Properties

Label 507.2.e.e.484.1
Level $507$
Weight $2$
Character 507.484
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 484.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.e.22.1

$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 1.50000i −0.612372 1.06066i −0.990839 0.135045i \(-0.956882\pi\)
0.378467 0.925615i \(-0.376451\pi\)
\(3\) 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 0.327327 + 0.944911i \(0.393852\pi\)
−0.981981 + 0.188982i \(0.939481\pi\)
\(8\) −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 −0.999665 0.0258656i \(-0.991766\pi\)
0.477432 0.878668i \(-0.341568\pi\)
\(12\) −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 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) 1.73205 0.408248
\(19\) −1.73205 + 3.00000i −0.397360 + 0.688247i −0.993399 0.114708i \(-0.963407\pi\)
0.596040 + 0.802955i \(0.296740\pi\)
\(20\) 0 0
\(21\) −3.46410 −0.755929
\(22\) −3.00000 + 5.19615i −0.639602 + 1.10782i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) −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 −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) −3.46410 −0.622171 −0.311086 0.950382i \(-0.600693\pi\)
−0.311086 + 0.950382i \(0.600693\pi\)
\(32\) 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 0.996616 + 0.0821995i \(0.0261945\pi\)
−0.427121 + 0.904194i \(0.640472\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) 0 0
\(41\) 3.46410 + 6.00000i 0.541002 + 0.937043i 0.998847 + 0.0480106i \(0.0152881\pi\)
−0.457845 + 0.889032i \(0.651379\pi\)
\(42\) 3.00000 + 5.19615i 0.462910 + 0.801784i
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) 3.46410 0.522233
\(45\) 0 0
\(46\) 0 0
\(47\) −3.46410 −0.505291 −0.252646 0.967559i \(-0.581301\pi\)
−0.252646 + 0.967559i \(0.581301\pi\)
\(48\) −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 −0.299552 0.954080i \(-0.596837\pi\)
0.976034 0.217620i \(-0.0698294\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 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 0.986555 + 0.163429i \(0.0522554\pi\)
−0.351744 + 0.936096i \(0.614411\pi\)
\(68\) −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 \(-0.899234\pi\)
0.744753 + 0.667340i \(0.232567\pi\)
\(72\) 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 \(-0.560887\pi\)
−0.190117 + 0.981761i \(0.560887\pi\)
\(84\) 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 \(-0.286348\pi\)
−0.989126 + 0.147073i \(0.953015\pi\)
\(90\) 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 −0.263795 0.964579i \(-0.584974\pi\)
0.967247 0.253837i \(-0.0816925\pi\)
\(98\) −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 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 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 −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 6.92820 0.663602 0.331801 0.943349i \(-0.392344\pi\)
0.331801 + 0.943349i \(0.392344\pi\)
\(110\) 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 −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 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 0.632166 0.774833i \(-0.282166\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(128\) −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 −0.0454914 + 0.998965i \(0.514485\pi\)
−0.842383 + 0.538879i \(0.818848\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 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 0.429224 + 0.903198i \(0.358787\pi\)
−0.996804 + 0.0798802i \(0.974546\pi\)
\(150\) −4.33013 + 7.50000i −0.353553 + 0.612372i
\(151\) −10.3923 −0.845714 −0.422857 0.906196i \(-0.638973\pi\)
−0.422857 + 0.906196i \(0.638973\pi\)
\(152\) 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 \(-0.790016\pi\)
0.925851 + 0.377888i \(0.123350\pi\)
\(164\) −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 0.977861 + 0.209255i \(0.0671038\pi\)
−0.307711 + 0.951480i \(0.599563\pi\)
\(168\) 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 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) −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 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 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 −0.00454614 + 0.999990i \(0.501447\pi\)
−0.863743 + 0.503932i \(0.831886\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) −24.0000 −1.72310
\(195\) 0 0
\(196\) 5.00000 0.357143
\(197\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(198\) −3.00000 5.19615i −0.213201 0.369274i
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) 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 0.972346 + 0.233544i \(0.0750324\pi\)
−0.283918 + 0.958849i \(0.591634\pi\)
\(212\) −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 \(-0.129664\pi\)
−0.802187 + 0.597073i \(0.796330\pi\)
\(224\) 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 −0.421262 0.906939i \(-0.638413\pi\)
0.996063 0.0886460i \(-0.0282540\pi\)
\(228\) 1.73205 3.00000i 0.114708 0.198680i
\(229\) 6.92820 0.457829 0.228914 0.973447i \(-0.426482\pi\)
0.228914 + 0.973447i \(0.426482\pi\)
\(230\) 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 \(-0.609112\pi\)
−0.336111 + 0.941822i \(0.609112\pi\)
\(240\) 0 0
\(241\) 6.92820 12.0000i 0.446285 0.772988i −0.551856 0.833939i \(-0.686080\pi\)
0.998141 + 0.0609515i \(0.0194135\pi\)
\(242\) 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 −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 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 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 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 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) −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 −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 0 0
\(271\) 5.19615 + 9.00000i 0.315644 + 0.546711i 0.979574 0.201083i \(-0.0644462\pi\)
−0.663930 + 0.747794i \(0.731113\pi\)
\(272\) −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 −0.976231 0.216731i \(-0.930460\pi\)
0.675810 + 0.737075i \(0.263794\pi\)
\(278\) −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 \(-0.566256\pi\)
−0.206651 + 0.978415i \(0.566256\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −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 −0.103711 0.994607i \(-0.533072\pi\)
0.913211 0.407487i \(-0.133595\pi\)
\(294\) −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 \(-0.404160\pi\)
0.296560 + 0.955014i \(0.404160\pi\)
\(308\) −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 \(-0.372777\pi\)
0.389127 + 0.921184i \(0.372777\pi\)
\(318\) 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 \(-0.863683\pi\)
0.814491 + 0.580176i \(0.197016\pi\)
\(332\) 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 −0.260184 + 0.965559i \(0.583783\pi\)
−0.706107 + 0.708105i \(0.749550\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) −3.46410 6.00000i −0.185429 0.321173i 0.758292 0.651915i \(-0.226034\pi\)
−0.943721 + 0.330743i \(0.892701\pi\)
\(350\) −30.0000 −1.60357
\(351\) 0 0
\(352\) −18.0000 −0.959403
\(353\) −17.3205 30.0000i −0.921878 1.59674i −0.796507 0.604629i \(-0.793321\pi\)
−0.125370 0.992110i \(-0.540012\pi\)
\(354\) −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 \(-0.651101\pi\)
−0.457071 + 0.889430i \(0.651101\pi\)
\(360\) 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 0.995697 0.0926670i \(-0.0295392\pi\)
−0.578101 + 0.815966i \(0.696206\pi\)
\(368\) 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 0.427051 + 0.904227i \(0.359552\pi\)
−0.996610 + 0.0822766i \(0.973781\pi\)
\(374\) −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 \(-0.313409\pi\)
−0.998042 + 0.0625541i \(0.980075\pi\)
\(380\) 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 \(-0.861542\pi\)
0.818375 + 0.574684i \(0.194875\pi\)
\(384\) 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 −0.00656933 + 0.999978i \(0.502091\pi\)
−0.862722 + 0.505678i \(0.831242\pi\)
\(398\) −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 \(-0.111324\pi\)
−0.766475 + 0.642275i \(0.777991\pi\)
\(402\) 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 0.288233 + 0.957560i \(0.406932\pi\)
−0.973388 + 0.229163i \(0.926401\pi\)
\(410\) 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 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) −34.6410 −1.68830 −0.844150 0.536107i \(-0.819894\pi\)
−0.844150 + 0.536107i \(0.819894\pi\)
\(422\) 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 0.994998 + 0.0998939i \(0.0318503\pi\)
−0.410988 + 0.911641i \(0.634816\pi\)
\(432\) −2.50000 4.33013i −0.120281 0.208333i
\(433\) 17.0000 29.4449i 0.816968 1.41503i −0.0909384 0.995857i \(-0.528987\pi\)
0.907906 0.419173i \(-0.137680\pi\)
\(434\) −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 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 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 \(-0.781061\pi\)
0.936115 + 0.351694i \(0.114394\pi\)
\(450\) −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 0.983558 + 0.180591i \(0.0578010\pi\)
−0.335383 + 0.942082i \(0.608866\pi\)
\(458\) −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 \(-0.728750\pi\)
0.981040 + 0.193806i \(0.0620834\pi\)
\(462\) 10.3923 18.0000i 0.483494 0.837436i
\(463\) 17.3205 0.804952 0.402476 0.915430i \(-0.368150\pi\)
0.402476 + 0.915430i \(0.368150\pi\)
\(464\) 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 \(-0.242968\pi\)
−0.959973 + 0.280094i \(0.909635\pi\)
\(480\) 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 0.00531860 + 0.999986i \(0.498307\pi\)
−0.868672 + 0.495387i \(0.835026\pi\)
\(488\) −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 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) −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 \(-0.574727\pi\)
−0.232612 + 0.972570i \(0.574727\pi\)
\(500\) 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 0.464107 + 0.885779i \(0.346375\pi\)
−0.999161 + 0.0409609i \(0.986958\pi\)
\(504\) 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 0.797466 + 0.603364i \(0.206173\pi\)
0.123796 + 0.992308i \(0.460493\pi\)
\(510\) 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 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) 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 \(-0.547584\pi\)
−0.148933 + 0.988847i \(0.547584\pi\)
\(542\) 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 \(-0.0718275\pi\)
−0.681091 + 0.732199i \(0.738494\pi\)
\(558\) −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 −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) 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 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 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 \(-0.235468\pi\)
−0.953108 + 0.302631i \(0.902135\pi\)
\(588\) 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 \(-0.545435\pi\)
−0.142254 + 0.989830i \(0.545435\pi\)
\(594\) 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 0.745845 0.666120i \(-0.232046\pi\)
−0.949799 + 0.312861i \(0.898713\pi\)
\(602\) −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 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 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 \(-0.0287875\pi\)
−0.576172 + 0.817328i \(0.695454\pi\)
\(614\) −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 \(-0.788797\pi\)
0.927292 + 0.374338i \(0.122130\pi\)
\(618\) −6.92820 + 12.0000i −0.278693 + 0.482711i
\(619\) −31.1769 −1.25311 −0.626553 0.779379i \(-0.715535\pi\)
−0.626553 + 0.779379i \(0.715535\pi\)
\(620\) 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 −0.185160 0.982708i \(-0.559280\pi\)
0.943630 0.331001i \(-0.107386\pi\)
\(632\) 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 −0.919171 0.393860i \(-0.871140\pi\)
0.800678 + 0.599095i \(0.204473\pi\)
\(642\) −20.7846 −0.820303
\(643\) 5.19615 9.00000i 0.204916 0.354925i −0.745190 0.666852i \(-0.767641\pi\)
0.950106 + 0.311927i \(0.100974\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −18.0000 + 31.1769i −0.708201 + 1.22664i
\(647\) −12.0000 20.7846i −0.471769 0.817127i 0.527710 0.849425i \(-0.323051\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(648\) 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 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 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 −0.958902 0.283738i \(-0.908425\pi\)
0.725175 + 0.688565i \(0.241759\pi\)
\(660\) 0 0
\(661\) −10.3923 18.0000i −0.404214 0.700119i 0.590016 0.807392i \(-0.299121\pi\)
−0.994230 + 0.107273i \(0.965788\pi\)
\(662\) 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 −0.843886 0.536522i \(-0.819738\pi\)
−0.0426985 0.999088i \(-0.513595\pi\)
\(674\) −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 0.396861 + 0.917879i \(0.370099\pi\)
−0.993337 + 0.115248i \(0.963234\pi\)
\(684\) 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 −0.875177 0.483803i \(-0.839255\pi\)
0.0186028 0.999827i \(-0.494078\pi\)
\(692\) −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 \(-0.874862\pi\)
0.793617 + 0.608418i \(0.208196\pi\)
\(710\) 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 −0.550700 0.834703i \(-0.685639\pi\)
0.998224 + 0.0595683i \(0.0189724\pi\)
\(720\) 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 \(-0.279039\pi\)
0.639748 + 0.768585i \(0.279039\pi\)
\(734\) 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 −0.968165 0.250313i \(-0.919467\pi\)
0.267305 0.963612i \(-0.413867\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 36.0000 1.32160
\(743\) −1.73205 3.00000i −0.0635428 0.110059i 0.832504 0.554019i \(-0.186907\pi\)
−0.896047 + 0.443960i \(0.853573\pi\)
\(744\) 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 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) −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 0.593899 0.804539i \(-0.297588\pi\)
−0.993701 + 0.112062i \(0.964254\pi\)
\(758\) −15.0000 + 25.9808i −0.544825 + 0.943664i
\(759\) 0 0
\(760\) 0 0
\(761\) −24.2487 + 42.0000i −0.879015 + 1.52250i −0.0265919 + 0.999646i \(0.508465\pi\)
−0.852423 + 0.522852i \(0.824868\pi\)
\(762\) −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 \(-0.333214\pi\)
−1.00000 0.000375472i \(0.999880\pi\)
\(770\) 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 \(-0.753169\pi\)
0.963301 + 0.268422i \(0.0865023\pi\)
\(774\) −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 \(-0.892634\pi\)
0.758429 + 0.651756i \(0.225967\pi\)