Properties

Label 810.2.i.b.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.b.379.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} +(-1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} +(-1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-5.19615 - 3.00000i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.00000i q^{17} +(1.86603 + 1.23205i) q^{20} +(-1.73205 - 1.00000i) q^{22} +(-3.46410 - 2.00000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +6.00000 q^{26} +2.00000i q^{28} +(4.00000 - 6.92820i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.00000 - 1.73205i) q^{34} +(-2.00000 - 4.00000i) q^{35} -2.00000i q^{37} +(-2.23205 - 0.133975i) q^{40} +(1.00000 - 1.73205i) q^{41} +(-3.46410 + 2.00000i) q^{43} +2.00000 q^{44} +4.00000 q^{46} +(-6.92820 + 4.00000i) q^{47} +(-1.50000 + 2.59808i) q^{49} +(4.59808 - 1.96410i) q^{50} +(-5.19615 + 3.00000i) q^{52} -6.00000i q^{53} +(-4.00000 + 2.00000i) q^{55} +(-1.00000 - 1.73205i) q^{56} +(-5.00000 + 8.66025i) q^{59} +(-1.00000 - 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(7.39230 - 11.1962i) q^{65} +(-6.92820 - 4.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} +(3.73205 + 2.46410i) q^{70} -12.0000 q^{71} -4.00000i q^{73} +(1.00000 + 1.73205i) q^{74} +(-3.46410 - 2.00000i) q^{77} +(2.00000 - 1.00000i) q^{80} +2.00000i q^{82} +(3.46410 - 2.00000i) q^{83} +(-4.46410 - 0.267949i) q^{85} +(2.00000 - 3.46410i) q^{86} +(-1.73205 + 1.00000i) q^{88} -10.0000 q^{89} +12.0000 q^{91} +(-3.46410 + 2.00000i) q^{92} +(4.00000 - 6.92820i) q^{94} +(6.92820 - 4.00000i) q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{5} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{5} - 4q^{10} + 4q^{11} + 4q^{14} - 2q^{16} + 4q^{20} - 6q^{25} + 24q^{26} + 16q^{31} - 4q^{34} - 8q^{35} - 2q^{40} + 4q^{41} + 8q^{44} + 16q^{46} - 6q^{49} + 8q^{50} - 16q^{55} - 4q^{56} - 20q^{59} - 4q^{61} - 4q^{64} - 12q^{65} + 8q^{70} - 48q^{71} + 4q^{74} + 8q^{80} - 4q^{85} + 8q^{86} - 40q^{89} + 48q^{91} + 16q^{94} + O(q^{100}) \)

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
\(5\) −0.133975 + 2.23205i −0.0599153 + 0.998203i
\(6\) 0 0
\(7\) −1.73205 + 1.00000i −0.654654 + 0.377964i −0.790237 0.612801i \(-0.790043\pi\)
0.135583 + 0.990766i \(0.456709\pi\)
\(8\) 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 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) −5.19615 3.00000i −1.44115 0.832050i −0.443227 0.896410i \(-0.646166\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) 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 \(0.5\pi\)
\(20\) 1.86603 + 1.23205i 0.417256 + 0.275495i
\(21\) 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
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) 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 \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −2.23205 0.133975i −0.352918 0.0211832i
\(41\) 1.00000 1.73205i 0.156174 0.270501i −0.777312 0.629115i \(-0.783417\pi\)
0.933486 + 0.358614i \(0.116751\pi\)
\(42\) 0 0
\(43\) −3.46410 + 2.00000i −0.528271 + 0.304997i −0.740312 0.672264i \(-0.765322\pi\)
0.212041 + 0.977261i \(0.431989\pi\)
\(44\) 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
\(50\) 4.59808 1.96410i 0.650266 0.277766i
\(51\) 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 \(0.392294\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(60\) 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
\(65\) 7.39230 11.1962i 0.916903 1.38871i
\(66\) 0 0
\(67\) −6.92820 4.00000i −0.846415 0.488678i 0.0130248 0.999915i \(-0.495854\pi\)
−0.859440 + 0.511237i \(0.829187\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) 0 0
\(70\) 3.73205 + 2.46410i 0.446065 + 0.294516i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 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
\(85\) −4.46410 0.267949i −0.484200 0.0290632i
\(86\) 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 \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 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 −0.105180 0.994453i \(-0.533542\pi\)
0.808632 + 0.588315i \(0.200208\pi\)
\(98\) 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 0.595466 0.803380i \(-0.296967\pi\)
−0.993481 + 0.113998i \(0.963634\pi\)
\(102\) 0 0
\(103\) 12.1244 + 7.00000i 1.19465 + 0.689730i 0.959357 0.282194i \(-0.0910623\pi\)
0.235291 + 0.971925i \(0.424396\pi\)
\(104\) 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 \(0.658969\pi\)
\(110\) 2.46410 3.73205i 0.234943 0.355837i
\(111\) 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
\(115\) 4.92820 7.46410i 0.459557 0.696031i
\(116\) 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 \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −0.803848 + 13.3923i −0.0705021 + 1.17458i
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 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 \(0.844360\pi\)
\(140\) −4.46410 0.267949i −0.377285 0.0226458i
\(141\) 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 \(-0.527733\pi\)
0.906249 0.422744i \(-0.138933\pi\)
\(150\) 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
\(155\) 14.9282 + 9.85641i 1.19906 + 0.791686i
\(156\) 0 0
\(157\) 19.0526 + 11.0000i 1.52056 + 0.877896i 0.999706 + 0.0242497i \(0.00771967\pi\)
0.520854 + 0.853646i \(0.325614\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −1.23205 + 1.86603i −0.0974022 + 0.147522i
\(161\) 8.00000 0.630488
\(162\) 0 0
\(163\) 16.0000i 1.25322i 0.779334 + 0.626608i \(0.215557\pi\)
−0.779334 + 0.626608i \(0.784443\pi\)
\(164\) −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
\(175\) 9.19615 3.92820i 0.695164 0.296944i
\(176\) 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 \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 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
\(185\) 4.46410 + 0.267949i 0.328207 + 0.0197000i
\(186\) 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 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) 3.46410 + 2.00000i 0.249351 + 0.143963i 0.619467 0.785022i \(-0.287349\pi\)
−0.370116 + 0.928986i \(0.620682\pi\)
\(194\) −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 \(0.5\pi\)
\(200\) 0.598076 4.96410i 0.0422904 0.351015i
\(201\) 0 0
\(202\) 6.92820 + 4.00000i 0.487467 + 0.281439i
\(203\) 0 0
\(204\) 0 0
\(205\) 3.73205 + 2.46410i 0.260658 + 0.172100i
\(206\) −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
\(220\) −0.267949 + 4.46410i −0.0180651 + 0.300970i
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) 22.5167 13.0000i 1.50783 0.870544i 0.507869 0.861435i \(-0.330434\pi\)
0.999959 0.00910984i \(-0.00289979\pi\)
\(224\) −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 \(0.273853\pi\)
\(230\) −0.535898 + 8.92820i −0.0353361 + 0.588708i
\(231\) 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 \(0.390579\pi\)
−0.983872 + 0.178875i \(0.942754\pi\)
\(240\) 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
\(245\) −5.59808 3.69615i −0.357648 0.236139i
\(246\) 0 0
\(247\) 0 0
\(248\) 6.92820 + 4.00000i 0.439941 + 0.254000i
\(249\) 0 0
\(250\) 3.76795 + 10.5263i 0.238306 + 0.665740i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 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
\(265\) 13.3923 + 0.803848i 0.822683 + 0.0493800i
\(266\) 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
\(275\) −3.92820 9.19615i −0.236880 0.554549i
\(276\) 0 0
\(277\) −1.73205 + 1.00000i −0.104069 + 0.0600842i −0.551131 0.834419i \(-0.685804\pi\)
0.447062 + 0.894503i \(0.352470\pi\)
\(278\) 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 \(-0.986264\pi\)
0.462174 0.886789i \(-0.347070\pi\)
\(282\) 0 0
\(283\) −13.8564 8.00000i −0.823678 0.475551i 0.0280052 0.999608i \(-0.491084\pi\)
−0.851683 + 0.524057i \(0.824418\pi\)
\(284\) −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
\(295\) −18.6603 12.3205i −1.08644 0.717328i
\(296\) 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 \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) −3.46410 + 2.00000i −0.197386 + 0.113961i
\(309\) 0 0
\(310\) −17.8564 1.07180i −1.01418 0.0608740i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 0 0
\(313\) −3.46410 + 2.00000i −0.195803 + 0.113047i −0.594696 0.803951i \(-0.702728\pi\)
0.398894 + 0.916997i \(0.369394\pi\)
\(314\) −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
\(320\) 0.133975 2.23205i 0.00748941 0.124775i
\(321\) 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
\(335\) 9.85641 14.9282i 0.538513 0.815615i
\(336\) 0 0
\(337\) −24.2487 14.0000i −1.32091 0.762629i −0.337037 0.941491i \(-0.609425\pi\)
−0.983874 + 0.178863i \(0.942758\pi\)
\(338\) −19.9186 11.5000i −1.08343 0.625518i
\(339\) 0 0
\(340\) −2.46410 + 3.73205i −0.133635 + 0.202399i
\(341\) 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
\(355\) 1.60770 26.7846i 0.0853276 1.42158i
\(356\) −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
\(365\) 8.92820 + 0.535898i 0.467324 + 0.0280502i
\(366\) 0 0
\(367\) −1.73205 + 1.00000i −0.0904123 + 0.0521996i −0.544524 0.838745i \(-0.683290\pi\)
0.454112 + 0.890945i \(0.349957\pi\)
\(368\) 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 0.359408 0.933181i \(-0.382979\pi\)
−0.628454 + 0.777847i \(0.716312\pi\)
\(374\) 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
\(385\) 4.92820 7.46410i 0.251164 0.380406i
\(386\) −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 \(-0.997414\pi\)
0.492947 0.870059i \(-0.335920\pi\)
\(390\) 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 \(-0.984018\pi\)
0.998740 0.0501886i \(-0.0159822\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.96410 + 4.59808i 0.0982051 + 0.229904i
\(401\) 11.0000 19.0526i 0.549314 0.951439i −0.449008 0.893528i \(-0.648223\pi\)
0.998322 0.0579116i \(-0.0184442\pi\)
\(402\) 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 \(0.246188\pi\)
\(410\) −4.46410 0.267949i −0.220466 0.0132331i
\(411\) 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 −0.717659 0.696395i \(-0.754786\pi\)
0.961925 + 0.273314i \(0.0881197\pi\)
\(420\) 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
\(425\) 1.19615 9.92820i 0.0580219 0.481589i
\(426\) 0 0
\(427\) 3.46410 + 2.00000i 0.167640 + 0.0967868i
\(428\) 10.3923 + 6.00000i 0.502331 + 0.290021i
\(429\) 0 0
\(430\) 7.46410 + 4.92820i 0.359951 + 0.237659i
\(431\) −32.0000 −1.54139 −0.770693 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) 4.00000i 0.192228i −0.995370 0.0961139i \(-0.969359\pi\)
0.995370 0.0961139i \(-0.0306413\pi\)
\(434\) −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
\(445\) 1.33975 22.3205i 0.0635100 1.05809i
\(446\) −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 \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 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
\(455\) −1.60770 + 26.7846i −0.0753699 + 1.25568i
\(456\) 0 0
\(457\) −27.7128 + 16.0000i −1.29635 + 0.748448i −0.979772 0.200118i \(-0.935868\pi\)
−0.316579 + 0.948566i \(0.602534\pi\)
\(458\) 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 0.971248 0.238071i \(-0.0765153\pi\)
−0.691800 + 0.722089i \(0.743182\pi\)
\(462\) 0 0
\(463\) −5.19615 3.00000i −0.241486 0.139422i 0.374374 0.927278i \(-0.377858\pi\)
−0.615859 + 0.787856i \(0.711191\pi\)
\(464\) 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
\(470\) 14.9282 + 9.85641i 0.688587 + 0.454642i
\(471\) 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 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) 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 \(0.133714\pi\)
−0.913058 + 0.407829i \(0.866286\pi\)
\(488\) 1.73205 1.00000i 0.0784063 0.0452679i
\(489\) 0 0
\(490\) 6.69615 + 0.401924i 0.302501 + 0.0181571i
\(491\) −9.00000 + 15.5885i −0.406164 + 0.703497i −0.994456 0.105151i \(-0.966467\pi\)
0.588292 + 0.808649i \(0.299801\pi\)
\(492\) 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 \(0.166667\pi\)
\(500\) −8.52628 7.23205i −0.381307 0.323427i
\(501\) 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
\(515\) −17.2487 + 26.1244i −0.760069 + 1.15118i
\(516\) 0 0
\(517\) −13.8564 8.00000i −0.609404 0.351840i
\(518\) −3.46410 2.00000i −0.152204 0.0878750i
\(519\) 0 0
\(520\) 11.1962 + 7.39230i 0.490984 + 0.324174i
\(521\) −22.0000 −0.963837 −0.481919 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) 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
\(535\) −26.7846 1.60770i −1.15800 0.0695067i
\(536\) 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
\(545\) 1.33975 22.3205i 0.0573884 0.956106i
\(546\) 0 0
\(547\) 24.2487 14.0000i 1.03680 0.598597i 0.117875 0.993028i \(-0.462392\pi\)
0.918925 + 0.394432i \(0.129059\pi\)
\(548\) 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
\(560\) −2.46410 + 3.73205i −0.104127 + 0.157708i
\(561\) 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
\(565\) −7.39230 + 11.1962i −0.310997 + 0.471026i
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) 5.00000 + 8.66025i 0.209611 + 0.363057i 0.951592 0.307364i \(-0.0994469\pi\)
−0.741981 + 0.670421i \(0.766114\pi\)
\(570\) 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 \(-0.767967\pi\)
0.745873 0.666089i \(-0.232033\pi\)
\(578\) −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
\(590\) 22.3205 + 1.33975i 0.918921 + 0.0551565i
\(591\) 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
\(605\) 13.0622 + 8.62436i 0.531053 + 0.350630i
\(606\) 0 0
\(607\) 19.0526 + 11.0000i 0.773320 + 0.446476i 0.834058 0.551678i \(-0.186012\pi\)
−0.0607380 + 0.998154i \(0.519345\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −2.46410 + 3.73205i −0.0997686 + 0.151106i
\(611\) 48.0000 1.94187
\(612\) 0 0
\(613\) 26.0000i 1.05013i 0.851062 + 0.525065i \(0.175959\pi\)
−0.851062 + 0.525065i \(0.824041\pi\)
\(614\) 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
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 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
\(635\) 4.46410 + 0.267949i 0.177152 + 0.0106332i
\(636\) 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 0.885098 0.465404i \(-0.154091\pi\)
−0.845601 + 0.533816i \(0.820758\pi\)
\(642\) 0 0
\(643\) 20.7846 + 12.0000i 0.819665 + 0.473234i 0.850301 0.526297i \(-0.176420\pi\)
−0.0306359 + 0.999531i \(0.509753\pi\)
\(644\) 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
\(650\) −29.7846 3.58846i −1.16825 0.140751i
\(651\) 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
\(655\) −33.5885 22.1769i −1.31241 0.866524i
\(656\) −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 \(0.260395\pi\)
0.290220 + 0.956960i \(0.406271\pi\)
\(660\) 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
\(670\) −1.07180 + 17.8564i −0.0414071 + 0.689853i
\(671\) 2.00000 3.46410i 0.0772091 0.133730i
\(672\) 0 0
\(673\) 31.1769 18.0000i 1.20178 0.693849i 0.240831 0.970567i \(-0.422580\pi\)
0.960951 + 0.276718i \(0.0892468\pi\)
\(674\) 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
\(680\) 0.267949 4.46410i 0.0102754 0.171190i
\(681\) 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
\(695\) −37.3205 24.6410i −1.41565 0.934687i
\(696\) 0 0
\(697\) 3.46410 + 2.00000i 0.131212 + 0.0757554i
\(698\) −8.66025 5.00000i −0.327795 0.189253i
\(699\) 0 0
\(700\) 1.19615 9.92820i 0.0452103 0.375251i
\(701\) −32.0000 −1.20862 −0.604312 0.796748i \(-0.706552\pi\)
−0.604312 + 0.796748i \(0.706552\pi\)
\(702\) 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
\(715\) 26.7846 + 1.60770i 1.00169 + 0.0601244i
\(716\) 5.00000 8.66025i 0.186859 0.323649i
\(717\) 0 0
\(718\) 0 0
\(719\) −40.0000 −1.49175 −0.745874 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) 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 −0.182252 0.983252i \(-0.558339\pi\)
0.760395 + 0.649460i \(0.225005\pi\)
\(728\) 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 0.706910 0.707303i \(-0.250088\pi\)
−0.259087 + 0.965854i \(0.583422\pi\)
\(734\) 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 \(0.763152\pi\)
\(740\) 2.46410 3.73205i 0.0905822 0.137193i
\(741\) 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
\(745\) 37.3205 + 24.6410i 1.36732 + 0.902777i
\(746\) 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 \(-0.988428\pi\)
0.999339 0.0363456i \(-0.0115717\pi\)
\(758\) 17.3205 10.0000i 0.629109 0.363216i
\(759\) 0 0
\(760\) 0 0
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) 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 \(0.984745\pi\)
\(770\) −0.535898 + 8.92820i −0.0193124 + 0.321750i
\(771\) 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
\(785\) −27.1051 + 41.0526i −0.967423 + 1.46523i
\(786\) 0 0
\(787\) 27.7128 + 16.0000i 0.987855 + 0.570338i 0.904632 0.426193i \(-0.140145\pi\)
0.0832226 + 0.996531i \(0.473479\pi\)
\(788\) 19.0526 + 11.0000i 0.678719 + 0.391859i
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 12.0000i 0.426132i
\(794\) 1.00000 + 1.73205i 0.0354887 + 0.0614682i
\(795\) 0 0
\(796\) 0 0
\(797\) −1.73205 1.00000i −0.0613524 0.0354218i 0.469010 0.883193i \(-0.344611\pi\)
−0.530362 + 0.847771i \(0.677944\pi\)
\(798\) 0 0
\(799\) −8.00000 13.8564i −0.283020 0.490204i
\(800\) −4.00000 3.00000i −0.141421