 0.0823299i
\(372\) 0 0
\(373\) 10.2929 4.26346i 0.532946 0.220753i −0.0999471 0.994993i \(-0.531867\pi\)
0.632893 + 0.774239i \(0.281867\pi\)
\(374\) 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
\(379\) −13.6777 33.0208i −0.702575 1.69617i −0.717769 0.696281i \(-0.754837\pi\)
0.0151948 0.999885i \(-0.495163\pi\)
\(380\) 0 0
\(381\) 9.17157 + 3.79899i 0.469874 + 0.194628i
\(382\) 0 0
\(383\) 16.9706 0.867155 0.433578 0.901116i \(-0.357251\pi\)
0.433578 + 0.901116i \(0.357251\pi\)
\(384\) 0 0
\(385\) −18.4853 −0.942097
\(386\) 0 0
\(387\) −11.3640 4.70711i −0.577663 0.239276i
\(388\) 0 0
\(389\) 8.39340 + 20.2635i 0.425562 + 1.02740i 0.980679 + 0.195625i \(0.0626737\pi\)
−0.555117 + 0.831773i \(0.687326\pi\)
\(390\) 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
\(395\) −16.2426 + 6.72792i −0.817256 + 0.338518i
\(396\) 0 0
\(397\) 9.22183 22.2635i 0.462830 1.11737i −0.504400 0.863470i \(-0.668286\pi\)
0.967230 0.253901i \(-0.0817137\pi\)
\(398\) 0 0
\(399\) 4.34315i 0.217429i
\(400\) 0 0
\(401\) 2.82843i 0.141245i −0.997503 0.0706225i \(-0.977501\pi\)
0.997503 0.0706225i \(-0.0224986\pi\)
\(402\) 0 0
\(403\) −1.17157 + 2.82843i −0.0583602 + 0.140894i
\(404\) 0 0
\(405\) 11.0208 4.56497i 0.547629 0.226835i
\(406\) 0 0
\(407\) 2.41421 + 2.41421i 0.119668 + 0.119668i
\(408\) 0 0
\(409\) 21.4853 21.4853i 1.06238 1.06238i 0.0644584 0.997920i \(-0.479468\pi\)
0.997920 0.0644584i \(-0.0205320\pi\)
\(410\) 0 0
\(411\) 3.58579 + 8.65685i 0.176874 + 0.427011i
\(412\) 0 0
\(413\) 6.41421 + 2.65685i 0.315623 + 0.130735i
\(414\) 0 0
\(415\) −14.3848 −0.706121
\(416\) 0 0
\(417\) −10.9289 −0.535192
\(418\) 0 0
\(419\) 12.6066 + 5.22183i 0.615873 + 0.255103i 0.668737 0.743499i \(-0.266835\pi\)
−0.0528644 + 0.998602i \(0.516835\pi\)
\(420\) 0 0
\(421\) −6.29289 15.1924i −0.306697 0.740432i −0.999808 0.0196009i \(-0.993760\pi\)
0.693111 0.720831i \(-0.256240\pi\)
\(422\) 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
\(427\) 2.41421 1.00000i 0.116832 0.0483934i
\(428\) 0 0
\(429\) −1.00000 + 2.41421i −0.0482805 + 0.116559i
\(430\) 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 \(-0.878400\pi\)
0.927914 0.372795i \(-0.121600\pi\)
\(434\) 0 0
\(435\) −2.89949 + 7.00000i −0.139020 + 0.335624i
\(436\) 0 0
\(437\) −30.5563 + 12.6569i −1.46171 + 0.605459i
\(438\) 0 0
\(439\) 17.0000 + 17.0000i 0.811366 + 0.811366i 0.984839 0.173473i \(-0.0554989\pi\)
−0.173473 + 0.984839i \(0.555499\pi\)
\(440\) 0 0
\(441\) 8.53553 8.53553i 0.406454 0.406454i
\(442\) 0 0
\(443\) 0.606602 + 1.46447i 0.0288205 + 0.0695789i 0.937635 0.347623i \(-0.113011\pi\)
−0.908814 + 0.417201i \(0.863011\pi\)
\(444\) 0 0
\(445\) −33.1421 13.7279i −1.57109 0.650766i
\(446\) 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
\(451\) 1.00000 + 0.414214i 0.0470882 + 0.0195046i
\(452\) 0 0
\(453\) −0.615224 1.48528i −0.0289057 0.0697846i
\(454\) 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 \(-0.329639\pi\)
−0.860164 + 0.510017i \(0.829639\pi\)
\(458\) 0 0
\(459\) 10.8284 4.48528i 0.505428 0.209355i
\(460\) 0 0
\(461\) −0.636039 + 1.53553i −0.0296233 + 0.0715169i −0.937999 0.346638i \(-0.887323\pi\)
0.908376 + 0.418155i \(0.137323\pi\)
\(462\) 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
\(467\) −9.09188 + 21.9497i −0.420722 + 1.01571i 0.561413 + 0.827536i \(0.310258\pi\)
−0.982135 + 0.188177i \(0.939742\pi\)
\(468\) 0 0
\(469\) 7.82843 3.24264i 0.361483 0.149731i
\(470\) 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
\(475\) 5.50610 + 13.2929i 0.252637 + 0.609920i
\(476\) 0 0
\(477\) −2.70711 1.12132i −0.123950 0.0513417i
\(478\) 0 0
\(479\) −28.9706 −1.32370 −0.661849 0.749637i \(-0.730228\pi\)
−0.661849 + 0.749637i \(0.730228\pi\)
\(480\) 0 0
\(481\) 0.585786 0.0267096
\(482\) 0 0
\(483\) −8.24264 3.41421i −0.375053 0.155352i
\(484\) 0 0
\(485\) 20.7279 + 50.0416i 0.941206 + 2.27227i
\(486\) 0 0
\(487\) 11.0000 11.0000i 0.498458 0.498458i −0.412500 0.910958i \(-0.635344\pi\)
0.910958 + 0.412500i \(0.135344\pi\)
\(488\) 0 0
\(489\) −0.272078 0.272078i −0.0123038 0.0123038i
\(490\) 0 0
\(491\) 39.3345 16.2929i 1.77514 0.735288i 0.781343 0.624102i \(-0.214535\pi\)
0.993800 0.111186i \(-0.0354648\pi\)
\(492\) 0 0
\(493\) 3.65685 8.82843i 0.164696 0.397612i
\(494\) 0 0
\(495\) 31.5563i 1.41835i
\(496\) 0 0
\(497\) 11.6569i 0.522881i
\(498\) 0 0
\(499\) −0.949747 + 2.29289i −0.0425165 + 0.102644i −0.943711 0.330771i \(-0.892691\pi\)
0.901195 + 0.433415i \(0.142691\pi\)
\(500\) 0 0
\(501\) 14.6569 6.07107i 0.654820 0.271235i
\(502\) 0 0
\(503\) 11.1421 + 11.1421i 0.496803 + 0.496803i 0.910441 0.413638i \(-0.135742\pi\)
−0.413638 + 0.910441i \(0.635742\pi\)
\(504\) 0 0
\(505\) 7.38478 7.38478i 0.328618 0.328618i
\(506\) 0 0
\(507\) −3.63604 8.77817i −0.161482 0.389852i
\(508\) 0 0
\(509\) 26.0919 + 10.8076i 1.15650 + 0.479039i 0.876709 0.481021i \(-0.159734\pi\)
0.279793 + 0.960060i \(0.409734\pi\)
\(510\) 0 0
\(511\) −14.0000 −0.619324
\(512\) 0 0
\(513\) 16.6274 0.734118
\(514\) 0 0
\(515\) 36.3137 + 15.0416i 1.60017 + 0.662813i
\(516\) 0 0
\(517\) −0.585786 1.41421i −0.0257629 0.0621970i
\(518\) 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 \(-0.216974\pi\)
−0.630071 + 0.776537i \(0.716974\pi\)
\(522\) 0 0
\(523\) 19.1924 7.94975i 0.839225 0.347618i 0.0786768 0.996900i \(-0.474930\pi\)
0.760548 + 0.649282i \(0.224930\pi\)
\(524\) 0 0
\(525\) −1.48528 + 3.58579i −0.0648230 + 0.156497i
\(526\) 0 0
\(527\) 11.3137i 0.492833i
\(528\) 0 0
\(529\) 44.9411i 1.95396i
\(530\) 0 0
\(531\) −4.53553 + 10.9497i −0.196825 + 0.475179i
\(532\) 0 0
\(533\) 0.171573 0.0710678i 0.00743165 0.00307829i
\(534\) 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
\(539\) −8.53553 20.6066i −0.367651 0.887589i
\(540\) 0 0
\(541\) 27.2635 + 11.2929i 1.17215 + 0.485519i 0.881902 0.471433i \(-0.156263\pi\)
0.290246 + 0.956952i \(0.406263\pi\)
\(542\) 0 0
\(543\) 13.4142 0.575659
\(544\) 0 0
\(545\) −43.6985 −1.87184
\(546\) 0 0
\(547\) −17.5355 7.26346i −0.749765 0.310563i −0.0251195 0.999684i \(-0.507997\pi\)
−0.724646 + 0.689122i \(0.757997\pi\)
\(548\) 0 0
\(549\) 1.70711 + 4.12132i 0.0728575 + 0.175894i
\(550\) 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
\(555\) 1.58579 0.656854i 0.0673129 0.0278819i
\(556\) 0 0
\(557\) −15.1213 + 36.5061i −0.640711 + 1.54681i 0.185012 + 0.982736i \(0.440768\pi\)
−0.825722 + 0.564077i \(0.809232\pi\)
\(558\) 0 0
\(559\) 3.89949i 0.164931i
\(560\) 0 0
\(561\) 9.65685i 0.407713i
\(562\) 0 0
\(563\) 7.87868 19.0208i 0.332047 0.801632i −0.666383 0.745610i \(-0.732158\pi\)
0.998430 0.0560220i \(-0.0178417\pi\)
\(564\) 0 0
\(565\) −17.1716 + 7.11270i −0.722414 + 0.299233i
\(566\) 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 \(-0.606932\pi\)
0.944102 + 0.329654i \(0.106932\pi\)
\(570\) 0 0
\(571\) −2.70711 6.53553i −0.113289 0.273504i 0.857058 0.515220i \(-0.172290\pi\)
−0.970347 + 0.241716i \(0.922290\pi\)
\(572\) 0 0
\(573\) −8.48528 3.51472i −0.354478 0.146829i
\(574\) 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
\(579\) 1.07107 + 0.443651i 0.0445121 + 0.0184375i
\(580\) 0 0
\(581\) 2.65685 + 6.41421i 0.110225 + 0.266106i
\(582\) 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
\(587\) −12.6066 + 5.22183i −0.520330 + 0.215528i −0.627362 0.778728i \(-0.715865\pi\)
0.107032 + 0.994256i \(0.465865\pi\)
\(588\) 0 0
\(589\) 6.14214 14.8284i 0.253082 0.610995i
\(590\) 0 0
\(591\) 9.27208i 0.381402i
\(592\) 0 0
\(593\) 28.2843i 1.16150i −0.814083 0.580748i \(-0.802760\pi\)
0.814083 0.580748i \(-0.197240\pi\)
\(594\) 0 0
\(595\) 4.48528 10.8284i 0.183879 0.443922i
\(596\) 0 0
\(597\) −15.9706 + 6.61522i −0.653632 + 0.270743i
\(598\) 0 0
\(599\) 26.6569 + 26.6569i 1.08917 + 1.08917i 0.995614 + 0.0935555i \(0.0298232\pi\)
0.0935555 + 0.995614i \(0.470177\pi\)
\(600\) 0 0
\(601\) −21.9706 + 21.9706i −0.896198 + 0.896198i −0.995097 0.0988995i \(-0.968468\pi\)
0.0988995 + 0.995097i \(0.468468\pi\)
\(602\) 0 0
\(603\) 5.53553 + 13.3640i 0.225424 + 0.544223i
\(604\) 0 0
\(605\) −24.0919 9.97918i −0.979474 0.405712i
\(606\) 0 0
\(607\) 32.9706 1.33823 0.669117 0.743157i \(-0.266673\pi\)
0.669117 + 0.743157i \(0.266673\pi\)
\(608\) 0 0
\(609\) 3.65685 0.148183
\(610\) 0 0
\(611\) −0.242641 0.100505i −0.00981619 0.00406600i
\(612\) 0 0
\(613\) −1.32233 3.19239i −0.0534084 0.128939i 0.894923 0.446220i \(-0.147230\pi\)
−0.948332 + 0.317281i \(0.897230\pi\)
\(614\) 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 \(-0.0251792\pi\)
−0.0790202 + 0.996873i \(0.525179\pi\)
\(618\) 0 0
\(619\) −21.7782 + 9.02082i −0.875339 + 0.362577i −0.774687 0.632345i \(-0.782093\pi\)
−0.100651 + 0.994922i \(0.532093\pi\)
\(620\) 0 0
\(621\) 13.0711 31.5563i 0.524524 1.26631i
\(622\) 0 0
\(623\) 17.3137i 0.693659i
\(624\) 0 0
\(625\) 30.0711i 1.20284i
\(626\) 0 0
\(627\) 5.24264 12.6569i 0.209371 0.505466i
\(628\) 0 0
\(629\) −2.00000 + 0.828427i −0.0797452 + 0.0330316i
\(630\) 0 0
\(631\) −32.4558 32.4558i −1.29205 1.29205i −0.933519 0.358528i \(-0.883279\pi\)
−0.358528 0.933519i \(-0.616721\pi\)
\(632\) 0 0
\(633\) −10.6569 + 10.6569i −0.423572 + 0.423572i
\(634\) 0 0
\(635\) 14.5442 + 35.1127i 0.577167 + 1.39340i
\(636\) 0 0
\(637\) −3.53553 1.46447i −0.140083 0.0580243i
\(638\) 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
\(643\) 11.4350 + 4.73654i 0.450954 + 0.186791i 0.596588 0.802547i \(-0.296522\pi\)
−0.145635 + 0.989338i \(0.546522\pi\)
\(644\) 0 0
\(645\) 4.37258 + 10.5563i 0.172170 + 0.415656i
\(646\) 0 0
\(647\) −6.17157 + 6.17157i −0.242630 + 0.242630i −0.817937 0.575308i \(-0.804882\pi\)
0.575308 + 0.817937i \(0.304882\pi\)
\(648\) 0 0
\(649\) 15.4853 + 15.4853i 0.607850 + 0.607850i
\(650\) 0 0
\(651\) 4.00000 1.65685i 0.156772 0.0649372i
\(652\) 0 0
\(653\) −2.09188 + 5.05025i −0.0818617 + 0.197632i −0.959511 0.281672i \(-0.909111\pi\)
0.877649 + 0.479304i \(0.159111\pi\)
\(654\) 0 0
\(655\) 51.8995i 2.02788i
\(656\) 0 0
\(657\) 23.8995i 0.932408i
\(658\) 0 0
\(659\) −10.1213 + 24.4350i −0.394271 + 0.951854i 0.594728 + 0.803927i \(0.297260\pi\)
−0.988998 + 0.147926i \(0.952740\pi\)
\(660\) 0 0
\(661\) 41.7487 17.2929i 1.62384 0.672616i 0.629316 0.777149i \(-0.283335\pi\)
0.994521 + 0.104534i \(0.0333350\pi\)
\(662\) 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
\(667\) −10.6569 25.7279i −0.412635 0.996189i
\(668\) 0 0
\(669\) −14.8284 6.14214i −0.573300 0.237469i
\(670\) 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
\(675\) −13.7279 5.68629i −0.528388 0.218865i
\(676\) 0 0
\(677\) −15.6066 37.6777i −0.599810 1.44807i −0.873775 0.486331i \(-0.838335\pi\)
0.273964 0.961740i \(-0.411665\pi\)
\(678\) 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
\(683\) −10.1213 + 4.19239i −0.387282 + 0.160417i −0.567824 0.823150i \(-0.692215\pi\)
0.180543 + 0.983567i \(0.442215\pi\)
\(684\) 0 0
\(685\) −13.7279 + 33.1421i −0.524517 + 1.26630i
\(686\) 0 0
\(687\) 18.4437i 0.703669i
\(688\) 0 0
\(689\) 0.928932i 0.0353895i
\(690\) 0 0
\(691\) 12.5061 30.1924i 0.475754 1.14857i −0.485828 0.874055i \(-0.661482\pi\)
0.961582 0.274518i \(-0.0885183\pi\)
\(692\) 0 0
\(693\) −14.0711 + 5.82843i −0.534516 + 0.221404i
\(694\) 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
\(699\) 1.10051 + 2.65685i 0.0416249 + 0.100491i
\(700\) 0 0
\(701\) −2.87868 1.19239i −0.108726 0.0450359i 0.327657 0.944797i \(-0.393741\pi\)
−0.436383 + 0.899761i \(0.643741\pi\)
\(702\) 0 0
\(703\) −3.07107 −0.115828
\(704\) 0 0
\(705\) −0.769553 −0.0289830
\(706\) 0 0
\(707\) −4.65685 1.92893i −0.175139 0.0725450i
\(708\) 0 0
\(709\) −8.77817 21.1924i −0.329671 0.795897i −0.998616 0.0525851i \(-0.983254\pi\)
0.668945 0.743312i \(-0.266746\pi\)
\(710\) 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
\(715\) −9.24264 + 3.82843i −0.345655 + 0.143175i
\(716\) 0 0
\(717\) 1.55635 3.75736i 0.0581229 0.140321i
\(718\) 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
\(723\) −2.48528 + 6.00000i −0.0924286 + 0.223142i
\(724\) 0 0
\(725\) −11.1924 + 4.63604i −0.415675 + 0.172178i
\(726\) 0 0
\(727\) 9.97056 + 9.97056i 0.369788 + 0.369788i 0.867400 0.497612i \(-0.165790\pi\)
−0.497612 + 0.867400i \(0.665790\pi\)
\(728\) 0 0
\(729\) 0.221825 0.221825i 0.00821576 0.00821576i
\(730\) 0 0
\(731\) −5.51472 13.3137i −0.203969 0.492425i
\(732\) 0 0
\(733\) 33.2635 + 13.7782i 1.22861 + 0.508908i 0.900138 0.435604i \(-0.143465\pi\)
0.328475 + 0.944513i \(0.393465\pi\)
\(734\) 0 0
\(735\) −11.2132 −0.413605
\(736\) 0 0
\(737\) 26.7279 0.984536
\(738\) 0 0
\(739\) 0.464466 + 0.192388i 0.0170857 + 0.00707711i 0.391210 0.920301i \(-0.372057\pi\)
−0.374124 + 0.927379i \(0.622057\pi\)
\(740\) 0 0
\(741\) −0.899495 2.17157i −0.0330438 0.0797747i
\(742\) 0 0
\(743\) −31.6274 + 31.6274i −1.16030 + 1.16030i −0.175887 + 0.984410i \(0.556279\pi\)
−0.984410 + 0.175887i \(0.943721\pi\)
\(744\) 0 0
\(745\) −35.0000 35.0000i −1.28230 1.28230i
\(746\) 0 0
\(747\) −10.9497 + 4.53553i −0.400630 + 0.165947i
\(748\) 0 0
\(749\) 2.41421 5.82843i 0.0882134 0.212966i
\(750\) 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
\(755\) 2.35534 5.68629i 0.0857196 0.206945i
\(756\) 0 0
\(757\) 33.2635 13.7782i 1.20898 0.500776i 0.315090 0.949062i \(-0.397965\pi\)
0.893890 + 0.448285i \(0.147965\pi\)
\(758\) 0 0
\(759\) −19.8995 19.8995i −0.722306 0.722306i
\(760\) 0 0
\(761\) −29.8284 + 29.8284i −1.08128 + 1.08128i −0.0848892 + 0.996390i \(0.527054\pi\)
−0.996390 + 0.0848892i \(0.972946\pi\)
\(762\) 0 0
\(763\) 8.07107 + 19.4853i 0.292192 + 0.705415i
\(764\) 0 0
\(765\) 18.4853 + 7.65685i 0.668337 + 0.276834i
\(766\) 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
\(771\) −4.24264 1.75736i −0.152795 0.0632897i
\(772\) 0 0
\(773\) −12.0919 29.1924i −0.434915 1.04998i −0.977681 0.210094i \(-0.932623\pi\)
0.542766 0.839884i \(-0.317377\pi\)
\(774\) 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
\(779\) −0.899495 + 0.372583i −0.0322278 + 0.0133492i
\(780\) 0 0
\(781\) −14.0711 + 33.9706i −0.503502 + 1.21556i
\(782\) 0 0
\(783\) 14.0000i 0.500319i
\(784\) 0 0
\(785\) 5.41421i 0.193242i
\(786\) 0 0
\(787\) −0.949747 + 2.29289i −0.0338548 + 0.0817328i −0.939903 0.341442i \(-0.889085\pi\)
0.906048 + 0.423175i \(0.139085\pi\)
\(788\) 0 0
\(789\) −5.82843 + 2.41421i −0.207498 + 0.0859483i
\(790\) 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
\(795\) 1.04163 + 2.51472i 0.0369428 + 0.0891879i