Properties

Label 810.2.i.e.109.1
Level $810$
Weight $2$
Character 810.109
Analytic conductor $6.468$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.46788256372\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 810.109
Dual form 810.2.i.e.379.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.86603 - 1.23205i) q^{5} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.86603 - 1.23205i) q^{5} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(5.19615 + 3.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.00000i q^{17} +(-0.133975 - 2.23205i) q^{20} +(1.73205 + 1.00000i) q^{22} +(-3.46410 - 2.00000i) q^{23} +(1.96410 - 4.59808i) q^{25} -6.00000 q^{26} -2.00000i q^{28} +(4.00000 - 6.92820i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.00000 - 1.73205i) q^{34} +(2.00000 - 4.00000i) q^{35} +2.00000i q^{37} +(1.23205 + 1.86603i) q^{40} +(-1.00000 + 1.73205i) q^{41} +(3.46410 - 2.00000i) q^{43} -2.00000 q^{44} +4.00000 q^{46} +(-6.92820 + 4.00000i) q^{47} +(-1.50000 + 2.59808i) q^{49} +(0.598076 + 4.96410i) q^{50} +(5.19615 - 3.00000i) q^{52} -6.00000i q^{53} +(-4.00000 - 2.00000i) q^{55} +(1.00000 + 1.73205i) q^{56} +(5.00000 - 8.66025i) q^{59} +(-1.00000 - 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(13.3923 - 0.803848i) q^{65} +(6.92820 + 4.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} +(0.267949 + 4.46410i) q^{70} +12.0000 q^{71} +4.00000i q^{73} +(-1.00000 - 1.73205i) q^{74} +(-3.46410 - 2.00000i) q^{77} +(-2.00000 - 1.00000i) q^{80} -2.00000i q^{82} +(3.46410 - 2.00000i) q^{83} +(2.46410 + 3.73205i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(1.73205 - 1.00000i) q^{88} +10.0000 q^{89} +12.0000 q^{91} +(-3.46410 + 2.00000i) q^{92} +(4.00000 - 6.92820i) q^{94} +(-6.92820 + 4.00000i) q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{5} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{5} - 4q^{10} - 4q^{11} - 4q^{14} - 2q^{16} - 4q^{20} - 6q^{25} - 24q^{26} + 16q^{31} - 4q^{34} + 8q^{35} - 2q^{40} - 4q^{41} - 8q^{44} + 16q^{46} - 6q^{49} - 8q^{50} - 16q^{55} + 4q^{56} + 20q^{59} - 4q^{61} - 4q^{64} + 12q^{65} + 8q^{70} + 48q^{71} - 4q^{74} - 8q^{80} - 4q^{85} - 8q^{86} + 40q^{89} + 48q^{91} + 16q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.86603 1.23205i 0.834512 0.550990i
\(6\) 0 0
\(7\) 1.73205 1.00000i 0.654654 0.377964i −0.135583 0.990766i \(-0.543291\pi\)
0.790237 + 0.612801i \(0.209957\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.00000 + 2.00000i −0.316228 + 0.632456i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 5.19615 + 3.00000i 1.44115 + 0.832050i 0.997927 0.0643593i \(-0.0205004\pi\)
0.443227 + 0.896410i \(0.353834\pi\)
\(14\) −1.00000 + 1.73205i −0.267261 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −0.133975 2.23205i −0.0299576 0.499102i
\(21\) 0 0
\(22\) 1.73205 + 1.00000i 0.369274 + 0.213201i
\(23\) −3.46410 2.00000i −0.722315 0.417029i 0.0932891 0.995639i \(-0.470262\pi\)
−0.815604 + 0.578610i \(0.803595\pi\)
\(24\) 0 0
\(25\) 1.96410 4.59808i 0.392820 0.919615i
\(26\) −6.00000 −1.17670
\(27\) 0 0
\(28\) 2.00000i 0.377964i
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −1.00000 1.73205i −0.171499 0.297044i
\(35\) 2.00000 4.00000i 0.338062 0.676123i
\(36\) 0 0
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 1.23205 + 1.86603i 0.194804 + 0.295045i
\(41\) −1.00000 + 1.73205i −0.156174 + 0.270501i −0.933486 0.358614i \(-0.883249\pi\)
0.777312 + 0.629115i \(0.216583\pi\)
\(42\) 0 0
\(43\) 3.46410 2.00000i 0.528271 0.304997i −0.212041 0.977261i \(-0.568011\pi\)
0.740312 + 0.672264i \(0.234678\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) −6.92820 + 4.00000i −1.01058 + 0.583460i −0.911362 0.411606i \(-0.864968\pi\)
−0.0992202 + 0.995066i \(0.531635\pi\)
\(48\) 0 0
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) 0.598076 + 4.96410i 0.0845807 + 0.702030i
\(51\) 0 0
\(52\) 5.19615 3.00000i 0.720577 0.416025i
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) 0 0
\(55\) −4.00000 2.00000i −0.539360 0.269680i
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) 0 0
\(58\) 0 0
\(59\) 5.00000 8.66025i 0.650945 1.12747i −0.331949 0.943297i \(-0.607706\pi\)
0.982894 0.184172i \(-0.0589603\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 13.3923 0.803848i 1.66111 0.0997050i
\(66\) 0 0
\(67\) 6.92820 + 4.00000i 0.846415 + 0.488678i 0.859440 0.511237i \(-0.170813\pi\)
−0.0130248 + 0.999915i \(0.504146\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) 0 0
\(70\) 0.267949 + 4.46410i 0.0320261 + 0.533562i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0 0
\(76\) 0 0
\(77\) −3.46410 2.00000i −0.394771 0.227921i
\(78\) 0 0
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −2.00000 1.00000i −0.223607 0.111803i
\(81\) 0 0
\(82\) 2.00000i 0.220863i
\(83\) 3.46410 2.00000i 0.380235 0.219529i −0.297686 0.954664i \(-0.596215\pi\)
0.677920 + 0.735135i \(0.262881\pi\)
\(84\) 0 0
\(85\) 2.46410 + 3.73205i 0.267269 + 0.404798i
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) 1.73205 1.00000i 0.184637 0.106600i
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) 12.0000 1.25794
\(92\) −3.46410 + 2.00000i −0.361158 + 0.208514i
\(93\) 0 0
\(94\) 4.00000 6.92820i 0.412568 0.714590i
\(95\) 0 0
\(96\) 0 0
\(97\) −6.92820 + 4.00000i −0.703452 + 0.406138i −0.808632 0.588315i \(-0.799792\pi\)
0.105180 + 0.994453i \(0.466458\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 4.00000 + 6.92820i 0.398015 + 0.689382i 0.993481 0.113998i \(-0.0363659\pi\)
−0.595466 + 0.803380i \(0.703033\pi\)
\(102\) 0 0
\(103\) −12.1244 7.00000i −1.19465 0.689730i −0.235291 0.971925i \(-0.575604\pi\)
−0.959357 + 0.282194i \(0.908938\pi\)
\(104\) −3.00000 + 5.19615i −0.294174 + 0.509525i
\(105\) 0 0
\(106\) 3.00000 + 5.19615i 0.291386 + 0.504695i
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 4.46410 0.267949i 0.425635 0.0255480i
\(111\) 0 0
\(112\) −1.73205 1.00000i −0.163663 0.0944911i
\(113\) 5.19615 + 3.00000i 0.488813 + 0.282216i 0.724082 0.689714i \(-0.242264\pi\)
−0.235269 + 0.971930i \(0.575597\pi\)
\(114\) 0 0
\(115\) −8.92820 + 0.535898i −0.832559 + 0.0499728i
\(116\) 0 0
\(117\) 0 0
\(118\) 10.0000i 0.920575i
\(119\) 2.00000 + 3.46410i 0.183340 + 0.317554i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 1.73205 + 1.00000i 0.156813 + 0.0905357i
\(123\) 0 0
\(124\) −4.00000 6.92820i −0.359211 0.622171i
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −11.1962 + 7.39230i −0.981968 + 0.648348i
\(131\) 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) −15.5885 + 9.00000i −1.33181 + 0.768922i −0.985577 0.169226i \(-0.945873\pi\)
−0.346235 + 0.938148i \(0.612540\pi\)
\(138\) 0 0
\(139\) −10.0000 + 17.3205i −0.848189 + 1.46911i 0.0346338 + 0.999400i \(0.488974\pi\)
−0.882823 + 0.469706i \(0.844360\pi\)
\(140\) −2.46410 3.73205i −0.208255 0.315416i
\(141\) 0 0
\(142\) −10.3923 + 6.00000i −0.872103 + 0.503509i
\(143\) 12.0000i 1.00349i
\(144\) 0 0
\(145\) 0 0
\(146\) −2.00000 3.46410i −0.165521 0.286691i
\(147\) 0 0
\(148\) 1.73205 + 1.00000i 0.142374 + 0.0821995i
\(149\) −10.0000 + 17.3205i −0.819232 + 1.41895i 0.0870170 + 0.996207i \(0.472267\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 4.00000 0.322329
\(155\) −1.07180 17.8564i −0.0860888 1.43426i
\(156\) 0 0
\(157\) −19.0526 11.0000i −1.52056 0.877896i −0.999706 0.0242497i \(-0.992280\pi\)
−0.520854 0.853646i \(-0.674386\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 2.23205 0.133975i 0.176459 0.0105916i
\(161\) −8.00000 −0.630488
\(162\) 0 0
\(163\) 16.0000i 1.25322i −0.779334 0.626608i \(-0.784443\pi\)
0.779334 0.626608i \(-0.215557\pi\)
\(164\) 1.00000 + 1.73205i 0.0780869 + 0.135250i
\(165\) 0 0
\(166\) −2.00000 + 3.46410i −0.155230 + 0.268866i
\(167\) −10.3923 6.00000i −0.804181 0.464294i 0.0407502 0.999169i \(-0.487025\pi\)
−0.844931 + 0.534875i \(0.820359\pi\)
\(168\) 0 0
\(169\) 11.5000 + 19.9186i 0.884615 + 1.53220i
\(170\) −4.00000 2.00000i −0.306786 0.153393i
\(171\) 0 0
\(172\) 4.00000i 0.304997i
\(173\) 12.1244 7.00000i 0.921798 0.532200i 0.0375896 0.999293i \(-0.488032\pi\)
0.884208 + 0.467093i \(0.154699\pi\)
\(174\) 0 0
\(175\) −1.19615 9.92820i −0.0904206 0.750502i
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 0 0
\(178\) −8.66025 + 5.00000i −0.649113 + 0.374766i
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −10.3923 + 6.00000i −0.770329 + 0.444750i
\(183\) 0 0
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) 2.46410 + 3.73205i 0.181164 + 0.274386i
\(186\) 0 0
\(187\) 3.46410 2.00000i 0.253320 0.146254i
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) 0 0
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0 0
\(193\) −3.46410 2.00000i −0.249351 0.143963i 0.370116 0.928986i \(-0.379318\pi\)
−0.619467 + 0.785022i \(0.712651\pi\)
\(194\) 4.00000 6.92820i 0.287183 0.497416i
\(195\) 0 0
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) 22.0000i 1.56744i 0.621117 + 0.783718i \(0.286679\pi\)
−0.621117 + 0.783718i \(0.713321\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 4.59808 + 1.96410i 0.325133 + 0.138883i
\(201\) 0 0
\(202\) −6.92820 4.00000i −0.487467 0.281439i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.267949 + 4.46410i 0.0187144 + 0.311786i
\(206\) 14.0000 0.975426
\(207\) 0 0
\(208\) 6.00000i 0.416025i
\(209\) 0 0
\(210\) 0 0
\(211\) −6.00000 + 10.3923i −0.413057 + 0.715436i −0.995222 0.0976347i \(-0.968872\pi\)
0.582165 + 0.813070i \(0.302206\pi\)
\(212\) −5.19615 3.00000i −0.356873 0.206041i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) 4.00000 8.00000i 0.272798 0.545595i
\(216\) 0 0
\(217\) 16.0000i 1.08615i
\(218\) 8.66025 5.00000i 0.586546 0.338643i
\(219\) 0 0
\(220\) −3.73205 + 2.46410i −0.251615 + 0.166130i
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) 0 0
\(223\) −22.5167 + 13.0000i −1.50783 + 0.870544i −0.507869 + 0.861435i \(0.669566\pi\)
−0.999959 + 0.00910984i \(0.997100\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) −24.2487 + 14.0000i −1.60944 + 0.929213i −0.619949 + 0.784642i \(0.712847\pi\)
−0.989494 + 0.144571i \(0.953820\pi\)
\(228\) 0 0
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) 7.46410 4.92820i 0.492168 0.324956i
\(231\) 0 0
\(232\) 0 0
\(233\) 14.0000i 0.917170i 0.888650 + 0.458585i \(0.151644\pi\)
−0.888650 + 0.458585i \(0.848356\pi\)
\(234\) 0 0
\(235\) −8.00000 + 16.0000i −0.521862 + 1.04372i
\(236\) −5.00000 8.66025i −0.325472 0.563735i
\(237\) 0 0
\(238\) −3.46410 2.00000i −0.224544 0.129641i
\(239\) 10.0000 17.3205i 0.646846 1.12037i −0.337026 0.941495i \(-0.609421\pi\)
0.983872 0.178875i \(-0.0572458\pi\)
\(240\) 0 0
\(241\) −11.0000 19.0526i −0.708572 1.22728i −0.965387 0.260822i \(-0.916006\pi\)
0.256814 0.966461i \(-0.417327\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 0 0
\(244\) −2.00000 −0.128037
\(245\) 0.401924 + 6.69615i 0.0256780 + 0.427801i
\(246\) 0 0
\(247\) 0 0
\(248\) 6.92820 + 4.00000i 0.439941 + 0.254000i
\(249\) 0 0
\(250\) 7.23205 + 8.52628i 0.457395 + 0.539249i
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) 8.00000i 0.502956i
\(254\) −1.00000 1.73205i −0.0627456 0.108679i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 15.5885 + 9.00000i 0.972381 + 0.561405i 0.899961 0.435970i \(-0.143595\pi\)
0.0724199 + 0.997374i \(0.476928\pi\)
\(258\) 0 0
\(259\) 2.00000 + 3.46410i 0.124274 + 0.215249i
\(260\) 6.00000 12.0000i 0.372104 0.744208i
\(261\) 0 0
\(262\) 18.0000i 1.11204i
\(263\) 3.46410 2.00000i 0.213606 0.123325i −0.389380 0.921077i \(-0.627311\pi\)
0.602986 + 0.797752i \(0.293977\pi\)
\(264\) 0 0
\(265\) −7.39230 11.1962i −0.454106 0.687774i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.92820 4.00000i 0.423207 0.244339i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 1.73205 1.00000i 0.105021 0.0606339i
\(273\) 0 0
\(274\) 9.00000 15.5885i 0.543710 0.941733i
\(275\) −9.92820 + 1.19615i −0.598693 + 0.0721307i
\(276\) 0 0
\(277\) 1.73205 1.00000i 0.104069 0.0600842i −0.447062 0.894503i \(-0.647530\pi\)
0.551131 + 0.834419i \(0.314196\pi\)
\(278\) 20.0000i 1.19952i
\(279\) 0 0
\(280\) 4.00000 + 2.00000i 0.239046 + 0.119523i
\(281\) 9.00000 + 15.5885i 0.536895 + 0.929929i 0.999069 + 0.0431402i \(0.0137362\pi\)
−0.462174 + 0.886789i \(0.652930\pi\)
\(282\) 0 0
\(283\) 13.8564 + 8.00000i 0.823678 + 0.475551i 0.851683 0.524057i \(-0.175582\pi\)
−0.0280052 + 0.999608i \(0.508916\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) 6.00000 + 10.3923i 0.354787 + 0.614510i
\(287\) 4.00000i 0.236113i
\(288\) 0 0
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 3.46410 + 2.00000i 0.202721 + 0.117041i
\(293\) 5.19615 + 3.00000i 0.303562 + 0.175262i 0.644042 0.764990i \(-0.277256\pi\)
−0.340480 + 0.940252i \(0.610589\pi\)
\(294\) 0 0
\(295\) −1.33975 22.3205i −0.0780030 1.29955i
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 20.0000i 1.15857i
\(299\) −12.0000 20.7846i −0.693978 1.20201i
\(300\) 0 0
\(301\) 4.00000 6.92820i 0.230556 0.399335i
\(302\) −6.92820 4.00000i −0.398673 0.230174i
\(303\) 0 0
\(304\) 0 0
\(305\) −4.00000 2.00000i −0.229039 0.114520i
\(306\) 0 0
\(307\) 12.0000i 0.684876i 0.939540 + 0.342438i \(0.111253\pi\)
−0.939540 + 0.342438i \(0.888747\pi\)
\(308\) −3.46410 + 2.00000i −0.197386 + 0.113961i
\(309\) 0 0
\(310\) 9.85641 + 14.9282i 0.559806 + 0.847865i
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) 0 0
\(313\) 3.46410 2.00000i 0.195803 0.113047i −0.398894 0.916997i \(-0.630606\pi\)
0.594696 + 0.803951i \(0.297272\pi\)
\(314\) 22.0000 1.24153
\(315\) 0 0
\(316\) 0 0
\(317\) 1.73205 1.00000i 0.0972817 0.0561656i −0.450570 0.892741i \(-0.648779\pi\)
0.547852 + 0.836576i \(0.315446\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.86603 + 1.23205i −0.104314 + 0.0688737i
\(321\) 0 0
\(322\) 6.92820 4.00000i 0.386094 0.222911i
\(323\) 0 0
\(324\) 0 0
\(325\) 24.0000 18.0000i 1.33128 0.998460i
\(326\) 8.00000 + 13.8564i 0.443079 + 0.767435i
\(327\) 0 0
\(328\) −1.73205 1.00000i −0.0956365 0.0552158i
\(329\) −8.00000 + 13.8564i −0.441054 + 0.763928i
\(330\) 0 0
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) 17.8564 1.07180i 0.975600 0.0585585i
\(336\) 0 0
\(337\) 24.2487 + 14.0000i 1.32091 + 0.762629i 0.983874 0.178863i \(-0.0572418\pi\)
0.337037 + 0.941491i \(0.390575\pi\)
\(338\) −19.9186 11.5000i −1.08343 0.625518i
\(339\) 0 0
\(340\) 4.46410 0.267949i 0.242100 0.0145316i
\(341\) −16.0000 −0.866449
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 2.00000 + 3.46410i 0.107833 + 0.186772i
\(345\) 0 0
\(346\) −7.00000 + 12.1244i −0.376322 + 0.651809i
\(347\) −10.3923 6.00000i −0.557888 0.322097i 0.194409 0.980921i \(-0.437721\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(348\) 0 0
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) 6.00000 + 8.00000i 0.320713 + 0.427618i
\(351\) 0 0
\(352\) 2.00000i 0.106600i
\(353\) 12.1244 7.00000i 0.645314 0.372572i −0.141344 0.989960i \(-0.545142\pi\)
0.786659 + 0.617388i \(0.211809\pi\)
\(354\) 0 0
\(355\) 22.3923 14.7846i 1.18846 0.784686i
\(356\) 5.00000 8.66025i 0.264999 0.458993i
\(357\) 0 0
\(358\) 8.66025 5.00000i 0.457709 0.264258i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −1.73205 + 1.00000i −0.0910346 + 0.0525588i
\(363\) 0 0
\(364\) 6.00000 10.3923i 0.314485 0.544705i
\(365\) 4.92820 + 7.46410i 0.257954 + 0.390689i
\(366\) 0 0
\(367\) 1.73205 1.00000i 0.0904123 0.0521996i −0.454112 0.890945i \(-0.650043\pi\)
0.544524 + 0.838745i \(0.316710\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 0 0
\(370\) −4.00000 2.00000i −0.207950 0.103975i
\(371\) −6.00000 10.3923i −0.311504 0.539542i
\(372\) 0 0
\(373\) 5.19615 + 3.00000i 0.269047 + 0.155334i 0.628454 0.777847i \(-0.283688\pi\)
−0.359408 + 0.933181i \(0.617021\pi\)
\(374\) −2.00000 + 3.46410i −0.103418 + 0.179124i
\(375\) 0 0
\(376\) −4.00000 6.92820i −0.206284 0.357295i
\(377\) 0 0
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 10.3923 + 6.00000i 0.531717 + 0.306987i
\(383\) 13.8564 + 8.00000i 0.708029 + 0.408781i 0.810331 0.585973i \(-0.199287\pi\)
−0.102302 + 0.994753i \(0.532621\pi\)
\(384\) 0 0
\(385\) −8.92820 + 0.535898i −0.455023 + 0.0273119i
\(386\) 4.00000 0.203595
\(387\) 0 0
\(388\) 8.00000i 0.406138i
\(389\) 10.0000 + 17.3205i 0.507020 + 0.878185i 0.999967 + 0.00812520i \(0.00258636\pi\)
−0.492947 + 0.870059i \(0.664080\pi\)
\(390\) 0 0
\(391\) 4.00000 6.92820i 0.202289 0.350374i
\(392\) −2.59808 1.50000i −0.131223 0.0757614i
\(393\) 0 0
\(394\) −11.0000 19.0526i −0.554172 0.959854i
\(395\) 0 0
\(396\) 0 0
\(397\) 2.00000i 0.100377i 0.998740 + 0.0501886i \(0.0159822\pi\)
−0.998740 + 0.0501886i \(0.984018\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −4.96410 + 0.598076i −0.248205 + 0.0299038i
\(401\) −11.0000 + 19.0526i −0.549314 + 0.951439i 0.449008 + 0.893528i \(0.351777\pi\)
−0.998322 + 0.0579116i \(0.981556\pi\)
\(402\) 0 0
\(403\) 41.5692 24.0000i 2.07071 1.19553i
\(404\) 8.00000 0.398015
\(405\) 0 0
\(406\) 0 0
\(407\) 3.46410 2.00000i 0.171709 0.0991363i
\(408\) 0 0
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) −2.46410 3.73205i −0.121693 0.184313i
\(411\) 0 0
\(412\) −12.1244 + 7.00000i −0.597324 + 0.344865i
\(413\) 20.0000i 0.984136i
\(414\) 0 0
\(415\) 4.00000 8.00000i 0.196352 0.392705i
\(416\) 3.00000 + 5.19615i 0.147087 + 0.254762i
\(417\) 0 0
\(418\) 0 0
\(419\) −5.00000 + 8.66025i −0.244266 + 0.423081i −0.961925 0.273314i \(-0.911880\pi\)
0.717659 + 0.696395i \(0.245214\pi\)
\(420\) 0 0
\(421\) −11.0000 19.0526i −0.536107 0.928565i −0.999109 0.0422075i \(-0.986561\pi\)
0.463002 0.886357i \(-0.346772\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 9.19615 + 3.92820i 0.446079 + 0.190546i
\(426\) 0 0
\(427\) −3.46410 2.00000i −0.167640 0.0967868i
\(428\) 10.3923 + 6.00000i 0.502331 + 0.290021i
\(429\) 0 0
\(430\) 0.535898 + 8.92820i 0.0258433 + 0.430556i
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 0 0
\(433\) 4.00000i 0.192228i 0.995370 + 0.0961139i \(0.0306413\pi\)
−0.995370 + 0.0961139i \(0.969359\pi\)
\(434\) 8.00000 + 13.8564i 0.384012 + 0.665129i
\(435\) 0 0
\(436\) −5.00000 + 8.66025i −0.239457 + 0.414751i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 2.00000 4.00000i 0.0953463 0.190693i
\(441\) 0 0
\(442\) 12.0000i 0.570782i
\(443\) −31.1769 + 18.0000i −1.48126 + 0.855206i −0.999774 0.0212481i \(-0.993236\pi\)
−0.481486 + 0.876454i \(0.659903\pi\)
\(444\) 0 0
\(445\) 18.6603 12.3205i 0.884581 0.584048i
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) 0 0
\(448\) −1.73205 + 1.00000i −0.0818317 + 0.0472456i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) 5.19615 3.00000i 0.244406 0.141108i
\(453\) 0 0
\(454\) 14.0000 24.2487i 0.657053 1.13805i
\(455\) 22.3923 14.7846i 1.04977 0.693113i
\(456\) 0 0
\(457\) 27.7128 16.0000i 1.29635 0.748448i 0.316579 0.948566i \(-0.397466\pi\)
0.979772 + 0.200118i \(0.0641325\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) −4.00000 + 8.00000i −0.186501 + 0.373002i
\(461\) −6.00000 10.3923i −0.279448 0.484018i 0.691800 0.722089i \(-0.256818\pi\)
−0.971248 + 0.238071i \(0.923485\pi\)
\(462\) 0 0
\(463\) 5.19615 + 3.00000i 0.241486 + 0.139422i 0.615859 0.787856i \(-0.288809\pi\)
−0.374374 + 0.927278i \(0.622142\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) 12.0000i 0.555294i 0.960683 + 0.277647i \(0.0895545\pi\)
−0.960683 + 0.277647i \(0.910445\pi\)
\(468\) 0 0
\(469\) 16.0000 0.738811
\(470\) −1.07180 17.8564i −0.0494383 0.823655i
\(471\) 0 0
\(472\) 8.66025 + 5.00000i 0.398621 + 0.230144i
\(473\) −6.92820 4.00000i −0.318559 0.183920i
\(474\) 0 0
\(475\) 0 0
\(476\) 4.00000 0.183340
\(477\) 0 0
\(478\) 20.0000i 0.914779i
\(479\) 10.0000 + 17.3205i 0.456912 + 0.791394i 0.998796 0.0490589i \(-0.0156222\pi\)
−0.541884 + 0.840453i \(0.682289\pi\)
\(480\) 0 0
\(481\) −6.00000 + 10.3923i −0.273576 + 0.473848i
\(482\) 19.0526 + 11.0000i 0.867820 + 0.501036i
\(483\) 0 0
\(484\) −3.50000 6.06218i −0.159091 0.275554i
\(485\) −8.00000 + 16.0000i −0.363261 + 0.726523i
\(486\) 0 0
\(487\) 18.0000i 0.815658i −0.913058 0.407829i \(-0.866286\pi\)
0.913058 0.407829i \(-0.133714\pi\)
\(488\) 1.73205 1.00000i 0.0784063 0.0452679i
\(489\) 0 0
\(490\) −3.69615 5.59808i −0.166975 0.252895i
\(491\) 9.00000 15.5885i 0.406164 0.703497i −0.588292 0.808649i \(-0.700199\pi\)
0.994456 + 0.105151i \(0.0335327\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 20.7846 12.0000i 0.932317 0.538274i
\(498\) 0 0
\(499\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(500\) −10.5263 3.76795i −0.470750 0.168508i
\(501\) 0 0
\(502\) 15.5885 9.00000i 0.695747 0.401690i
\(503\) 24.0000i 1.07011i 0.844818 + 0.535054i \(0.179709\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(504\) 0 0
\(505\) 16.0000 + 8.00000i 0.711991 + 0.355995i
\(506\) −4.00000 6.92820i −0.177822 0.307996i
\(507\) 0 0
\(508\) 1.73205 + 1.00000i 0.0768473 + 0.0443678i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) 4.00000 + 6.92820i 0.176950 + 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −18.0000 −0.793946
\(515\) −31.2487 + 1.87564i −1.37698 + 0.0826508i
\(516\) 0 0
\(517\) 13.8564 + 8.00000i 0.609404 + 0.351840i
\(518\) −3.46410 2.00000i −0.152204 0.0878750i
\(519\) 0 0
\(520\) 0.803848 + 13.3923i 0.0352510 + 0.587291i
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) −9.00000 15.5885i −0.393167 0.680985i
\(525\) 0 0
\(526\) −2.00000 + 3.46410i −0.0872041 + 0.151042i
\(527\) 13.8564 + 8.00000i 0.603595 + 0.348485i
\(528\) 0 0
\(529\) −3.50000 6.06218i −0.152174 0.263573i
\(530\) 12.0000 + 6.00000i 0.521247 + 0.260623i
\(531\) 0 0
\(532\) 0 0
\(533\) −10.3923 + 6.00000i −0.450141 + 0.259889i
\(534\) 0 0
\(535\) 14.7846 + 22.3923i 0.639194 + 0.968104i
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) 0 0
\(538\) 0 0
\(539\) 6.00000 0.258438
\(540\) 0 0
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 6.92820 4.00000i 0.297592 0.171815i
\(543\) 0 0
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) −18.6603 + 12.3205i −0.799317 + 0.527753i
\(546\) 0 0
\(547\) −24.2487 + 14.0000i −1.03680 + 0.598597i −0.918925 0.394432i \(-0.870941\pi\)
−0.117875 + 0.993028i \(0.537608\pi\)
\(548\) 18.0000i 0.768922i
\(549\) 0 0
\(550\) 8.00000 6.00000i 0.341121 0.255841i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −1.00000 + 1.73205i −0.0424859 + 0.0735878i
\(555\) 0 0
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) 18.0000i 0.762684i −0.924434 0.381342i \(-0.875462\pi\)
0.924434 0.381342i \(-0.124538\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) −4.46410 + 0.267949i −0.188643 + 0.0113229i
\(561\) 0 0
\(562\) −15.5885 9.00000i −0.657559 0.379642i
\(563\) −38.1051 22.0000i −1.60594 0.927189i −0.990266 0.139188i \(-0.955551\pi\)
−0.615673 0.788002i \(-0.711116\pi\)
\(564\) 0 0
\(565\) 13.3923 0.803848i 0.563418 0.0338181i
\(566\) −16.0000 −0.672530
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 0 0
\(571\) 4.00000 6.92820i 0.167395 0.289936i −0.770108 0.637913i \(-0.779798\pi\)
0.937503 + 0.347977i \(0.113131\pi\)
\(572\) −10.3923 6.00000i −0.434524 0.250873i
\(573\) 0 0
\(574\) −2.00000 3.46410i −0.0834784 0.144589i
\(575\) −16.0000 + 12.0000i −0.667246 + 0.500435i
\(576\) 0 0
\(577\) 32.0000i 1.33218i 0.745873 + 0.666089i \(0.232033\pi\)
−0.745873 + 0.666089i \(0.767967\pi\)
\(578\) −11.2583 + 6.50000i −0.468285 + 0.270364i
\(579\) 0 0
\(580\) 0 0
\(581\) 4.00000 6.92820i 0.165948 0.287430i
\(582\) 0 0
\(583\) −10.3923 + 6.00000i −0.430405 + 0.248495i
\(584\) −4.00000 −0.165521
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 10.3923 6.00000i 0.428936 0.247647i −0.269957 0.962872i \(-0.587010\pi\)
0.698893 + 0.715226i \(0.253676\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 12.3205 + 18.6603i 0.507227 + 0.768231i
\(591\) 0 0
\(592\) 1.73205 1.00000i 0.0711868 0.0410997i
\(593\) 6.00000i 0.246390i −0.992382 0.123195i \(-0.960686\pi\)
0.992382 0.123195i \(-0.0393141\pi\)
\(594\) 0 0
\(595\) 8.00000 + 4.00000i 0.327968 + 0.163984i
\(596\) 10.0000 + 17.3205i 0.409616 + 0.709476i
\(597\) 0 0
\(598\) 20.7846 + 12.0000i 0.849946 + 0.490716i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −1.00000 1.73205i −0.0407909 0.0706518i 0.844909 0.534910i \(-0.179654\pi\)
−0.885700 + 0.464258i \(0.846321\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) −0.937822 15.6244i −0.0381279 0.635220i
\(606\) 0 0
\(607\) −19.0526 11.0000i −0.773320 0.446476i 0.0607380 0.998154i \(-0.480655\pi\)
−0.834058 + 0.551678i \(0.813988\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 4.46410 0.267949i 0.180746 0.0108489i
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) 26.0000i 1.05013i −0.851062 0.525065i \(-0.824041\pi\)
0.851062 0.525065i \(-0.175959\pi\)
\(614\) −6.00000 10.3923i −0.242140 0.419399i
\(615\) 0 0
\(616\) 2.00000 3.46410i 0.0805823 0.139573i
\(617\) −1.73205 1.00000i −0.0697297 0.0402585i 0.464730 0.885453i \(-0.346151\pi\)
−0.534460 + 0.845194i \(0.679485\pi\)
\(618\) 0 0
\(619\) 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i \(-0.0350048\pi\)
−0.592025 + 0.805919i \(0.701671\pi\)
\(620\) −16.0000 8.00000i −0.642575 0.321288i
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) 17.3205 10.0000i 0.693932 0.400642i
\(624\) 0 0
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) −2.00000 + 3.46410i −0.0799361 + 0.138453i
\(627\) 0 0
\(628\) −19.0526 + 11.0000i −0.760280 + 0.438948i
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) 2.46410 + 3.73205i 0.0977849 + 0.148102i
\(636\) 0 0
\(637\) −15.5885 + 9.00000i −0.617637 + 0.356593i
\(638\) 0 0
\(639\) 0 0
\(640\) 1.00000 2.00000i 0.0395285 0.0790569i
\(641\) −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) 0 0
\(643\) −20.7846 12.0000i −0.819665 0.473234i 0.0306359 0.999531i \(-0.490247\pi\)
−0.850301 + 0.526297i \(0.823580\pi\)
\(644\) −4.00000 + 6.92820i −0.157622 + 0.273009i
\(645\) 0 0
\(646\) 0 0
\(647\) 48.0000i 1.88707i −0.331266 0.943537i \(-0.607476\pi\)
0.331266 0.943537i \(-0.392524\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) −11.7846 + 27.5885i −0.462230 + 1.08211i
\(651\) 0 0
\(652\) −13.8564 8.00000i −0.542659 0.313304i
\(653\) 22.5167 + 13.0000i 0.881145 + 0.508729i 0.871036 0.491220i \(-0.163449\pi\)
0.0101092 + 0.999949i \(0.496782\pi\)
\(654\) 0 0
\(655\) −2.41154 40.1769i −0.0942268 1.56984i
\(656\) 2.00000 0.0780869
\(657\) 0 0
\(658\) 16.0000i 0.623745i
\(659\) −25.0000 43.3013i −0.973862 1.68678i −0.683641 0.729818i \(-0.739605\pi\)
−0.290220 0.956960i \(-0.593729\pi\)
\(660\) 0 0
\(661\) −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i \(-0.845717\pi\)
0.845922 + 0.533306i \(0.179051\pi\)
\(662\) −6.92820 4.00000i −0.269272 0.155464i
\(663\) 0 0
\(664\) 2.00000 + 3.46410i 0.0776151 + 0.134433i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −10.3923 + 6.00000i −0.402090 + 0.232147i
\(669\) 0 0
\(670\) −14.9282 + 9.85641i −0.576727 + 0.380786i
\(671\) −2.00000 + 3.46410i −0.0772091 + 0.133730i
\(672\) 0 0
\(673\) −31.1769 + 18.0000i −1.20178 + 0.693849i −0.960951 0.276718i \(-0.910753\pi\)
−0.240831 + 0.970567i \(0.577420\pi\)
\(674\) −28.0000 −1.07852
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 1.73205 1.00000i 0.0665681 0.0384331i −0.466347 0.884602i \(-0.654430\pi\)
0.532915 + 0.846169i \(0.321097\pi\)
\(678\) 0 0
\(679\) −8.00000 + 13.8564i −0.307012 + 0.531760i
\(680\) −3.73205 + 2.46410i −0.143118 + 0.0944940i
\(681\) 0 0
\(682\) 13.8564 8.00000i 0.530589 0.306336i
\(683\) 4.00000i 0.153056i 0.997067 + 0.0765279i \(0.0243834\pi\)
−0.997067 + 0.0765279i \(0.975617\pi\)
\(684\) 0 0
\(685\) −18.0000 + 36.0000i −0.687745 + 1.37549i
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 0 0
\(688\) −3.46410 2.00000i −0.132068 0.0762493i
\(689\) 18.0000 31.1769i 0.685745 1.18775i
\(690\) 0 0
\(691\) 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i \(-0.118041\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 2.67949 + 44.6410i 0.101639 + 1.69333i
\(696\) 0 0
\(697\) −3.46410 2.00000i −0.131212 0.0757554i
\(698\) −8.66025 5.00000i −0.327795 0.189253i
\(699\) 0 0
\(700\) −9.19615 3.92820i −0.347582 0.148472i
\(701\) 32.0000 1.20862 0.604312 0.796748i \(-0.293448\pi\)
0.604312 + 0.796748i \(0.293448\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.00000 + 1.73205i 0.0376889 + 0.0652791i
\(705\) 0 0
\(706\) −7.00000 + 12.1244i −0.263448 + 0.456306i
\(707\) 13.8564 + 8.00000i 0.521124 + 0.300871i
\(708\) 0 0
\(709\) 15.0000 + 25.9808i 0.563337 + 0.975728i 0.997202 + 0.0747503i \(0.0238160\pi\)
−0.433865 + 0.900978i \(0.642851\pi\)
\(710\) −12.0000 + 24.0000i −0.450352 + 0.900704i
\(711\) 0 0
\(712\) 10.0000i 0.374766i
\(713\) −27.7128 + 16.0000i −1.03785 + 0.599205i
\(714\) 0 0
\(715\) −14.7846 22.3923i −0.552913 0.837425i
\(716\) −5.00000 + 8.66025i −0.186859 + 0.323649i
\(717\) 0 0
\(718\) 0 0
\(719\) 40.0000 1.49175 0.745874 0.666087i \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) 0 0
\(721\) −28.0000 −1.04277
\(722\) 16.4545 9.50000i 0.612372 0.353553i
\(723\) 0 0
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) −15.5885 + 9.00000i −0.578144 + 0.333792i −0.760395 0.649460i \(-0.774995\pi\)
0.182252 + 0.983252i \(0.441661\pi\)
\(728\) 12.0000i 0.444750i
\(729\) 0 0
\(730\) −8.00000 4.00000i −0.296093 0.148047i
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 0 0
\(733\) −12.1244 7.00000i −0.447823 0.258551i 0.259087 0.965854i \(-0.416578\pi\)
−0.706910 + 0.707303i \(0.749912\pi\)
\(734\) −1.00000 + 1.73205i −0.0369107 + 0.0639312i
\(735\) 0 0
\(736\) −2.00000 3.46410i −0.0737210 0.127688i
\(737\) 16.0000i 0.589368i
\(738\) 0 0
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 4.46410 0.267949i 0.164104 0.00985001i
\(741\) 0 0
\(742\) 10.3923 + 6.00000i 0.381514 + 0.220267i
\(743\) −20.7846 12.0000i −0.762513 0.440237i 0.0676840 0.997707i \(-0.478439\pi\)
−0.830197 + 0.557470i \(0.811772\pi\)
\(744\) 0 0
\(745\) 2.67949 + 44.6410i 0.0981690 + 1.63552i
\(746\) −6.00000 −0.219676
\(747\) 0 0
\(748\) 4.00000i 0.146254i
\(749\) 12.0000 + 20.7846i 0.438470 + 0.759453i
\(750\) 0 0
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 6.92820 + 4.00000i 0.252646 + 0.145865i
\(753\) 0 0
\(754\) 0 0
\(755\) 16.0000 + 8.00000i 0.582300 + 0.291150i
\(756\) 0 0
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 17.3205 10.0000i 0.629109 0.363216i
\(759\) 0 0
\(760\) 0 0
\(761\) 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i \(-0.727548\pi\)
0.981764 + 0.190101i \(0.0608816\pi\)
\(762\) 0 0
\(763\) −17.3205 + 10.0000i −0.627044 + 0.362024i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) 51.9615 30.0000i 1.87622 1.08324i
\(768\) 0 0
\(769\) −15.0000 + 25.9808i −0.540914 + 0.936890i 0.457938 + 0.888984i \(0.348588\pi\)
−0.998852 + 0.0479061i \(0.984745\pi\)
\(770\) 7.46410 4.92820i 0.268988 0.177600i
\(771\) 0 0
\(772\) −3.46410 + 2.00000i −0.124676 + 0.0719816i
\(773\) 54.0000i 1.94225i 0.238581 + 0.971123i \(0.423318\pi\)
−0.238581 + 0.971123i \(0.576682\pi\)
\(774\) 0 0
\(775\) −24.0000 32.0000i −0.862105 1.14947i
\(776\) −4.00000 6.92820i −0.143592 0.248708i
\(777\) 0 0
\(778\) −17.3205 10.0000i −0.620970 0.358517i
\(779\) 0 0
\(780\) 0 0
\(781\) −12.0000 20.7846i −0.429394 0.743732i
\(782\) 8.00000i 0.286079i
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −49.1051 + 2.94744i −1.75264 + 0.105199i
\(786\) 0 0
\(787\) −27.7128 16.0000i −0.987855 0.570338i −0.0832226 0.996531i \(-0.526521\pi\)
−0.904632 + 0.426193i \(0.859855\pi\)
\(788\) 19.0526 + 11.0000i 0.678719 + 0.391859i
\(789\) 0 0
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 0 0