Properties

Label 1470.2.n.h.949.1
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 949.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.949
Dual form 1470.2.n.h.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.23205 - 1.86603i) 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} +(-4.96410 + 0.598076i) q^{25} +(3.00000 + 5.19615i) q^{26} -1.00000i q^{27} +(0.133975 + 2.23205i) 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} +(-2.23205 + 0.133975i) q^{40} +2.00000 q^{41} +4.00000i q^{43} +(1.00000 + 1.73205i) q^{44} +(-1.86603 + 1.23205i) 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} +(-1.23205 - 1.86603i) q^{60} +(-1.00000 - 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(13.3923 - 0.803848i) 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} +(4.59808 + 1.96410i) q^{75} -6.00000i q^{78} +(1.86603 - 1.23205i) 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
\(5\) 0.133975 + 2.23205i 0.0599153 + 0.998203i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −1.23205 1.86603i −0.389609 0.590089i
\(11\) −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 −0.0932891 0.995639i \(-0.529738\pi\)
0.815604 + 0.578610i \(0.196405\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) 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 \(0.5\pi\)
\(30\) 0.133975 + 2.23205i 0.0244603 + 0.407515i
\(31\) 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
\(33\) 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 −0.350823 0.936442i \(-0.614098\pi\)
0.635571 + 0.772043i \(0.280765\pi\)
\(38\) 0 0
\(39\) −3.00000 + 5.19615i −0.480384 + 0.832050i
\(40\) −2.23205 + 0.133975i −0.352918 + 0.0211832i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) −1.86603 + 1.23205i −0.278171 + 0.183663i
\(46\) −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 0.812447 0.583036i \(-0.198135\pi\)
−0.0987002 + 0.995117i \(0.531468\pi\)
\(54\) 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 \(-0.607706\pi\)
0.982894 0.184172i \(-0.0589603\pi\)
\(60\) −1.23205 1.86603i −0.159057 0.240903i
\(61\) −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
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) 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
\(69\) −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
\(75\) 4.59808 + 1.96410i 0.530940 + 0.226795i
\(76\) 0 0
\(77\) 0 0
\(78\) 6.00000i 0.679366i
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 1.86603 1.23205i 0.208628 0.137747i
\(81\) −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 \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 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
\(100\) −1.96410 + 4.59808i −0.196410 + 0.459808i
\(101\) 4.00000 6.92820i 0.398015 0.689382i −0.595466 0.803380i \(-0.703033\pi\)
0.993481 + 0.113998i \(0.0363659\pi\)
\(102\) −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 0.0950377 0.995474i \(-0.469703\pi\)
0.909624 + 0.415432i \(0.136370\pi\)
\(108\) −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 \(0.00769755\pi\)
\(110\) 4.46410 0.267949i 0.425635 0.0255480i
\(111\) −2.00000 −0.189832
\(112\) 0 0
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 4.92820 + 7.46410i 0.459557 + 0.696031i
\(116\) 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 \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) −11.1962 + 7.39230i −0.981968 + 0.648348i
\(131\) 9.00000 + 15.5885i 0.786334 + 1.36197i 0.928199 + 0.372084i \(0.121357\pi\)
−0.141865 + 0.989886i \(0.545310\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 2.23205 0.133975i 0.192104 0.0115307i
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) 15.5885 + 9.00000i 1.33181 + 0.768922i 0.985577 0.169226i \(-0.0541268\pi\)
0.346235 + 0.938148i \(0.387460\pi\)
\(138\) 3.46410 2.00000i 0.294884 0.170251i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 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 \(-0.472267\pi\)
\(150\) −4.96410 + 0.598076i −0.405317 + 0.0488327i
\(151\) 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 −0.932326 0.361619i \(-0.882224\pi\)
−0.152992 + 0.988227i \(0.548891\pi\)
\(164\) 1.00000 1.73205i 0.0780869 0.135250i
\(165\) 2.46410 + 3.73205i 0.191830 + 0.290540i
\(166\) −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
\(170\) 0.267949 + 4.46410i 0.0205508 + 0.342381i
\(171\) 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 \(0.0447496\pi\)
\(180\) 0.133975 + 2.23205i 0.00998588 + 0.166367i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) 2.46410 + 3.73205i 0.181164 + 0.274386i
\(186\) 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 0.370116 0.928986i \(-0.379318\pi\)
−0.619467 + 0.785022i \(0.712651\pi\)
\(194\) 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 \(0.286679\pi\)
−0.621117 + 0.783718i \(0.713321\pi\)
\(198\) 1.73205 1.00000i 0.123091 0.0710669i
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) −0.598076 4.96410i −0.0422904 0.351015i
\(201\) −4.00000 6.92820i −0.282138 0.488678i
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 0.267949 + 4.46410i 0.0187144 + 0.311786i
\(206\) −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
\(215\) −8.92820 + 0.535898i −0.608898 + 0.0365480i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 10.0000i 0.677285i
\(219\) 2.00000 + 3.46410i 0.135147 + 0.234082i
\(220\) −3.73205 + 2.46410i −0.251615 + 0.166130i
\(221\) −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 0.652183 0.758062i \(-0.273853\pi\)
−0.982592 + 0.185776i \(0.940520\pi\)
\(230\) −8.00000 4.00000i −0.527504 0.263752i
\(231\) 0 0
\(232\) 0 0
\(233\) 12.1244 7.00000i 0.794293 0.458585i −0.0471787 0.998886i \(-0.515023\pi\)
0.841472 + 0.540301i \(0.181690\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) −9.85641 14.9282i −0.642961 0.973809i
\(236\) −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 \(0.723912\pi\)
\(240\) −2.23205 + 0.133975i −0.144078 + 0.00864802i
\(241\) −11.0000 + 19.0526i −0.708572 + 1.22728i 0.256814 + 0.966461i \(0.417327\pi\)
−0.965387 + 0.260822i \(0.916006\pi\)
\(242\) −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
\(250\) 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
\(255\) −3.73205 + 2.46410i −0.233710 + 0.154308i
\(256\) −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 0.389380 0.921077i \(-0.372689\pi\)
−0.602986 + 0.797752i \(0.706023\pi\)
\(264\) 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 \(0.166667\pi\)
\(270\) −1.86603 + 1.23205i −0.113563 + 0.0749802i
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 3.92820 9.19615i 0.236880 0.554549i
\(276\) −2.00000 + 3.46410i −0.120386 + 0.208514i
\(277\) −1.73205 1.00000i −0.104069 0.0600842i 0.447062 0.894503i \(-0.352470\pi\)
−0.551131 + 0.834419i \(0.685804\pi\)
\(278\) −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
\(305\) 3.73205 2.46410i 0.213697 0.141094i
\(306\) 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
\(310\) −17.8564 + 1.07180i −1.01418 + 0.0608740i
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) −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 −0.450570 0.892741i \(-0.648779\pi\)
0.547852 + 0.836576i \(0.315446\pi\)
\(318\) 5.19615 + 3.00000i 0.291386 + 0.168232i
\(319\) 0 0
\(320\) −0.133975 2.23205i −0.00748941 0.124775i
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 3.58846 + 29.7846i 0.199052 + 1.65215i
\(326\) 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 \(-0.723908\pi\)
0.646837 0.762629i \(-0.276092\pi\)
\(338\) 19.9186 11.5000i 1.08343 0.625518i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) −2.46410 3.73205i −0.133635 0.202399i
\(341\) 8.00000 + 13.8564i 0.433224 + 0.750366i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) −0.535898 8.92820i −0.0288518 0.480678i
\(346\) −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
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 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
\(355\) 1.60770 + 26.7846i 0.0853276 + 1.42158i
\(356\) −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 \(0.833333\pi\)
\(360\) −1.23205 1.86603i −0.0649348 0.0983482i
\(361\) 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 −0.628454 0.777847i \(-0.716312\pi\)
0.359408 + 0.933181i \(0.382979\pi\)
\(374\) −2.00000 + 3.46410i −0.103418 + 0.179124i
\(375\) −3.76795 + 10.5263i −0.194576 + 0.543575i
\(376\) −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 \(-0.00258636\pi\)
\(390\) 13.3923 0.803848i 0.678146 0.0407044i
\(391\) −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 −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) −2.46410 3.73205i −0.121693 0.184313i
\(411\) −9.00000 15.5885i −0.443937 0.768922i
\(412\) 14.0000i 0.689730i
\(413\) 0 0
\(414\) −4.00000 −0.196589
\(415\) −8.92820 + 0.535898i −0.438268 + 0.0263062i
\(416\) 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 \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) 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
\(425\) 9.19615 + 3.92820i 0.446079 + 0.190546i
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) −6.00000 10.3923i −0.289683 0.501745i
\(430\) 7.46410 4.92820i 0.359951 0.237659i
\(431\) −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 −0.999774 0.0212481i \(-0.993236\pi\)
−0.481486 + 0.876454i \(0.659903\pi\)
\(444\) −1.00000 + 1.73205i −0.0474579 + 0.0821995i
\(445\) 18.6603 12.3205i 0.884581 0.584048i
\(446\) 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 \(0.750354\pi\)
\(450\) 4.59808 + 1.96410i 0.216755 + 0.0925886i
\(451\) −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 0.316579 0.948566i \(-0.397466\pi\)
0.979772 + 0.200118i \(0.0641325\pi\)
\(458\) 8.66025 + 5.00000i 0.404667 + 0.233635i
\(459\) −1.00000 + 1.73205i −0.0466760 + 0.0808452i
\(460\) 8.92820 0.535898i 0.416280 0.0249864i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 6.00000i 0.278844i −0.990233 0.139422i \(-0.955476\pi\)
0.990233 0.139422i \(-0.0445244\pi\)
\(464\) 0 0
\(465\) −9.85641 14.9282i −0.457080 0.692279i
\(466\) −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 −0.541884 0.840453i \(-0.682289\pi\)
0.998796 + 0.0490589i \(0.0156222\pi\)
\(480\) 1.86603 1.23205i 0.0851720 0.0562352i
\(481\) −6.00000 10.3923i −0.273576 0.473848i
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) 17.8564 1.07180i 0.810818 0.0486678i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 15.5885 + 9.00000i 0.706380 + 0.407829i 0.809719 0.586817i \(-0.199619\pi\)
−0.103339 + 0.994646i \(0.532953\pi\)
\(488\) 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
\(495\) −0.267949 4.46410i −0.0120434 0.200646i
\(496\) −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 \(0.833333\pi\)
\(500\) −10.5263 3.76795i −0.470750 0.168508i
\(501\) 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
\(515\) 17.2487 + 26.1244i 0.760069 + 1.15118i
\(516\) −2.00000 3.46410i −0.0880451 0.152499i
\(517\) 16.0000i 0.703679i
\(518\) 0 0
\(519\) −14.0000 −0.614532
\(520\) 0.803848 + 13.3923i 0.0352510 + 0.587291i
\(521\) −11.0000 + 19.0526i −0.481919 + 0.834708i −0.999785 0.0207541i \(-0.993393\pi\)
0.517866 + 0.855462i \(0.326727\pi\)
\(522\) 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
\(530\) −0.803848 13.3923i −0.0349169 0.581725i
\(531\) 10.0000 0.433963
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) −5.00000 8.66025i −0.216371 0.374766i
\(535\) 14.7846 + 22.3923i 0.639194 + 0.968104i
\(536\) −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 \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) 15.5885 9.00000i 0.665906 0.384461i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 1.19615 + 9.92820i 0.0510041 + 0.423340i
\(551\) 0 0
\(552\) 4.00000i 0.170251i
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) −0.267949 4.46410i −0.0113738 0.189491i
\(556\) 10.0000 17.3205i 0.424094 0.734553i
\(557\) 15.5885 + 9.00000i 0.660504 + 0.381342i 0.792469 0.609912i \(-0.208795\pi\)
−0.131965 + 0.991254i \(0.542129\pi\)
\(558\) −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
\(565\) 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
\(573\) 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
\(585\) 7.39230 + 11.1962i 0.305634 + 0.462904i
\(586\) 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
\(590\) −22.3205 + 1.33975i −0.918921 + 0.0551565i
\(591\) 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 \(0.166667\pi\)
\(600\) −1.96410 + 4.59808i −0.0801841 + 0.187716i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) 8.00000i 0.325785i
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) −13.0622 + 8.62436i −0.531053 + 0.350630i
\(606\) 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 0.880251 0.474509i \(-0.157374\pi\)
0.0291886 + 0.999574i \(0.490708\pi\)
\(614\) −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 \(0.0128181\pi\)
−0.999189 + 0.0402585i \(0.987182\pi\)
\(618\) 12.1244 7.00000i 0.487713 0.281581i
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) 14.9282 9.85641i 0.599531 0.395843i
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 6.00000 0.240192
\(625\) 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
\(633\) −10.3923 6.00000i −0.413057 0.238479i
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) −4.46410 + 0.267949i −0.177152 + 0.0106332i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 + 10.3923i 0.237356 + 0.411113i
\(640\) 1.23205 + 1.86603i 0.0487011 + 0.0737611i
\(641\) −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 −0.871036 0.491220i \(-0.836551\pi\)
−0.0101092 + 0.999949i \(0.503218\pi\)
\(654\) 5.00000 8.66025i 0.195515 0.338643i
\(655\) −33.5885 + 22.1769i −1.31241 + 0.866524i
\(656\) −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 \(0.0729380\pi\)
\(660\) 4.46410 0.267949i 0.173765 0.0104299i
\(661\) −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
\(663\) 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
\(670\) −1.07180 17.8564i −0.0414071 0.689853i
\(671\) 4.00000 0.154418
\(672\) 0 0
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) 14.0000 + 24.2487i 0.539260 + 0.934025i
\(675\) 0.598076 + 4.96410i 0.0230200 + 0.191068i
\(676\) −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 0.432259 0.901750i \(-0.357717\pi\)
−0.564809 + 0.825222i \(0.691050\pi\)
\(684\) 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
\(690\) 4.92820 + 7.46410i 0.187613 + 0.284153i
\(691\) 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
\(699\) −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
\(705\) 1.07180 + 17.8564i 0.0403662 + 0.672511i
\(706\) 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 \(0.642851\pi\)
\(710\) −14.7846 22.3923i −0.554857 0.840368i
\(711\) 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 \(-0.898699\pi\)
0.203911 0.978989i \(-0.434635\pi\)
\(720\) 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
\(730\) 0.535898 + 8.92820i 0.0198345 + 0.330448i
\(731\) 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 \(-0.0964856\pi\)
\(740\) 4.46410 0.267949i 0.164104 0.00985001i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000i 0.880475i 0.897881 + 0.440237i \(0.145106\pi\)
−0.897881 + 0.440237i \(0.854894\pi\)
\(744\) −4.00000 6.92820i −0.146647 0.254000i
\(745\) 37.3205 24.6410i 1.36732 0.902777i
\(746\) 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 \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 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 0.981764 0.190101i \(-0.0608816\pi\)
−0.655515 + 0.755182i \(0.727548\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) 4.46410 0.267949i 0.161400 0.00968772i
\(766\) 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 \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 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
\(775\) −15.7128 + 36.7846i −0.564421 + 1.32134i
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) 20.0000i 0.717035i
\(779\) 0 0
\(780\) −11.1962 + 7.39230i −0.400887 + 0.264687i
\(781\) −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 0.785214