Properties

Label 1470.2.n.a.949.2
Level $1470$
Weight $2$
Character 1470.949
Analytic conductor $11.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
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 949.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.949
Dual form 1470.2.n.a.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.23205 - 0.133975i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.866025 + 0.500000i) q^{12} -6.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-2.00000 + 1.00000i) q^{20} +2.00000i q^{22} +(-3.46410 + 2.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(-3.00000 - 5.19615i) q^{26} -1.00000i q^{27} +(1.86603 + 1.23205i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.73205 - 1.00000i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(-1.73205 + 1.00000i) q^{37} +(-3.00000 + 5.19615i) q^{39} +(-1.23205 + 1.86603i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +(1.00000 + 1.73205i) q^{44} +(0.133975 - 2.23205i) q^{45} +(-2.00000 + 3.46410i) q^{46} +(-6.92820 + 4.00000i) q^{47} +1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(1.00000 + 1.73205i) q^{51} +(-5.19615 - 3.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(4.00000 - 2.00000i) q^{55} +(-5.00000 + 8.66025i) q^{59} +(2.23205 + 0.133975i) q^{60} +(1.00000 + 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(-7.39230 + 11.1962i) q^{65} +(1.00000 - 1.73205i) q^{66} +(-6.92820 - 4.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +4.00000 q^{69} +12.0000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.598076 - 4.96410i) q^{75} +6.00000i q^{78} +(-0.133975 + 2.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.73205 + 1.00000i) q^{82} +4.00000i q^{83} +(2.00000 + 4.00000i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(1.73205 + 1.00000i) q^{88} +(5.00000 + 8.66025i) q^{89} +(-1.00000 - 2.00000i) q^{90} +4.00000i q^{92} +(6.92820 - 4.00000i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(0.500000 + 0.866025i) q^{96} -8.00000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{5} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{5} - 4q^{6} + 2q^{9} - 2q^{10} - 4q^{11} + 4q^{15} - 2q^{16} - 8q^{20} - 2q^{24} - 6q^{25} - 12q^{26} + 4q^{30} - 16q^{31} - 8q^{34} + 4q^{36} - 12q^{39} + 2q^{40} - 8q^{41} + 4q^{44} + 4q^{45} - 8q^{46} + 16q^{50} + 4q^{51} - 2q^{54} + 16q^{55} - 20q^{59} + 2q^{60} + 4q^{61} - 4q^{64} + 12q^{65} + 4q^{66} + 16q^{69} + 48q^{71} - 4q^{74} - 8q^{75} - 4q^{80} - 2q^{81} + 8q^{85} - 8q^{86} + 20q^{89} - 4q^{90} - 16q^{94} + 2q^{96} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.86603 1.23205i −0.834512 0.550990i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −2.23205 0.133975i −0.705836 0.0423665i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 6.00000i 1.66410i −0.554700 0.832050i \(-0.687167\pi\)
0.554700 0.832050i \(-0.312833\pi\)
\(14\) 0 0
\(15\) 1.00000 + 2.00000i 0.258199 + 0.516398i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.73205 1.00000i −0.420084 0.242536i 0.275029 0.961436i \(-0.411312\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) −2.00000 + 1.00000i −0.447214 + 0.223607i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) −3.46410 + 2.00000i −0.722315 + 0.417029i −0.815604 0.578610i \(-0.803595\pi\)
0.0932891 + 0.995639i \(0.470262\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 1.96410 + 4.59808i 0.392820 + 0.919615i
\(26\) −3.00000 5.19615i −0.588348 1.01905i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.86603 + 1.23205i 0.340688 + 0.224941i
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 1.73205 1.00000i 0.301511 0.174078i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −1.73205 + 1.00000i −0.284747 + 0.164399i −0.635571 0.772043i \(-0.719235\pi\)
0.350823 + 0.936442i \(0.385902\pi\)
\(38\) 0 0
\(39\) −3.00000 + 5.19615i −0.480384 + 0.832050i
\(40\) −1.23205 + 1.86603i −0.194804 + 0.295045i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 0.133975 2.23205i 0.0199718 0.332734i
\(46\) −2.00000 + 3.46410i −0.294884 + 0.510754i
\(47\) −6.92820 + 4.00000i −1.01058 + 0.583460i −0.911362 0.411606i \(-0.864968\pi\)
−0.0992202 + 0.995066i \(0.531635\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) −5.19615 3.00000i −0.720577 0.416025i
\(53\) −5.19615 3.00000i −0.713746 0.412082i 0.0987002 0.995117i \(-0.468532\pi\)
−0.812447 + 0.583036i \(0.801865\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 4.00000 2.00000i 0.539360 0.269680i
\(56\) 0 0
\(57\) 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 \(0.941040\pi\)
\(60\) 2.23205 + 0.133975i 0.288157 + 0.0172960i
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −7.39230 + 11.1962i −0.916903 + 1.38871i
\(66\) 1.00000 1.73205i 0.123091 0.213201i
\(67\) −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
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) −3.46410 2.00000i −0.405442 0.234082i 0.283387 0.959006i \(-0.408542\pi\)
−0.688830 + 0.724923i \(0.741875\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 0.598076 4.96410i 0.0690599 0.573205i
\(76\) 0 0
\(77\) 0 0
\(78\) 6.00000i 0.679366i
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −0.133975 + 2.23205i −0.0149788 + 0.249551i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.73205 + 1.00000i −0.191273 + 0.110432i
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 2.00000 + 4.00000i 0.216930 + 0.433861i
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) 1.73205 + 1.00000i 0.184637 + 0.106600i
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) −1.00000 2.00000i −0.105409 0.210819i
\(91\) 0 0
\(92\) 4.00000i 0.417029i
\(93\) 6.92820 4.00000i 0.718421 0.414781i
\(94\) −4.00000 + 6.92820i −0.412568 + 0.714590i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 8.00000i 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 4.96410 + 0.598076i 0.496410 + 0.0598076i
\(101\) −4.00000 + 6.92820i −0.398015 + 0.689382i −0.993481 0.113998i \(-0.963634\pi\)
0.595466 + 0.803380i \(0.296967\pi\)
\(102\) 1.73205 + 1.00000i 0.171499 + 0.0990148i
\(103\) 12.1244 7.00000i 1.19465 0.689730i 0.235291 0.971925i \(-0.424396\pi\)
0.959357 + 0.282194i \(0.0910623\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −10.3923 + 6.00000i −1.00466 + 0.580042i −0.909624 0.415432i \(-0.863630\pi\)
−0.0950377 + 0.995474i \(0.530297\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) 2.46410 3.73205i 0.234943 0.355837i
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) 8.92820 + 0.535898i 0.832559 + 0.0499728i
\(116\) 0 0
\(117\) 5.19615 3.00000i 0.480384 0.277350i
\(118\) 10.0000i 0.920575i
\(119\) 0 0
\(120\) 2.00000 1.00000i 0.182574 0.0912871i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 1.73205 + 1.00000i 0.156813 + 0.0905357i
\(123\) 1.73205 + 1.00000i 0.156174 + 0.0901670i
\(124\) 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
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) −0.803848 + 13.3923i −0.0705021 + 1.17458i
\(131\) −9.00000 15.5885i −0.786334 1.36197i −0.928199 0.372084i \(-0.878643\pi\)
0.141865 0.989886i \(-0.454690\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −1.23205 + 1.86603i −0.106038 + 0.160602i
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −15.5885 9.00000i −1.33181 0.768922i −0.346235 0.938148i \(-0.612540\pi\)
−0.985577 + 0.169226i \(0.945873\pi\)
\(138\) 3.46410 2.00000i 0.294884 0.170251i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 10.3923 6.00000i 0.872103 0.503509i
\(143\) 10.3923 + 6.00000i 0.869048 + 0.501745i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) −10.0000 17.3205i −0.819232 1.41895i −0.906249 0.422744i \(-0.861067\pi\)
0.0870170 0.996207i \(-0.472267\pi\)
\(150\) −1.96410 4.59808i −0.160368 0.375431i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 16.0000 8.00000i 1.28515 0.642575i
\(156\) 3.00000 + 5.19615i 0.240192 + 0.416025i
\(157\) −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
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) 1.00000 + 2.00000i 0.0790569 + 0.158114i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 13.8564 8.00000i 1.08532 0.626608i 0.152992 0.988227i \(-0.451109\pi\)
0.932326 + 0.361619i \(0.117776\pi\)
\(164\) −1.00000 + 1.73205i −0.0780869 + 0.135250i
\(165\) −4.46410 0.267949i −0.347530 0.0208598i
\(166\) 2.00000 + 3.46410i 0.155230 + 0.268866i
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) −23.0000 −1.76923
\(170\) 3.73205 + 2.46410i 0.286235 + 0.188988i
\(171\) 0 0
\(172\) −3.46410 2.00000i −0.264135 0.152499i
\(173\) 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
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) 8.66025 5.00000i 0.650945 0.375823i
\(178\) 8.66025 + 5.00000i 0.649113 + 0.374766i
\(179\) 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i \(-0.711416\pi\)
0.990134 + 0.140122i \(0.0447496\pi\)
\(180\) −1.86603 1.23205i −0.139085 0.0918316i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) 4.46410 + 0.267949i 0.328207 + 0.0197000i
\(186\) 4.00000 6.92820i 0.293294 0.508001i
\(187\) 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 \(0.976283\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 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
\(195\) 12.0000 6.00000i 0.859338 0.429669i
\(196\) 0 0
\(197\) 22.0000i 1.56744i −0.621117 0.783718i \(-0.713321\pi\)
0.621117 0.783718i \(-0.286679\pi\)
\(198\) −1.73205 + 1.00000i −0.123091 + 0.0710669i
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 4.59808 1.96410i 0.325133 0.138883i
\(201\) 4.00000 + 6.92820i 0.282138 + 0.488678i
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 3.73205 + 2.46410i 0.260658 + 0.172100i
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) −3.46410 2.00000i −0.240772 0.139010i
\(208\) −5.19615 + 3.00000i −0.360288 + 0.208013i
\(209\) 0 0
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −5.19615 + 3.00000i −0.356873 + 0.206041i
\(213\) −10.3923 6.00000i −0.712069 0.411113i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −4.92820 + 7.46410i −0.336101 + 0.509048i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 10.0000i 0.677285i
\(219\) 2.00000 + 3.46410i 0.135147 + 0.234082i
\(220\) 0.267949 4.46410i 0.0180651 0.300970i
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) 1.73205 1.00000i 0.116248 0.0671156i
\(223\) 26.0000i 1.74109i −0.492090 0.870544i \(-0.663767\pi\)
0.492090 0.870544i \(-0.336233\pi\)
\(224\) 0 0
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) 24.2487 + 14.0000i 1.60944 + 0.929213i 0.989494 + 0.144571i \(0.0461801\pi\)
0.619949 + 0.784642i \(0.287153\pi\)
\(228\) 0 0
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 8.00000 4.00000i 0.527504 0.263752i
\(231\) 0 0
\(232\) 0 0
\(233\) −12.1244 + 7.00000i −0.794293 + 0.458585i −0.841472 0.540301i \(-0.818310\pi\)
0.0471787 + 0.998886i \(0.484977\pi\)
\(234\) 3.00000 5.19615i 0.196116 0.339683i
\(235\) 17.8564 + 1.07180i 1.16482 + 0.0699163i
\(236\) 5.00000 + 8.66025i 0.325472 + 0.563735i
\(237\) 0 0
\(238\) 0 0
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 1.23205 1.86603i 0.0795285 0.120451i
\(241\) 11.0000 19.0526i 0.708572 1.22728i −0.256814 0.966461i \(-0.582673\pi\)
0.965387 0.260822i \(-0.0839937\pi\)
\(242\) 6.06218 + 3.50000i 0.389692 + 0.224989i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) 6.92820 + 4.00000i 0.439941 + 0.254000i
\(249\) 2.00000 3.46410i 0.126745 0.219529i
\(250\) −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
\(255\) 0.267949 4.46410i 0.0167796 0.279553i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −15.5885 + 9.00000i −0.972381 + 0.561405i −0.899961 0.435970i \(-0.856405\pi\)
−0.0724199 + 0.997374i \(0.523072\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) 6.00000 + 12.0000i 0.372104 + 0.744208i
\(261\) 0 0
\(262\) −15.5885 9.00000i −0.963058 0.556022i
\(263\) 3.46410 + 2.00000i 0.213606 + 0.123325i 0.602986 0.797752i \(-0.293977\pi\)
−0.389380 + 0.921077i \(0.627311\pi\)
\(264\) −1.00000 1.73205i −0.0615457 0.106600i
\(265\) 6.00000 + 12.0000i 0.368577 + 0.737154i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) −6.92820 + 4.00000i −0.423207 + 0.244339i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) −0.133975 + 2.23205i −0.00815343 + 0.135838i
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) −9.92820 1.19615i −0.598693 0.0721307i
\(276\) 2.00000 3.46410i 0.120386 0.208514i
\(277\) 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i \(-0.314196\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(278\) −17.3205 + 10.0000i −1.03882 + 0.599760i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 6.92820 4.00000i 0.412568 0.238197i
\(283\) 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
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 0 0
\(291\) −4.00000 + 6.92820i −0.234484 + 0.406138i
\(292\) −3.46410 + 2.00000i −0.202721 + 0.117041i
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) 0 0
\(295\) 20.0000 10.0000i 1.16445 0.582223i
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) 1.73205 + 1.00000i 0.100504 + 0.0580259i
\(298\) −17.3205 10.0000i −1.00335 0.579284i
\(299\) 12.0000 + 20.7846i 0.693978 + 1.20201i
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 6.92820 4.00000i 0.398015 0.229794i
\(304\) 0 0
\(305\) 0.267949 4.46410i 0.0153427 0.255614i
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) 12.0000i 0.684876i 0.939540 + 0.342438i \(0.111253\pi\)
−0.939540 + 0.342438i \(0.888747\pi\)
\(308\) 0 0
\(309\) −14.0000 −0.796432
\(310\) 9.85641 14.9282i 0.559806 0.847865i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 5.19615 + 3.00000i 0.294174 + 0.169842i
\(313\) 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 −0.547852 0.836576i \(-0.684554\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(318\) 5.19615 + 3.00000i 0.291386 + 0.168232i
\(319\) 0 0
\(320\) 1.86603 + 1.23205i 0.104314 + 0.0688737i
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 27.5885 11.7846i 1.53033 0.653693i
\(326\) 8.00000 13.8564i 0.443079 0.767435i
\(327\) −8.66025 + 5.00000i −0.478913 + 0.276501i
\(328\) 2.00000i 0.110432i
\(329\) 0 0
\(330\) −4.00000 + 2.00000i −0.220193 + 0.110096i
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) 3.46410 + 2.00000i 0.190117 + 0.109764i
\(333\) −1.73205 1.00000i −0.0949158 0.0547997i
\(334\) 6.00000 + 10.3923i 0.328305 + 0.568642i
\(335\) 8.00000 + 16.0000i 0.437087 + 0.874173i
\(336\) 0 0
\(337\) 28.0000i 1.52526i 0.646837 + 0.762629i \(0.276092\pi\)
−0.646837 + 0.762629i \(0.723908\pi\)
\(338\) −19.9186 + 11.5000i −1.08343 + 0.625518i
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 4.46410 + 0.267949i 0.242100 + 0.0145316i
\(341\) −8.00000 13.8564i −0.433224 0.750366i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) −7.46410 4.92820i −0.401854 0.265326i
\(346\) 7.00000 12.1244i 0.376322 0.651809i
\(347\) 10.3923 + 6.00000i 0.557888 + 0.322097i 0.752297 0.658824i \(-0.228946\pi\)
−0.194409 + 0.980921i \(0.562279\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) 1.73205 1.00000i 0.0923186 0.0533002i
\(353\) −12.1244 7.00000i −0.645314 0.372572i 0.141344 0.989960i \(-0.454858\pi\)
−0.786659 + 0.617388i \(0.788191\pi\)
\(354\) 5.00000 8.66025i 0.265747 0.460287i
\(355\) −22.3923 14.7846i −1.18846 0.784686i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 10.0000i 0.528516i
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) −2.23205 0.133975i −0.117639 0.00706108i
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) −1.73205 + 1.00000i −0.0910346 + 0.0525588i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 4.00000 + 8.00000i 0.209370 + 0.418739i
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) −1.73205 1.00000i −0.0904123 0.0521996i 0.454112 0.890945i \(-0.349957\pi\)
−0.544524 + 0.838745i \(0.683290\pi\)
\(368\) 3.46410 + 2.00000i 0.180579 + 0.104257i
\(369\) −1.00000 1.73205i −0.0520579 0.0901670i
\(370\) 4.00000 2.00000i 0.207950 0.103975i
\(371\) 0 0
\(372\) 8.00000i 0.414781i
\(373\) 5.19615 3.00000i 0.269047 0.155334i −0.359408 0.933181i \(-0.617021\pi\)
0.628454 + 0.777847i \(0.283688\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) −7.23205 + 8.52628i −0.373461 + 0.440295i
\(376\) 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
\(381\) −1.00000 + 1.73205i −0.0512316 + 0.0887357i
\(382\) −10.3923 6.00000i −0.531717 0.306987i
\(383\) −13.8564 + 8.00000i −0.708029 + 0.408781i −0.810331 0.585973i \(-0.800713\pi\)
0.102302 + 0.994753i \(0.467379\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) 3.46410 2.00000i 0.176090 0.101666i
\(388\) −6.92820 4.00000i −0.351726 0.203069i
\(389\) 10.0000 17.3205i 0.507020 0.878185i −0.492947 0.870059i \(-0.664080\pi\)
0.999967 0.00812520i \(-0.00258636\pi\)
\(390\) 7.39230 11.1962i 0.374324 0.566939i
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 18.0000i 0.907980i
\(394\) −11.0000 19.0526i −0.554172 0.959854i
\(395\) 0 0
\(396\) −1.00000 + 1.73205i −0.0502519 + 0.0870388i
\(397\) 1.73205 1.00000i 0.0869291 0.0501886i −0.455905 0.890028i \(-0.650684\pi\)
0.542834 + 0.839840i \(0.317351\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) −11.0000 19.0526i −0.549314 0.951439i −0.998322 0.0579116i \(-0.981556\pi\)
0.449008 0.893528i \(-0.351777\pi\)
\(402\) 6.92820 + 4.00000i 0.345547 + 0.199502i
\(403\) 41.5692 + 24.0000i 2.07071 + 1.19553i
\(404\) 4.00000 + 6.92820i 0.199007 + 0.344691i
\(405\) 2.00000 1.00000i 0.0993808 0.0496904i
\(406\) 0 0
\(407\) 4.00000i 0.198273i
\(408\) 1.73205 1.00000i 0.0857493 0.0495074i
\(409\) 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i \(-0.753812\pi\)
0.962757 + 0.270367i \(0.0871450\pi\)
\(410\) 4.46410 + 0.267949i 0.220466 + 0.0132331i
\(411\) 9.00000 + 15.5885i 0.443937 + 0.768922i
\(412\) 14.0000i 0.689730i
\(413\) 0 0
\(414\) −4.00000 −0.196589
\(415\) 4.92820 7.46410i 0.241916 0.366398i
\(416\) −3.00000 + 5.19615i −0.147087 + 0.254762i
\(417\) 17.3205 + 10.0000i 0.848189 + 0.489702i
\(418\) 0 0
\(419\) −10.0000 −0.488532 −0.244266 0.969708i \(-0.578547\pi\)
−0.244266 + 0.969708i \(0.578547\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 10.3923 6.00000i 0.505889 0.292075i
\(423\) −6.92820 4.00000i −0.336861 0.194487i
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 1.19615 9.92820i 0.0580219 0.481589i
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) −6.00000 10.3923i −0.289683 0.501745i
\(430\) −0.535898 + 8.92820i −0.0258433 + 0.430556i
\(431\) −16.0000 + 27.7128i −0.770693 + 1.33488i 0.166491 + 0.986043i \(0.446756\pi\)
−0.937184 + 0.348836i \(0.886577\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 4.00000i 0.192228i 0.995370 + 0.0961139i \(0.0306413\pi\)
−0.995370 + 0.0961139i \(0.969359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.00000 8.66025i −0.239457 0.414751i
\(437\) 0 0
\(438\) 3.46410 + 2.00000i 0.165521 + 0.0955637i
\(439\) 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 0.481486 0.876454i \(-0.340097\pi\)
0.999774 + 0.0212481i \(0.00676401\pi\)
\(444\) 1.00000 1.73205i 0.0474579 0.0821995i
\(445\) 1.33975 22.3205i 0.0635100 1.05809i
\(446\) −13.0000 22.5167i −0.615568 1.06619i
\(447\) 20.0000i 0.945968i
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −0.598076 + 4.96410i −0.0281936 + 0.234010i
\(451\) 2.00000 3.46410i 0.0941763 0.163118i
\(452\) 5.19615 + 3.00000i 0.244406 + 0.141108i
\(453\) −6.92820 + 4.00000i −0.325515 + 0.187936i
\(454\) 28.0000 1.31411
\(455\) 0 0
\(456\) 0 0
\(457\) −27.7128 + 16.0000i −1.29635 + 0.748448i −0.979772 0.200118i \(-0.935868\pi\)
−0.316579 + 0.948566i \(0.602534\pi\)
\(458\) 8.66025 + 5.00000i 0.404667 + 0.233635i
\(459\) −1.00000 + 1.73205i −0.0466760 + 0.0808452i
\(460\) 4.92820 7.46410i 0.229779 0.348016i
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 6.00000i 0.278844i 0.990233 + 0.139422i \(0.0445244\pi\)
−0.990233 + 0.139422i \(0.955476\pi\)
\(464\) 0 0
\(465\) −17.8564 1.07180i −0.828071 0.0497034i
\(466\) −7.00000 + 12.1244i −0.324269 + 0.561650i
\(467\) 10.3923 6.00000i 0.480899 0.277647i −0.239892 0.970799i \(-0.577112\pi\)
0.720791 + 0.693153i \(0.243779\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 0 0
\(470\) 16.0000 8.00000i 0.738025 0.369012i
\(471\) 11.0000 + 19.0526i 0.506853 + 0.877896i
\(472\) 8.66025 + 5.00000i 0.398621 + 0.230144i
\(473\) 6.92820 + 4.00000i 0.318559 + 0.183920i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) −17.3205 + 10.0000i −0.792222 + 0.457389i
\(479\) −10.0000 + 17.3205i −0.456912 + 0.791394i −0.998796 0.0490589i \(-0.984378\pi\)
0.541884 + 0.840453i \(0.317711\pi\)
\(480\) 0.133975 2.23205i 0.00611508 0.101879i
\(481\) 6.00000 + 10.3923i 0.273576 + 0.473848i
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −9.85641 + 14.9282i −0.447556 + 0.677855i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −15.5885 9.00000i −0.706380 0.407829i 0.103339 0.994646i \(-0.467047\pi\)
−0.809719 + 0.586817i \(0.800381\pi\)
\(488\) 1.73205 1.00000i 0.0784063 0.0452679i
\(489\) −16.0000 −0.723545
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 1.73205 1.00000i 0.0780869 0.0450835i
\(493\) 0 0
\(494\) 0 0
\(495\) 3.73205 + 2.46410i 0.167743 + 0.110753i
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 4.00000i 0.179244i
\(499\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(500\) −8.52628 7.23205i −0.381307 0.323427i
\(501\) 6.00000 10.3923i 0.268060 0.464294i
\(502\) 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
\(507\) 19.9186 + 11.5000i 0.884615 + 0.510733i
\(508\) −1.73205 1.00000i −0.0768473 0.0443678i
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) −2.00000 4.00000i −0.0885615 0.177123i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −9.00000 + 15.5885i −0.396973 + 0.687577i
\(515\) −31.2487 1.87564i −1.37698 0.0826508i
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) 16.0000i 0.703679i
\(518\) 0 0
\(519\) −14.0000 −0.614532
\(520\) 11.1962 + 7.39230i 0.490984 + 0.324174i
\(521\) 11.0000 19.0526i 0.481919 0.834708i −0.517866 0.855462i \(-0.673273\pi\)
0.999785 + 0.0207541i \(0.00660670\pi\)
\(522\) 0 0
\(523\) −13.8564 + 8.00000i −0.605898 + 0.349816i −0.771358 0.636401i \(-0.780422\pi\)
0.165460 + 0.986216i \(0.447089\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) 4.00000 0.174408
\(527\) 13.8564 8.00000i 0.603595 0.348485i
\(528\) −1.73205 1.00000i −0.0753778 0.0435194i
\(529\) −3.50000 + 6.06218i −0.152174 + 0.263573i
\(530\) 11.1962 + 7.39230i 0.486330 + 0.321101i
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) −5.00000 8.66025i −0.216371 0.374766i
\(535\) 26.7846 + 1.60770i 1.15800 + 0.0695067i
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) −8.66025 + 5.00000i −0.373718 + 0.215766i
\(538\) 0 0
\(539\) 0 0
\(540\) 1.00000 + 2.00000i 0.0430331 + 0.0860663i
\(541\) 19.0000 + 32.9090i 0.816874 + 1.41487i 0.907975 + 0.419025i \(0.137628\pi\)
−0.0911008 + 0.995842i \(0.529039\pi\)
\(542\) −6.92820 4.00000i −0.297592 0.171815i
\(543\) 1.73205 + 1.00000i 0.0743294 + 0.0429141i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) −20.0000 + 10.0000i −0.856706 + 0.428353i
\(546\) 0 0
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) −15.5885 + 9.00000i −0.665906 + 0.384461i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) −9.19615 + 3.92820i −0.392125 + 0.167499i
\(551\) 0 0
\(552\) 4.00000i 0.170251i
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) −3.73205 2.46410i −0.158417 0.104595i
\(556\) −10.0000 + 17.3205i −0.424094 + 0.734553i
\(557\) −15.5885 9.00000i −0.660504 0.381342i 0.131965 0.991254i \(-0.457871\pi\)
−0.792469 + 0.609912i \(0.791205\pi\)
\(558\) −6.92820 + 4.00000i −0.293294 + 0.169334i
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) −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 \(-0.711116\pi\)
\(564\) 4.00000 6.92820i 0.168430 0.291730i
\(565\) 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 0.741981 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
\(573\) 12.0000i 0.501307i
\(574\) 0 0
\(575\) −16.0000 12.0000i −0.667246 0.500435i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −27.7128 16.0000i −1.15370 0.666089i −0.203913 0.978989i \(-0.565366\pi\)
−0.949786 + 0.312900i \(0.898699\pi\)
\(578\) −11.2583 6.50000i −0.468285 0.270364i
\(579\) −2.00000 3.46410i −0.0831172 0.143963i
\(580\) 0 0
\(581\) 0 0
\(582\) 8.00000i 0.331611i
\(583\) 10.3923 6.00000i 0.430405 0.248495i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) −13.3923 0.803848i −0.553704 0.0332350i
\(586\) −3.00000 5.19615i −0.123929 0.214651i
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 12.3205 18.6603i 0.507227 0.768231i
\(591\) −11.0000 + 19.0526i −0.452480 + 0.783718i
\(592\) 1.73205 + 1.00000i 0.0711868 + 0.0410997i
\(593\) −5.19615 + 3.00000i −0.213380 + 0.123195i −0.602881 0.797831i \(-0.705981\pi\)
0.389501 + 0.921026i \(0.372647\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) −20.0000 −0.819232
\(597\) 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 \(0.166667\pi\)
\(600\) −4.96410 0.598076i −0.202659 0.0244164i
\(601\) −2.00000 −0.0815817 −0.0407909 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 0 0
\(603\) 8.00000i 0.325785i
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 0.937822 15.6244i 0.0381279 0.635220i
\(606\) 4.00000 6.92820i 0.162489 0.281439i
\(607\) 19.0526 11.0000i 0.773320 0.446476i −0.0607380 0.998154i \(-0.519345\pi\)
0.834058 + 0.551678i \(0.186012\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −2.00000 4.00000i −0.0809776 0.161955i
\(611\) 24.0000 + 41.5692i 0.970936 + 1.68171i
\(612\) −1.73205 1.00000i −0.0700140 0.0404226i
\(613\) −22.5167 13.0000i −0.909439 0.525065i −0.0291886 0.999574i \(-0.509292\pi\)
−0.880251 + 0.474509i \(0.842626\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) −2.00000 4.00000i −0.0806478 0.161296i
\(616\) 0 0
\(617\) 2.00000i 0.0805170i −0.999189 0.0402585i \(-0.987182\pi\)
0.999189 0.0402585i \(-0.0128181\pi\)
\(618\) −12.1244 + 7.00000i −0.487713 + 0.281581i
\(619\) −10.0000 + 17.3205i −0.401934 + 0.696170i −0.993959 0.109749i \(-0.964995\pi\)
0.592025 + 0.805919i \(0.298329\pi\)
\(620\) 1.07180 17.8564i 0.0430444 0.717131i
\(621\) 2.00000 + 3.46410i 0.0802572 + 0.139010i
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 6.00000 0.240192
\(625\) −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
\(633\) −10.3923 6.00000i −0.413057 0.238479i
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) −2.46410 + 3.73205i −0.0977849 + 0.148102i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 + 10.3923i 0.237356 + 0.411113i
\(640\) 2.23205 + 0.133975i 0.0882296 + 0.00529581i
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 10.3923 6.00000i 0.410152 0.236801i
\(643\) 24.0000i 0.946468i 0.880937 + 0.473234i \(0.156913\pi\)
−0.880937 + 0.473234i \(0.843087\pi\)
\(644\) 0 0
\(645\) 8.00000 4.00000i 0.315000 0.157500i
\(646\) 0 0
\(647\) 41.5692 + 24.0000i 1.63425 + 0.943537i 0.982760 + 0.184884i \(0.0591909\pi\)
0.651494 + 0.758654i \(0.274142\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −10.0000 17.3205i −0.392534 0.679889i
\(650\) 18.0000 24.0000i 0.706018 0.941357i
\(651\) 0 0
\(652\) 16.0000i 0.626608i
\(653\) 22.5167 13.0000i 0.881145 0.508729i 0.0101092 0.999949i \(-0.496782\pi\)
0.871036 + 0.491220i \(0.163449\pi\)
\(654\) −5.00000 + 8.66025i −0.195515 + 0.338643i
\(655\) −2.41154 + 40.1769i −0.0942268 + 1.56984i
\(656\) 1.00000 + 1.73205i 0.0390434 + 0.0676252i
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) 50.0000 1.94772 0.973862 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) −2.46410 + 3.73205i −0.0959150 + 0.145270i
\(661\) 1.00000 1.73205i 0.0388955 0.0673690i −0.845922 0.533306i \(-0.820949\pi\)
0.884818 + 0.465937i \(0.154283\pi\)
\(662\) 6.92820 + 4.00000i 0.269272 + 0.155464i
\(663\) 10.3923 6.00000i 0.403604 0.233021i
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 10.3923 + 6.00000i 0.402090 + 0.232147i
\(669\) −13.0000 + 22.5167i −0.502609 + 0.870544i
\(670\) 14.9282 + 9.85641i 0.576727 + 0.380786i
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) 14.0000 + 24.2487i 0.539260 + 0.934025i
\(675\) 4.59808 1.96410i 0.176980 0.0755983i
\(676\) −11.5000 + 19.9186i −0.442308 + 0.766099i
\(677\) 1.73205 1.00000i 0.0665681 0.0384331i −0.466347 0.884602i \(-0.654430\pi\)
0.532915 + 0.846169i \(0.321097\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) 4.00000 2.00000i 0.153393 0.0766965i
\(681\) −14.0000 24.2487i −0.536481 0.929213i
\(682\) −13.8564 8.00000i −0.530589 0.306336i
\(683\) 3.46410 + 2.00000i 0.132550 + 0.0765279i 0.564809 0.825222i \(-0.308950\pi\)
−0.432259 + 0.901750i \(0.642283\pi\)
\(684\) 0 0
\(685\) 18.0000 + 36.0000i 0.687745 + 1.37549i
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) −3.46410 + 2.00000i −0.132068 + 0.0762493i
\(689\) −18.0000 + 31.1769i −0.685745 + 1.18775i
\(690\) −8.92820 0.535898i −0.339891 0.0204013i
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 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
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) 32.0000 1.20862 0.604312 0.796748i \(-0.293448\pi\)
0.604312 + 0.796748i \(0.293448\pi\)
\(702\) −5.19615 + 3.00000i −0.196116 + 0.113228i
\(703\) 0 0
\(704\) 1.00000 1.73205i 0.0376889 0.0652791i
\(705\) −14.9282 9.85641i −0.562229 0.371214i
\(706\) −14.0000 −0.526897
\(707\) 0 0
\(708\) 10.0000i 0.375823i
\(709\) 15.0000 + 25.9808i 0.563337 + 0.975728i 0.997202 + 0.0747503i \(0.0238160\pi\)
−0.433865 + 0.900978i \(0.642851\pi\)
\(710\) −26.7846 1.60770i −1.00521 0.0603357i
\(711\) 0 0
\(712\) 8.66025 5.00000i 0.324557 0.187383i
\(713\) 32.0000i 1.19841i
\(714\) 0 0
\(715\) −12.0000 24.0000i −0.448775 0.897549i
\(716\) −5.00000 8.66025i −0.186859 0.323649i
\(717\) 17.3205 + 10.0000i 0.646846 + 0.373457i
\(718\) 0 0
\(719\) 20.0000 + 34.6410i 0.745874 + 1.29189i 0.949785 + 0.312903i \(0.101301\pi\)
−0.203911 + 0.978989i \(0.565365\pi\)
\(720\) −2.00000 + 1.00000i −0.0745356 + 0.0372678i
\(721\) 0 0
\(722\) 19.0000i 0.707107i
\(723\) −19.0526 + 11.0000i −0.708572 + 0.409094i
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) −3.50000 6.06218i −0.129897 0.224989i
\(727\) 18.0000i 0.667583i −0.942647 0.333792i \(-0.891672\pi\)
0.942647 0.333792i \(-0.108328\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 7.46410 + 4.92820i 0.276259 + 0.182401i
\(731\) −4.00000 + 6.92820i −0.147945 + 0.256249i
\(732\) −1.73205 1.00000i −0.0640184 0.0369611i
\(733\) 12.1244 7.00000i 0.447823 0.258551i −0.259087 0.965854i \(-0.583422\pi\)
0.706910 + 0.707303i \(0.250088\pi\)
\(734\) −2.00000 −0.0738213
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 13.8564 8.00000i 0.510407 0.294684i
\(738\) −1.73205 1.00000i −0.0637577 0.0368105i
\(739\) 20.0000 34.6410i 0.735712 1.27429i −0.218698 0.975793i \(-0.570181\pi\)
0.954410 0.298498i \(-0.0964856\pi\)
\(740\) 2.46410 3.73205i 0.0905822 0.137193i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000i 0.880475i −0.897881 0.440237i \(-0.854894\pi\)
0.897881 0.440237i \(-0.145106\pi\)
\(744\) −4.00000 6.92820i −0.146647 0.254000i
\(745\) −2.67949 + 44.6410i −0.0981690 + 1.63552i
\(746\) 3.00000 5.19615i 0.109838 0.190245i
\(747\) −3.46410 + 2.00000i −0.126745 + 0.0731762i
\(748\) 4.00000i 0.146254i
\(749\) 0 0
\(750\) −2.00000 + 11.0000i −0.0730297 + 0.401663i
\(751\) −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) 6.92820 + 4.00000i 0.252646 + 0.145865i
\(753\) −15.5885 9.00000i −0.568075 0.327978i
\(754\) 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
\(759\) −4.00000 + 6.92820i −0.145191 + 0.251478i
\(760\) 0 0
\(761\) −9.00000 15.5885i −0.326250 0.565081i 0.655515 0.755182i \(-0.272452\pi\)
−0.981764 + 0.190101i \(0.939118\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) −2.46410 + 3.73205i −0.0890898 + 0.134933i
\(766\) −8.00000 + 13.8564i −0.289052 + 0.500652i
\(767\) 51.9615 + 30.0000i 1.87622 + 1.08324i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 3.46410 2.00000i 0.124676 0.0719816i
\(773\) −46.7654 27.0000i −1.68203 0.971123i −0.960307 0.278944i \(-0.910016\pi\)
−0.721726 0.692179i \(-0.756651\pi\)
\(774\) 2.00000 3.46410i 0.0718885 0.124515i
\(775\) −39.7128 4.78461i −1.42653 0.171868i
\(776\) −8.00000 −0.287183
\(777\) 0 0
\(778\) 20.0000i 0.717035i
\(779\) 0 0
\(780\) 0.803848 13.3923i 0.0287824 0.479521i
\(781\) −12.0000 + 20.7846i −0.429394 + 0.743732i
\(782\) 6.92820 4.00000i 0.247752 0.143040i
\(783\) 0 0
\(784\) 0 0
\(785\) 22.0000 + 44.0000i