Properties

Label 507.2.e.e.22.2
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.e.484.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{6} +(1.73205 + 3.00000i) q^{7} +1.73205 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 1.50000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{6} +(1.73205 + 3.00000i) q^{7} +1.73205 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.73205 - 3.00000i) q^{11} -1.00000 q^{12} +6.00000 q^{14} +(2.50000 - 4.33013i) q^{16} +(-3.00000 - 5.19615i) q^{17} -1.73205 q^{18} +(1.73205 + 3.00000i) q^{19} +3.46410 q^{21} +(-3.00000 - 5.19615i) q^{22} +(0.866025 - 1.50000i) q^{24} -5.00000 q^{25} -1.00000 q^{27} +(1.73205 - 3.00000i) q^{28} +(-3.00000 + 5.19615i) q^{29} +3.46410 q^{31} +(-2.59808 - 4.50000i) q^{32} +(-1.73205 - 3.00000i) q^{33} -10.3923 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.46410 + 6.00000i) q^{37} +6.00000 q^{38} +(-3.46410 + 6.00000i) q^{41} +(3.00000 - 5.19615i) q^{42} +(-2.00000 - 3.46410i) q^{43} -3.46410 q^{44} +3.46410 q^{47} +(-2.50000 - 4.33013i) q^{48} +(-2.50000 + 4.33013i) q^{49} +(-4.33013 + 7.50000i) q^{50} -6.00000 q^{51} +6.00000 q^{53} +(-0.866025 + 1.50000i) q^{54} +(3.00000 + 5.19615i) q^{56} +3.46410 q^{57} +(5.19615 + 9.00000i) q^{58} +(-5.19615 - 9.00000i) q^{59} +(1.00000 + 1.73205i) q^{61} +(3.00000 - 5.19615i) q^{62} +(1.73205 - 3.00000i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(-5.19615 + 9.00000i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(1.73205 + 3.00000i) q^{71} +(-0.866025 - 1.50000i) q^{72} +(6.00000 + 10.3923i) q^{74} +(-2.50000 + 4.33013i) q^{75} +(1.73205 - 3.00000i) q^{76} +12.0000 q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(6.00000 + 10.3923i) q^{82} +3.46410 q^{83} +(-1.73205 - 3.00000i) q^{84} -6.92820 q^{86} +(3.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{88} +(3.46410 - 6.00000i) q^{89} +(1.73205 - 3.00000i) q^{93} +(3.00000 - 5.19615i) q^{94} -5.19615 q^{96} +(-6.92820 - 12.0000i) q^{97} +(4.33013 + 7.50000i) q^{98} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9} - 4 q^{12} + 24 q^{14} + 10 q^{16} - 12 q^{17} - 12 q^{22} - 20 q^{25} - 4 q^{27} - 12 q^{29} - 2 q^{36} + 24 q^{38} + 12 q^{42} - 8 q^{43} - 10 q^{48} - 10 q^{49} - 24 q^{51} + 24 q^{53} + 12 q^{56} + 4 q^{61} + 12 q^{62} + 4 q^{64} - 24 q^{66} - 12 q^{68} + 24 q^{74} - 10 q^{75} + 48 q^{77} - 32 q^{79} - 2 q^{81} + 24 q^{82} + 12 q^{87} + 12 q^{88} + 12 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 1.50000i 0.612372 1.06066i −0.378467 0.925615i \(-0.623549\pi\)
0.990839 0.135045i \(-0.0431180\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) −0.866025 1.50000i −0.353553 0.612372i
\(7\) 1.73205 + 3.00000i 0.654654 + 1.13389i 0.981981 + 0.188982i \(0.0605189\pi\)
−0.327327 + 0.944911i \(0.606148\pi\)
\(8\) 1.73205 0.612372
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 1.73205 3.00000i 0.522233 0.904534i −0.477432 0.878668i \(-0.658432\pi\)
0.999665 0.0258656i \(-0.00823419\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 6.00000 1.60357
\(15\) 0 0
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) −1.73205 −0.408248
\(19\) 1.73205 + 3.00000i 0.397360 + 0.688247i 0.993399 0.114708i \(-0.0365932\pi\)
−0.596040 + 0.802955i \(0.703260\pi\)
\(20\) 0 0
\(21\) 3.46410 0.755929
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0.866025 1.50000i 0.176777 0.306186i
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.73205 3.00000i 0.327327 0.566947i
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 3.46410 0.622171 0.311086 0.950382i \(-0.399307\pi\)
0.311086 + 0.950382i \(0.399307\pi\)
\(32\) −2.59808 4.50000i −0.459279 0.795495i
\(33\) −1.73205 3.00000i −0.301511 0.522233i
\(34\) −10.3923 −1.78227
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −3.46410 + 6.00000i −0.569495 + 0.986394i 0.427121 + 0.904194i \(0.359528\pi\)
−0.996616 + 0.0821995i \(0.973806\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) 0 0
\(41\) −3.46410 + 6.00000i −0.541002 + 0.937043i 0.457845 + 0.889032i \(0.348621\pi\)
−0.998847 + 0.0480106i \(0.984712\pi\)
\(42\) 3.00000 5.19615i 0.462910 0.801784i
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) −3.46410 −0.522233
\(45\) 0 0
\(46\) 0 0
\(47\) 3.46410 0.505291 0.252646 0.967559i \(-0.418699\pi\)
0.252646 + 0.967559i \(0.418699\pi\)
\(48\) −2.50000 4.33013i −0.360844 0.625000i
\(49\) −2.50000 + 4.33013i −0.357143 + 0.618590i
\(50\) −4.33013 + 7.50000i −0.612372 + 1.06066i
\(51\) −6.00000 −0.840168
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −0.866025 + 1.50000i −0.117851 + 0.204124i
\(55\) 0 0
\(56\) 3.00000 + 5.19615i 0.400892 + 0.694365i
\(57\) 3.46410 0.458831
\(58\) 5.19615 + 9.00000i 0.682288 + 1.18176i
\(59\) −5.19615 9.00000i −0.676481 1.17170i −0.976034 0.217620i \(-0.930171\pi\)
0.299552 0.954080i \(-0.403163\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 3.00000 5.19615i 0.381000 0.659912i
\(63\) 1.73205 3.00000i 0.218218 0.377964i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.00000 −0.738549
\(67\) −5.19615 + 9.00000i −0.634811 + 1.09952i 0.351744 + 0.936096i \(0.385589\pi\)
−0.986555 + 0.163429i \(0.947745\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.73205 + 3.00000i 0.205557 + 0.356034i 0.950310 0.311305i \(-0.100766\pi\)
−0.744753 + 0.667340i \(0.767433\pi\)
\(72\) −0.866025 1.50000i −0.102062 0.176777i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 6.00000 + 10.3923i 0.697486 + 1.20808i
\(75\) −2.50000 + 4.33013i −0.288675 + 0.500000i
\(76\) 1.73205 3.00000i 0.198680 0.344124i
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 6.00000 + 10.3923i 0.662589 + 1.14764i
\(83\) 3.46410 0.380235 0.190117 0.981761i \(-0.439113\pi\)
0.190117 + 0.981761i \(0.439113\pi\)
\(84\) −1.73205 3.00000i −0.188982 0.327327i
\(85\) 0 0
\(86\) −6.92820 −0.747087
\(87\) 3.00000 + 5.19615i 0.321634 + 0.557086i
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) 3.46410 6.00000i 0.367194 0.635999i −0.621932 0.783072i \(-0.713652\pi\)
0.989126 + 0.147073i \(0.0469852\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.73205 3.00000i 0.179605 0.311086i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) −5.19615 −0.530330
\(97\) −6.92820 12.0000i −0.703452 1.21842i −0.967247 0.253837i \(-0.918307\pi\)
0.263795 0.964579i \(-0.415026\pi\)
\(98\) 4.33013 + 7.50000i 0.437409 + 0.757614i
\(99\) −3.46410 −0.348155
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) −5.19615 + 9.00000i −0.514496 + 0.891133i
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 5.19615 9.00000i 0.504695 0.874157i
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −6.92820 −0.663602 −0.331801 0.943349i \(-0.607656\pi\)
−0.331801 + 0.943349i \(0.607656\pi\)
\(110\) 0 0
\(111\) 3.46410 + 6.00000i 0.328798 + 0.569495i
\(112\) 17.3205 1.63663
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 3.00000 5.19615i 0.280976 0.486664i
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) −18.0000 −1.65703
\(119\) 10.3923 18.0000i 0.952661 1.65006i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 3.46410 0.313625
\(123\) 3.46410 + 6.00000i 0.312348 + 0.541002i
\(124\) −1.73205 3.00000i −0.155543 0.269408i
\(125\) 0 0
\(126\) −3.00000 5.19615i −0.267261 0.462910i
\(127\) −4.00000 + 6.92820i −0.354943 + 0.614779i −0.987108 0.160055i \(-0.948833\pi\)
0.632166 + 0.774833i \(0.282166\pi\)
\(128\) 6.06218 10.5000i 0.535826 0.928078i
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −1.73205 + 3.00000i −0.150756 + 0.261116i
\(133\) −6.00000 + 10.3923i −0.520266 + 0.901127i
\(134\) 9.00000 + 15.5885i 0.777482 + 1.34664i
\(135\) 0 0
\(136\) −5.19615 9.00000i −0.445566 0.771744i
\(137\) 10.3923 + 18.0000i 0.887875 + 1.53784i 0.842383 + 0.538879i \(0.181152\pi\)
0.0454914 + 0.998965i \(0.485515\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) 1.73205 3.00000i 0.145865 0.252646i
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) −5.00000 −0.416667
\(145\) 0 0
\(146\) 0 0
\(147\) 2.50000 + 4.33013i 0.206197 + 0.357143i
\(148\) 6.92820 0.569495
\(149\) 6.92820 + 12.0000i 0.567581 + 0.983078i 0.996804 + 0.0798802i \(0.0254538\pi\)
−0.429224 + 0.903198i \(0.641213\pi\)
\(150\) 4.33013 + 7.50000i 0.353553 + 0.612372i
\(151\) 10.3923 0.845714 0.422857 0.906196i \(-0.361027\pi\)
0.422857 + 0.906196i \(0.361027\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) −3.00000 + 5.19615i −0.242536 + 0.420084i
\(154\) 10.3923 18.0000i 0.837436 1.45048i
\(155\) 0 0
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −6.92820 + 12.0000i −0.551178 + 0.954669i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) 0 0
\(162\) 0.866025 + 1.50000i 0.0680414 + 0.117851i
\(163\) −1.73205 3.00000i −0.135665 0.234978i 0.790186 0.612866i \(-0.209984\pi\)
−0.925851 + 0.377888i \(0.876650\pi\)
\(164\) 6.92820 0.541002
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) −8.66025 + 15.0000i −0.670151 + 1.16073i 0.307711 + 0.951480i \(0.400437\pi\)
−0.977861 + 0.209255i \(0.932896\pi\)
\(168\) 6.00000 0.462910
\(169\) 0 0
\(170\) 0 0
\(171\) 1.73205 3.00000i 0.132453 0.229416i
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) −9.00000 15.5885i −0.684257 1.18517i −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 10.3923 0.787839
\(175\) −8.66025 15.0000i −0.654654 1.13389i
\(176\) −8.66025 15.0000i −0.652791 1.13067i
\(177\) −10.3923 −0.781133
\(178\) −6.00000 10.3923i −0.449719 0.778936i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 0 0
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) −20.7846 −1.51992
\(188\) −1.73205 3.00000i −0.126323 0.218797i
\(189\) −1.73205 3.00000i −0.125988 0.218218i
\(190\) 0 0
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) −24.0000 −1.72310
\(195\) 0 0
\(196\) 5.00000 0.357143
\(197\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(198\) −3.00000 + 5.19615i −0.213201 + 0.369274i
\(199\) 8.00000 + 13.8564i 0.567105 + 0.982255i 0.996850 + 0.0793045i \(0.0252700\pi\)
−0.429745 + 0.902950i \(0.641397\pi\)
\(200\) −8.66025 −0.612372
\(201\) 5.19615 + 9.00000i 0.366508 + 0.634811i
\(202\) −5.19615 9.00000i −0.365600 0.633238i
\(203\) −20.7846 −1.45879
\(204\) 3.00000 + 5.19615i 0.210042 + 0.363803i
\(205\) 0 0
\(206\) −6.92820 + 12.0000i −0.482711 + 0.836080i
\(207\) 0 0
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 10.0000 17.3205i 0.688428 1.19239i −0.283918 0.958849i \(-0.591634\pi\)
0.972346 0.233544i \(-0.0750324\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 3.46410 0.237356
\(214\) 10.3923 + 18.0000i 0.710403 + 1.23045i
\(215\) 0 0
\(216\) −1.73205 −0.117851
\(217\) 6.00000 + 10.3923i 0.407307 + 0.705476i
\(218\) −6.00000 + 10.3923i −0.406371 + 0.703856i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 12.0000 0.805387
\(223\) −1.73205 + 3.00000i −0.115987 + 0.200895i −0.918174 0.396178i \(-0.870336\pi\)
0.802187 + 0.597073i \(0.203670\pi\)
\(224\) 9.00000 15.5885i 0.601338 1.04155i
\(225\) 2.50000 + 4.33013i 0.166667 + 0.288675i
\(226\) 10.3923 0.691286
\(227\) −8.66025 15.0000i −0.574801 0.995585i −0.996063 0.0886460i \(-0.971746\pi\)
0.421262 0.906939i \(-0.361587\pi\)
\(228\) −1.73205 3.00000i −0.114708 0.198680i
\(229\) −6.92820 −0.457829 −0.228914 0.973447i \(-0.573518\pi\)
−0.228914 + 0.973447i \(0.573518\pi\)
\(230\) 0 0
\(231\) 6.00000 10.3923i 0.394771 0.683763i
\(232\) −5.19615 + 9.00000i −0.341144 + 0.590879i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −5.19615 + 9.00000i −0.338241 + 0.585850i
\(237\) −4.00000 + 6.92820i −0.259828 + 0.450035i
\(238\) −18.0000 31.1769i −1.16677 2.02090i
\(239\) 10.3923 0.672222 0.336111 0.941822i \(-0.390888\pi\)
0.336111 + 0.941822i \(0.390888\pi\)
\(240\) 0 0
\(241\) −6.92820 12.0000i −0.446285 0.772988i 0.551856 0.833939i \(-0.313920\pi\)
−0.998141 + 0.0609515i \(0.980586\pi\)
\(242\) −1.73205 −0.111340
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 1.00000 1.73205i 0.0640184 0.110883i
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 0 0
\(248\) 6.00000 0.381000
\(249\) 1.73205 3.00000i 0.109764 0.190117i
\(250\) 0 0
\(251\) −6.00000 10.3923i −0.378717 0.655956i 0.612159 0.790735i \(-0.290301\pi\)
−0.990876 + 0.134778i \(0.956968\pi\)
\(252\) −3.46410 −0.218218
\(253\) 0 0
\(254\) 6.92820 + 12.0000i 0.434714 + 0.752947i
\(255\) 0 0
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) −3.46410 + 6.00000i −0.215666 + 0.373544i
\(259\) −24.0000 −1.49129
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) −10.3923 + 18.0000i −0.642039 + 1.11204i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) −3.00000 5.19615i −0.184637 0.319801i
\(265\) 0 0
\(266\) 10.3923 + 18.0000i 0.637193 + 1.10365i
\(267\) −3.46410 6.00000i −0.212000 0.367194i
\(268\) 10.3923 0.634811
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) −5.19615 + 9.00000i −0.315644 + 0.546711i −0.979574 0.201083i \(-0.935554\pi\)
0.663930 + 0.747794i \(0.268887\pi\)
\(272\) −30.0000 −1.81902
\(273\) 0 0
\(274\) 36.0000 2.17484
\(275\) −8.66025 + 15.0000i −0.522233 + 0.904534i
\(276\) 0 0
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) 6.92820 0.415526
\(279\) −1.73205 3.00000i −0.103695 0.179605i
\(280\) 0 0
\(281\) 6.92820 0.413302 0.206651 0.978415i \(-0.433744\pi\)
0.206651 + 0.978415i \(0.433744\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) 1.73205 3.00000i 0.102778 0.178017i
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) −2.59808 + 4.50000i −0.153093 + 0.265165i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) −13.8564 −0.812277
\(292\) 0 0
\(293\) −13.8564 24.0000i −0.809500 1.40209i −0.913211 0.407487i \(-0.866405\pi\)
0.103711 0.994607i \(-0.466928\pi\)
\(294\) 8.66025 0.505076
\(295\) 0 0
\(296\) −6.00000 + 10.3923i −0.348743 + 0.604040i
\(297\) −1.73205 + 3.00000i −0.100504 + 0.174078i
\(298\) 24.0000 1.39028
\(299\) 0 0
\(300\) 5.00000 0.288675
\(301\) 6.92820 12.0000i 0.399335 0.691669i
\(302\) 9.00000 15.5885i 0.517892 0.897015i
\(303\) −3.00000 5.19615i −0.172345 0.298511i
\(304\) 17.3205 0.993399
\(305\) 0 0
\(306\) 5.19615 + 9.00000i 0.297044 + 0.514496i
\(307\) −10.3923 −0.593120 −0.296560 0.955014i \(-0.595840\pi\)
−0.296560 + 0.955014i \(0.595840\pi\)
\(308\) −6.00000 10.3923i −0.341882 0.592157i
\(309\) −4.00000 + 6.92820i −0.227552 + 0.394132i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 12.1244 21.0000i 0.684217 1.18510i
\(315\) 0 0
\(316\) 4.00000 + 6.92820i 0.225018 + 0.389742i
\(317\) −13.8564 −0.778253 −0.389127 0.921184i \(-0.627223\pi\)
−0.389127 + 0.921184i \(0.627223\pi\)
\(318\) −5.19615 9.00000i −0.291386 0.504695i
\(319\) 10.3923 + 18.0000i 0.581857 + 1.00781i
\(320\) 0 0
\(321\) 6.00000 + 10.3923i 0.334887 + 0.580042i
\(322\) 0 0
\(323\) 10.3923 18.0000i 0.578243 1.00155i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) −3.46410 + 6.00000i −0.191565 + 0.331801i
\(328\) −6.00000 + 10.3923i −0.331295 + 0.573819i
\(329\) 6.00000 + 10.3923i 0.330791 + 0.572946i
\(330\) 0 0
\(331\) 1.73205 + 3.00000i 0.0952021 + 0.164895i 0.909693 0.415282i \(-0.136317\pi\)
−0.814491 + 0.580176i \(0.802984\pi\)
\(332\) −1.73205 3.00000i −0.0950586 0.164646i
\(333\) 6.92820 0.379663
\(334\) 15.0000 + 25.9808i 0.820763 + 1.42160i
\(335\) 0 0
\(336\) 8.66025 15.0000i 0.472456 0.818317i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) −3.00000 5.19615i −0.162221 0.280976i
\(343\) 6.92820 0.374088
\(344\) −3.46410 6.00000i −0.186772 0.323498i
\(345\) 0 0
\(346\) −31.1769 −1.67608
\(347\) −18.0000 31.1769i −0.966291 1.67366i −0.706107 0.708105i \(-0.749550\pi\)
−0.260184 0.965559i \(-0.583783\pi\)
\(348\) 3.00000 5.19615i 0.160817 0.278543i
\(349\) 3.46410 6.00000i 0.185429 0.321173i −0.758292 0.651915i \(-0.773966\pi\)
0.943721 + 0.330743i \(0.107299\pi\)
\(350\) −30.0000 −1.60357
\(351\) 0 0
\(352\) −18.0000 −0.959403
\(353\) 17.3205 30.0000i 0.921878 1.59674i 0.125370 0.992110i \(-0.459988\pi\)
0.796507 0.604629i \(-0.206679\pi\)
\(354\) −9.00000 + 15.5885i −0.478345 + 0.828517i
\(355\) 0 0
\(356\) −6.92820 −0.367194
\(357\) −10.3923 18.0000i −0.550019 0.952661i
\(358\) 10.3923 + 18.0000i 0.549250 + 0.951330i
\(359\) 17.3205 0.914141 0.457071 0.889430i \(-0.348899\pi\)
0.457071 + 0.889430i \(0.348899\pi\)
\(360\) 0 0
\(361\) 3.50000 6.06218i 0.184211 0.319062i
\(362\) 8.66025 15.0000i 0.455173 0.788382i
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) 0 0
\(366\) 1.73205 3.00000i 0.0905357 0.156813i
\(367\) 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i \(-0.696206\pi\)
0.995697 + 0.0926670i \(0.0295392\pi\)
\(368\) 0 0
\(369\) 6.92820 0.360668
\(370\) 0 0
\(371\) 10.3923 + 18.0000i 0.539542 + 0.934513i
\(372\) −3.46410 −0.179605
\(373\) −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) −18.0000 + 31.1769i −0.930758 + 1.61212i
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) 0 0
\(378\) −6.00000 −0.308607
\(379\) 8.66025 15.0000i 0.444847 0.770498i −0.553194 0.833052i \(-0.686591\pi\)
0.998042 + 0.0625541i \(0.0199246\pi\)
\(380\) 0 0
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) −41.5692 −2.12687
\(383\) 1.73205 + 3.00000i 0.0885037 + 0.153293i 0.906879 0.421392i \(-0.138458\pi\)
−0.818375 + 0.574684i \(0.805125\pi\)
\(384\) −6.06218 10.5000i −0.309359 0.535826i
\(385\) 0 0
\(386\) 0 0
\(387\) −2.00000 + 3.46410i −0.101666 + 0.176090i
\(388\) −6.92820 + 12.0000i −0.351726 + 0.609208i
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −4.33013 + 7.50000i −0.218704 + 0.378807i
\(393\) −6.00000 + 10.3923i −0.302660 + 0.524222i
\(394\) 0 0
\(395\) 0 0
\(396\) 1.73205 + 3.00000i 0.0870388 + 0.150756i
\(397\) 17.3205 + 30.0000i 0.869291 + 1.50566i 0.862722 + 0.505678i \(0.168758\pi\)
0.00656933 + 0.999978i \(0.497909\pi\)
\(398\) 27.7128 1.38912
\(399\) 6.00000 + 10.3923i 0.300376 + 0.520266i
\(400\) −12.5000 + 21.6506i −0.625000 + 1.08253i
\(401\) −3.46410 + 6.00000i −0.172989 + 0.299626i −0.939463 0.342649i \(-0.888676\pi\)
0.766475 + 0.642275i \(0.222009\pi\)
\(402\) 18.0000 0.897758
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) −18.0000 + 31.1769i −0.893325 + 1.54728i
\(407\) 12.0000 + 20.7846i 0.594818 + 1.03025i
\(408\) −10.3923 −0.514496
\(409\) 13.8564 + 24.0000i 0.685155 + 1.18672i 0.973388 + 0.229163i \(0.0735990\pi\)
−0.288233 + 0.957560i \(0.593068\pi\)
\(410\) 0 0
\(411\) 20.7846 1.02523
\(412\) 4.00000 + 6.92820i 0.197066 + 0.341328i
\(413\) 18.0000 31.1769i 0.885722 1.53412i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.00000 0.195881
\(418\) 10.3923 18.0000i 0.508304 0.880409i
\(419\) 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) 34.6410 1.68830 0.844150 0.536107i \(-0.180106\pi\)
0.844150 + 0.536107i \(0.180106\pi\)
\(422\) −17.3205 30.0000i −0.843149 1.46038i
\(423\) −1.73205 3.00000i −0.0842152 0.145865i
\(424\) 10.3923 0.504695
\(425\) 15.0000 + 25.9808i 0.727607 + 1.26025i
\(426\) 3.00000 5.19615i 0.145350 0.251754i
\(427\) −3.46410 + 6.00000i −0.167640 + 0.290360i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −12.1244 + 21.0000i −0.584010 + 1.01153i 0.410988 + 0.911641i \(0.365184\pi\)
−0.994998 + 0.0998939i \(0.968150\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) 17.0000 + 29.4449i 0.816968 + 1.41503i 0.907906 + 0.419173i \(0.137680\pi\)
−0.0909384 + 0.995857i \(0.528987\pi\)
\(434\) 20.7846 0.997693
\(435\) 0 0
\(436\) 3.46410 + 6.00000i 0.165900 + 0.287348i
\(437\) 0 0
\(438\) 0 0
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 3.46410 6.00000i 0.164399 0.284747i
\(445\) 0 0
\(446\) 3.00000 + 5.19615i 0.142054 + 0.246045i
\(447\) 13.8564 0.655386
\(448\) 1.73205 + 3.00000i 0.0818317 + 0.141737i
\(449\) −3.46410 6.00000i −0.163481 0.283158i 0.772634 0.634852i \(-0.218939\pi\)
−0.936115 + 0.351694i \(0.885606\pi\)
\(450\) 8.66025 0.408248
\(451\) 12.0000 + 20.7846i 0.565058 + 0.978709i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 5.19615 9.00000i 0.244137 0.422857i
\(454\) −30.0000 −1.40797
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −13.8564 + 24.0000i −0.648175 + 1.12267i 0.335383 + 0.942082i \(0.391134\pi\)
−0.983558 + 0.180591i \(0.942199\pi\)
\(458\) −6.00000 + 10.3923i −0.280362 + 0.485601i
\(459\) 3.00000 + 5.19615i 0.140028 + 0.242536i
\(460\) 0 0
\(461\) −6.92820 12.0000i −0.322679 0.558896i 0.658361 0.752702i \(-0.271250\pi\)
−0.981040 + 0.193806i \(0.937917\pi\)
\(462\) −10.3923 18.0000i −0.483494 0.837436i
\(463\) −17.3205 −0.804952 −0.402476 0.915430i \(-0.631850\pi\)
−0.402476 + 0.915430i \(0.631850\pi\)
\(464\) 15.0000 + 25.9808i 0.696358 + 1.20613i
\(465\) 0 0
\(466\) 5.19615 9.00000i 0.240707 0.416917i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −36.0000 −1.66233
\(470\) 0 0
\(471\) 7.00000 12.1244i 0.322543 0.558661i
\(472\) −9.00000 15.5885i −0.414259 0.717517i
\(473\) −13.8564 −0.637118
\(474\) 6.92820 + 12.0000i 0.318223 + 0.551178i
\(475\) −8.66025 15.0000i −0.397360 0.688247i
\(476\) −20.7846 −0.952661
\(477\) −3.00000 5.19615i −0.137361 0.237915i
\(478\) 9.00000 15.5885i 0.411650 0.712999i
\(479\) 5.19615 9.00000i 0.237418 0.411220i −0.722554 0.691314i \(-0.757032\pi\)
0.959973 + 0.280094i \(0.0903655\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −24.0000 −1.09317
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.0227273 + 0.0393648i
\(485\) 0 0
\(486\) 1.73205 0.0785674
\(487\) 19.0526 + 33.0000i 0.863354 + 1.49537i 0.868672 + 0.495387i \(0.164974\pi\)
−0.00531860 + 0.999986i \(0.501693\pi\)
\(488\) 1.73205 + 3.00000i 0.0784063 + 0.135804i
\(489\) −3.46410 −0.156652
\(490\) 0 0
\(491\) −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) 3.46410 6.00000i 0.156174 0.270501i
\(493\) 36.0000 1.62136
\(494\) 0 0
\(495\) 0 0
\(496\) 8.66025 15.0000i 0.388857 0.673520i
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) 10.3923 0.465223 0.232612 0.972570i \(-0.425273\pi\)
0.232612 + 0.972570i \(0.425273\pi\)
\(500\) 0 0
\(501\) 8.66025 + 15.0000i 0.386912 + 0.670151i
\(502\) −20.7846 −0.927663
\(503\) −12.0000 20.7846i −0.535054 0.926740i −0.999161 0.0409609i \(-0.986958\pi\)
0.464107 0.885779i \(-0.346375\pi\)
\(504\) 3.00000 5.19615i 0.133631 0.231455i
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) −20.7846 + 36.0000i −0.921262 + 1.59567i −0.123796 + 0.992308i \(0.539507\pi\)
−0.797466 + 0.603364i \(0.793827\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −8.66025 −0.382733
\(513\) −1.73205 3.00000i −0.0764719 0.132453i
\(514\) −15.5885 27.0000i −0.687577 1.19092i
\(515\) 0 0
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) 6.00000 10.3923i 0.263880 0.457053i
\(518\) −20.7846 + 36.0000i −0.913223 + 1.58175i
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 5.19615 9.00000i 0.227429 0.393919i
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) 6.00000 + 10.3923i 0.262111 + 0.453990i
\(525\) −17.3205 −0.755929
\(526\) −20.7846 36.0000i −0.906252 1.56967i
\(527\) −10.3923 18.0000i −0.452696 0.784092i
\(528\) −17.3205 −0.753778
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) −5.19615 + 9.00000i −0.225494 + 0.390567i
\(532\) 12.0000 0.520266
\(533\) 0 0
\(534\) −12.0000 −0.519291
\(535\) 0 0
\(536\) −9.00000 + 15.5885i −0.388741 + 0.673319i
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) −10.3923 −0.448044
\(539\) 8.66025 + 15.0000i 0.373024 + 0.646096i
\(540\) 0 0
\(541\) 6.92820 0.297867 0.148933 0.988847i \(-0.452416\pi\)
0.148933 + 0.988847i \(0.452416\pi\)
\(542\) 9.00000 + 15.5885i 0.386583 + 0.669582i
\(543\) 5.00000 8.66025i 0.214571 0.371647i
\(544\) −15.5885 + 27.0000i −0.668350 + 1.15762i
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 10.3923 18.0000i 0.443937 0.768922i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 15.0000 + 25.9808i 0.639602 + 1.10782i
\(551\) −20.7846 −0.885454
\(552\) 0 0
\(553\) −13.8564 24.0000i −0.589234 1.02058i
\(554\) −17.3205 −0.735878
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −6.92820 + 12.0000i −0.293557 + 0.508456i −0.974648 0.223743i \(-0.928173\pi\)
0.681091 + 0.732199i \(0.261506\pi\)
\(558\) −6.00000 −0.254000
\(559\) 0 0
\(560\) 0 0
\(561\) −10.3923 + 18.0000i −0.438763 + 0.759961i
\(562\) 6.00000 10.3923i 0.253095 0.438373i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) −3.46410 −0.145865
\(565\) 0 0
\(566\) −3.46410 6.00000i −0.145607 0.252199i
\(567\) −3.46410 −0.145479
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) −20.7846 + 36.0000i −0.867533 + 1.50261i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 16.4545 + 28.5000i 0.684416 + 1.18544i
\(579\) 0 0
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) −12.0000 + 20.7846i −0.497416 + 0.861550i
\(583\) 10.3923 18.0000i 0.430405 0.745484i
\(584\) 0 0
\(585\) 0 0
\(586\) −48.0000 −1.98286
\(587\) 5.19615 9.00000i 0.214468 0.371470i −0.738640 0.674100i \(-0.764532\pi\)
0.953108 + 0.302631i \(0.0978648\pi\)
\(588\) 2.50000 4.33013i 0.103098 0.178571i
\(589\) 6.00000 + 10.3923i 0.247226 + 0.428207i
\(590\) 0 0
\(591\) 0 0
\(592\) 17.3205 + 30.0000i 0.711868 + 1.23299i
\(593\) 6.92820 0.284507 0.142254 0.989830i \(-0.454565\pi\)
0.142254 + 0.989830i \(0.454565\pi\)
\(594\) 3.00000 + 5.19615i 0.123091 + 0.213201i
\(595\) 0 0
\(596\) 6.92820 12.0000i 0.283790 0.491539i
\(597\) 16.0000 0.654836
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −4.33013 + 7.50000i −0.176777 + 0.306186i
\(601\) −5.00000 + 8.66025i −0.203954 + 0.353259i −0.949799 0.312861i \(-0.898713\pi\)
0.745845 + 0.666120i \(0.232046\pi\)
\(602\) −12.0000 20.7846i −0.489083 0.847117i
\(603\) 10.3923 0.423207
\(604\) −5.19615 9.00000i −0.211428 0.366205i
\(605\) 0 0
\(606\) −10.3923 −0.422159
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 9.00000 15.5885i 0.364998 0.632195i
\(609\) −10.3923 + 18.0000i −0.421117 + 0.729397i
\(610\) 0 0
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) −10.3923 + 18.0000i −0.419741 + 0.727013i −0.995913 0.0903153i \(-0.971213\pi\)
0.576172 + 0.817328i \(0.304546\pi\)
\(614\) −9.00000 + 15.5885i −0.363210 + 0.629099i
\(615\) 0 0
\(616\) 20.7846 0.837436
\(617\) −3.46410 6.00000i −0.139459 0.241551i 0.787833 0.615889i \(-0.211203\pi\)
−0.927292 + 0.374338i \(0.877870\pi\)
\(618\) 6.92820 + 12.0000i 0.278693 + 0.482711i
\(619\) 31.1769 1.25311 0.626553 0.779379i \(-0.284465\pi\)
0.626553 + 0.779379i \(0.284465\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 24.0000 0.961540
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 8.66025 15.0000i 0.346133 0.599521i
\(627\) 6.00000 10.3923i 0.239617 0.415029i
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) 41.5692 1.65747
\(630\) 0 0
\(631\) −19.0526 33.0000i −0.758470 1.31371i −0.943630 0.331001i \(-0.892614\pi\)
0.185160 0.982708i \(-0.440720\pi\)
\(632\) −13.8564 −0.551178
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) −12.0000 + 20.7846i −0.476581 + 0.825462i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 36.0000 1.42525
\(639\) 1.73205 3.00000i 0.0685189 0.118678i
\(640\) 0 0
\(641\) −3.00000 5.19615i −0.118493 0.205236i 0.800678 0.599095i \(-0.204473\pi\)
−0.919171 + 0.393860i \(0.871140\pi\)
\(642\) 20.7846 0.820303
\(643\) −5.19615 9.00000i −0.204916 0.354925i 0.745190 0.666852i \(-0.232359\pi\)
−0.950106 + 0.311927i \(0.899026\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −18.0000 31.1769i −0.708201 1.22664i
\(647\) −12.0000 + 20.7846i −0.471769 + 0.817127i −0.999478 0.0322975i \(-0.989718\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(648\) −0.866025 + 1.50000i −0.0340207 + 0.0589256i
\(649\) −36.0000 −1.41312
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) −1.73205 + 3.00000i −0.0678323 + 0.117489i
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 6.00000 + 10.3923i 0.234619 + 0.406371i
\(655\) 0 0
\(656\) 17.3205 + 30.0000i 0.676252 + 1.17130i
\(657\) 0 0
\(658\) 20.7846 0.810268
\(659\) −6.00000 10.3923i −0.233727 0.404827i 0.725175 0.688565i \(-0.241759\pi\)
−0.958902 + 0.283738i \(0.908425\pi\)
\(660\) 0 0
\(661\) 10.3923 18.0000i 0.404214 0.700119i −0.590016 0.807392i \(-0.700879\pi\)
0.994230 + 0.107273i \(0.0342118\pi\)
\(662\) 6.00000 0.233197
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 6.00000 10.3923i 0.232495 0.402694i
\(667\) 0 0
\(668\) 17.3205 0.670151
\(669\) 1.73205 + 3.00000i 0.0669650 + 0.115987i
\(670\) 0 0
\(671\) 6.92820 0.267460
\(672\) −9.00000 15.5885i −0.347183 0.601338i
\(673\) −23.0000 + 39.8372i −0.886585 + 1.53561i −0.0426985 + 0.999088i \(0.513595\pi\)
−0.843886 + 0.536522i \(0.819738\pi\)
\(674\) 12.1244 21.0000i 0.467013 0.808890i
\(675\) 5.00000 0.192450
\(676\) 0 0
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 5.19615 9.00000i 0.199557 0.345643i
\(679\) 24.0000 41.5692i 0.921035 1.59528i
\(680\) 0 0
\(681\) −17.3205 −0.663723
\(682\) −10.3923 18.0000i −0.397942 0.689256i
\(683\) 15.5885 + 27.0000i 0.596476 + 1.03313i 0.993337 + 0.115248i \(0.0367661\pi\)
−0.396861 + 0.917879i \(0.629901\pi\)
\(684\) −3.46410 −0.132453
\(685\) 0 0
\(686\) 6.00000 10.3923i 0.229081 0.396780i
\(687\) −3.46410 + 6.00000i −0.132164 + 0.228914i
\(688\) −20.0000 −0.762493
\(689\) 0 0
\(690\) 0 0
\(691\) 22.5167 39.0000i 0.856574 1.48363i −0.0186028 0.999827i \(-0.505922\pi\)
0.875177 0.483803i \(-0.160745\pi\)
\(692\) −9.00000 + 15.5885i −0.342129 + 0.592584i
\(693\) −6.00000 10.3923i −0.227921 0.394771i
\(694\) −62.3538 −2.36692
\(695\) 0 0
\(696\) 5.19615 + 9.00000i 0.196960 + 0.341144i
\(697\) 41.5692 1.57455
\(698\) −6.00000 10.3923i −0.227103 0.393355i
\(699\) 3.00000 5.19615i 0.113470 0.196537i
\(700\) −8.66025 + 15.0000i −0.327327 + 0.566947i
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 1.73205 3.00000i 0.0652791 0.113067i
\(705\) 0 0
\(706\) −30.0000 51.9615i −1.12906 1.95560i
\(707\) 20.7846 0.781686
\(708\) 5.19615 + 9.00000i 0.195283 + 0.338241i
\(709\) 3.46410 + 6.00000i 0.130097 + 0.225335i 0.923714 0.383083i \(-0.125138\pi\)
−0.793617 + 0.608418i \(0.791804\pi\)
\(710\) 0 0
\(711\) 4.00000 + 6.92820i 0.150012 + 0.259828i
\(712\) 6.00000 10.3923i 0.224860 0.389468i
\(713\) 0 0
\(714\) −36.0000 −1.34727
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 5.19615 9.00000i 0.194054 0.336111i
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) 12.0000 + 20.7846i 0.447524 + 0.775135i 0.998224 0.0595683i \(-0.0189724\pi\)
−0.550700 + 0.834703i \(0.685639\pi\)
\(720\) 0 0
\(721\) −13.8564 24.0000i −0.516040 0.893807i
\(722\) −6.06218 10.5000i −0.225611 0.390770i
\(723\) −13.8564 −0.515325
\(724\) −5.00000 8.66025i −0.185824 0.321856i
\(725\) 15.0000 25.9808i 0.557086 0.964901i
\(726\) −0.866025 + 1.50000i −0.0321412 + 0.0556702i
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) −34.6410 −1.27950 −0.639748 0.768585i \(-0.720961\pi\)
−0.639748 + 0.768585i \(0.720961\pi\)
\(734\) −13.8564 24.0000i −0.511449 0.885856i
\(735\) 0 0
\(736\) 0 0
\(737\) 18.0000 + 31.1769i 0.663039 + 1.14842i
\(738\) 6.00000 10.3923i 0.220863 0.382546i
\(739\) 19.0526 33.0000i 0.700860 1.21392i −0.267305 0.963612i \(-0.586133\pi\)
0.968165 0.250313i \(-0.0805334\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 36.0000 1.32160
\(743\) 1.73205 3.00000i 0.0635428 0.110059i −0.832504 0.554019i \(-0.813093\pi\)
0.896047 + 0.443960i \(0.146427\pi\)
\(744\) 3.00000 5.19615i 0.109985 0.190500i
\(745\) 0 0
\(746\) −38.1051 −1.39513
\(747\) −1.73205 3.00000i −0.0633724 0.109764i
\(748\) 10.3923 + 18.0000i 0.379980 + 0.658145i
\(749\) −41.5692 −1.51891
\(750\) 0 0
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 8.66025 15.0000i 0.315807 0.546994i
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) 0 0
\(756\) −1.73205 + 3.00000i −0.0629941 + 0.109109i
\(757\) −11.0000 + 19.0526i −0.399802 + 0.692477i −0.993701 0.112062i \(-0.964254\pi\)
0.593899 + 0.804539i \(0.297588\pi\)
\(758\) −15.0000 25.9808i −0.544825 0.943664i
\(759\) 0 0
\(760\) 0 0
\(761\) 24.2487 + 42.0000i 0.879015 + 1.52250i 0.852423 + 0.522852i \(0.175132\pi\)
0.0265919 + 0.999646i \(0.491535\pi\)
\(762\) 13.8564 0.501965
\(763\) −12.0000 20.7846i −0.434429 0.752453i
\(764\) −12.0000 + 20.7846i −0.434145 + 0.751961i
\(765\) 0 0
\(766\) 6.00000 0.216789
\(767\) 0 0
\(768\) −19.0000 −0.685603
\(769\) 13.8564 24.0000i 0.499675 0.865462i −0.500325 0.865838i \(-0.666786\pi\)
1.00000 0.000375472i \(0.000119516\pi\)
\(770\) 0 0
\(771\) −9.00000 15.5885i −0.324127 0.561405i
\(772\) 0 0
\(773\) −6.92820 12.0000i −0.249190 0.431610i 0.714111 0.700032i \(-0.246831\pi\)
−0.963301 + 0.268422i \(0.913498\pi\)
\(774\) 3.46410 + 6.00000i 0.124515 + 0.215666i
\(775\) −17.3205 −0.622171
\(776\) −12.0000 20.7846i −0.430775 0.746124i
\(777\) −12.0000 + 20.7846i −0.430498 + 0.745644i
\(778\) 15.5885 27.0000i 0.558873 0.967997i
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) 3.00000 5.19615i 0.107211 0.185695i
\(784\) 12.5000 + 21.6506i 0.446429 + 0.773237i
\(785\) 0 0
\(786\) 10.3923 + 18.0000i 0.370681 + 0.642039i
\(787\) 5.19615 + 9.00000i 0.185223 + 0.320815i 0.943652 0.330941i \(-0.107366\pi\)
−0.758429 + 0.651756i \(0.774033\pi\)