Properties

Label 507.2.e.c.484.1
Level $507$
Weight $2$
Character 507.484
Analytic conductor $4.048$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 484.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.c.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} +1.00000 q^{12} +2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.50000 - 6.06218i) q^{17} -1.00000 q^{18} +(-3.00000 + 5.19615i) q^{19} +(0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(3.00000 + 5.19615i) q^{23} +(1.50000 + 2.59808i) q^{24} -4.00000 q^{25} -1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(0.500000 + 0.866025i) q^{29} +(-0.500000 + 0.866025i) q^{30} -4.00000 q^{31} +(2.50000 - 4.33013i) q^{32} +(1.00000 - 1.73205i) q^{33} +7.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{36} +(0.500000 + 0.866025i) q^{37} -6.00000 q^{38} +3.00000 q^{40} +(4.50000 + 7.79423i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-3.00000 + 5.19615i) q^{43} -2.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{50} +7.00000 q^{51} -9.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(3.00000 - 5.19615i) q^{56} -6.00000 q^{57} +(-0.500000 + 0.866025i) q^{58} +1.00000 q^{60} +(-0.500000 + 0.866025i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(1.00000 + 1.73205i) q^{63} +7.00000 q^{64} +2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(-3.00000 + 5.19615i) q^{69} +2.00000 q^{70} +(3.00000 - 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} -11.0000 q^{73} +(-0.500000 + 0.866025i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(3.00000 + 5.19615i) q^{76} -4.00000 q^{77} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} +14.0000 q^{83} +(1.00000 - 1.73205i) q^{84} +(3.50000 - 6.06218i) q^{85} -6.00000 q^{86} +(-0.500000 + 0.866025i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(-7.00000 - 12.1244i) q^{89} -1.00000 q^{90} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} +5.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-1.50000 + 2.59808i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} - q^{9} + q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{14} + q^{15} + q^{16} + 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 2 q^{22} + 6 q^{23} + 3 q^{24} - 8 q^{25} - 2 q^{27} - 2 q^{28} + q^{29} - q^{30} - 8 q^{31} + 5 q^{32} + 2 q^{33} + 14 q^{34} + 2 q^{35} + q^{36} + q^{37} - 12 q^{38} + 6 q^{40} + 9 q^{41} + 2 q^{42} - 6 q^{43} - 4 q^{44} - q^{45} - 6 q^{46} - 12 q^{47} - q^{48} + 3 q^{49} - 4 q^{50} + 14 q^{51} - 18 q^{53} - q^{54} - 2 q^{55} + 6 q^{56} - 12 q^{57} - q^{58} + 2 q^{60} - q^{61} - 4 q^{62} + 2 q^{63} + 14 q^{64} + 4 q^{66} - 2 q^{67} - 7 q^{68} - 6 q^{69} + 4 q^{70} + 6 q^{71} - 3 q^{72} - 22 q^{73} - q^{74} - 4 q^{75} + 6 q^{76} - 8 q^{77} - 8 q^{79} + q^{80} - q^{81} - 9 q^{82} + 28 q^{83} + 2 q^{84} + 7 q^{85} - 12 q^{86} - q^{87} - 6 q^{88} - 14 q^{89} - 2 q^{90} + 12 q^{92} - 4 q^{93} - 6 q^{94} - 6 q^{95} + 10 q^{96} - 2 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i \(-0.709957\pi\)
0.990766 + 0.135583i \(0.0432908\pi\)
\(8\) 3.00000 1.06066
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 2.00000 0.534522
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 3.50000 6.06218i 0.848875 1.47029i −0.0333386 0.999444i \(-0.510614\pi\)
0.882213 0.470850i \(-0.156053\pi\)
\(18\) −1.00000 −0.235702
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 2.00000 0.436436
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 1.50000 + 2.59808i 0.306186 + 0.530330i
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.00000 1.73205i −0.188982 0.327327i
\(29\) 0.500000 + 0.866025i 0.0928477 + 0.160817i 0.908708 0.417432i \(-0.137070\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) 7.00000 1.20049
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) −3.00000 + 5.19615i −0.457496 + 0.792406i −0.998828 0.0484030i \(-0.984587\pi\)
0.541332 + 0.840809i \(0.317920\pi\)
\(44\) −2.00000 −0.301511
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 7.00000 0.980196
\(52\) 0 0
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −1.00000 1.73205i −0.134840 0.233550i
\(56\) 3.00000 5.19615i 0.400892 0.694365i
\(57\) −6.00000 −0.794719
\(58\) −0.500000 + 0.866025i −0.0656532 + 0.113715i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 1.00000 0.129099
\(61\) −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i \(-0.853725\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) 1.00000 + 1.73205i 0.125988 + 0.218218i
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 2.00000 0.246183
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) −3.50000 6.06218i −0.424437 0.735147i
\(69\) −3.00000 + 5.19615i −0.361158 + 0.625543i
\(70\) 2.00000 0.239046
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 3.00000 + 5.19615i 0.344124 + 0.596040i
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.50000 + 7.79423i −0.496942 + 0.860729i
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) 1.00000 1.73205i 0.109109 0.188982i
\(85\) 3.50000 6.06218i 0.379628 0.657536i
\(86\) −6.00000 −0.646997
\(87\) −0.500000 + 0.866025i −0.0536056 + 0.0928477i
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) −7.00000 12.1244i −0.741999 1.28518i −0.951584 0.307389i \(-0.900545\pi\)
0.209585 0.977790i \(-0.432789\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) −2.00000 3.46410i −0.207390 0.359211i
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 5.00000 0.510310
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) −1.50000 + 2.59808i −0.151523 + 0.262445i
\(99\) 2.00000 0.201008
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 3.50000 + 6.06218i 0.346552 + 0.600245i
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) 0 0
\(105\) 2.00000 0.195180
\(106\) −4.50000 7.79423i −0.437079 0.757042i
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 1.00000 1.73205i 0.0953463 0.165145i
\(111\) −0.500000 + 0.866025i −0.0474579 + 0.0821995i
\(112\) 2.00000 0.188982
\(113\) 7.50000 12.9904i 0.705541 1.22203i −0.260955 0.965351i \(-0.584038\pi\)
0.966496 0.256681i \(-0.0826291\pi\)
\(114\) −3.00000 5.19615i −0.280976 0.486664i
\(115\) 3.00000 + 5.19615i 0.279751 + 0.484544i
\(116\) 1.00000 0.0928477
\(117\) 0 0
\(118\) 0 0
\(119\) −7.00000 12.1244i −0.641689 1.11144i
\(120\) 1.50000 + 2.59808i 0.136931 + 0.237171i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −1.00000 −0.0905357
\(123\) −4.50000 + 7.79423i −0.405751 + 0.702782i
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) −9.00000 −0.804984
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) −10.0000 17.3205i −0.887357 1.53695i −0.842989 0.537931i \(-0.819206\pi\)
−0.0443678 0.999015i \(-0.514127\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) −6.00000 −0.528271
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) −1.00000 1.73205i −0.0870388 0.150756i
\(133\) 6.00000 + 10.3923i 0.520266 + 0.901127i
\(134\) 1.00000 1.73205i 0.0863868 0.149626i
\(135\) −1.00000 −0.0860663
\(136\) 10.5000 18.1865i 0.900368 1.55948i
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) −6.00000 −0.510754
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) −3.00000 5.19615i −0.252646 0.437595i
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) 0.500000 + 0.866025i 0.0415227 + 0.0719195i
\(146\) −5.50000 9.52628i −0.455183 0.788400i
\(147\) −1.50000 + 2.59808i −0.123718 + 0.214286i
\(148\) 1.00000 0.0821995
\(149\) 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i \(-0.794119\pi\)
0.920904 + 0.389789i \(0.127452\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) −9.00000 + 15.5885i −0.729996 + 1.26439i
\(153\) 3.50000 + 6.06218i 0.282958 + 0.490098i
\(154\) −2.00000 3.46410i −0.161165 0.279145i
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −3.00000 −0.239426 −0.119713 0.992809i \(-0.538197\pi\)
−0.119713 + 0.992809i \(0.538197\pi\)
\(158\) −2.00000 3.46410i −0.159111 0.275589i
\(159\) −4.50000 7.79423i −0.356873 0.618123i
\(160\) 2.50000 4.33013i 0.197642 0.342327i
\(161\) 12.0000 0.945732
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 9.00000 0.702782
\(165\) 1.00000 1.73205i 0.0778499 0.134840i
\(166\) 7.00000 + 12.1244i 0.543305 + 0.941033i
\(167\) 8.00000 + 13.8564i 0.619059 + 1.07224i 0.989658 + 0.143448i \(0.0458190\pi\)
−0.370599 + 0.928793i \(0.620848\pi\)
\(168\) 6.00000 0.462910
\(169\) 0 0
\(170\) 7.00000 0.536875
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) 3.00000 + 5.19615i 0.228748 + 0.396203i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −1.00000 −0.0758098
\(175\) −4.00000 + 6.92820i −0.302372 + 0.523723i
\(176\) 1.00000 1.73205i 0.0753778 0.130558i
\(177\) 0 0
\(178\) 7.00000 12.1244i 0.524672 0.908759i
\(179\) 1.00000 + 1.73205i 0.0747435 + 0.129460i 0.900975 0.433872i \(-0.142853\pi\)
−0.826231 + 0.563331i \(0.809520\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 9.00000 + 15.5885i 0.663489 + 1.14920i
\(185\) 0.500000 + 0.866025i 0.0367607 + 0.0636715i
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) −14.0000 −1.02378
\(188\) −3.00000 + 5.19615i −0.218797 + 0.378968i
\(189\) −1.00000 + 1.73205i −0.0727393 + 0.125988i
\(190\) −6.00000 −0.435286
\(191\) 2.00000 3.46410i 0.144715 0.250654i −0.784552 0.620063i \(-0.787107\pi\)
0.929267 + 0.369410i \(0.120440\pi\)
\(192\) 3.50000 + 6.06218i 0.252591 + 0.437500i
\(193\) −4.50000 7.79423i −0.323917 0.561041i 0.657376 0.753563i \(-0.271667\pi\)
−0.981293 + 0.192522i \(0.938333\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) 3.00000 + 5.19615i 0.213741 + 0.370211i 0.952882 0.303340i \(-0.0981018\pi\)
−0.739141 + 0.673550i \(0.764768\pi\)
\(198\) 1.00000 + 1.73205i 0.0710669 + 0.123091i
\(199\) −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i \(-0.998611\pi\)
0.503774 + 0.863836i \(0.331945\pi\)
\(200\) −12.0000 −0.848528
\(201\) 1.00000 1.73205i 0.0705346 0.122169i
\(202\) 1.50000 2.59808i 0.105540 0.182800i
\(203\) 2.00000 0.140372
\(204\) 3.50000 6.06218i 0.245049 0.424437i
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) 3.00000 + 5.19615i 0.209020 + 0.362033i
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 1.00000 + 1.73205i 0.0690066 + 0.119523i
\(211\) 4.00000 + 6.92820i 0.275371 + 0.476957i 0.970229 0.242190i \(-0.0778659\pi\)
−0.694857 + 0.719148i \(0.744533\pi\)
\(212\) −4.50000 + 7.79423i −0.309061 + 0.535310i
\(213\) 6.00000 0.411113
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) −3.00000 + 5.19615i −0.204598 + 0.354375i
\(216\) −3.00000 −0.204124
\(217\) −4.00000 + 6.92820i −0.271538 + 0.470317i
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) −5.50000 9.52628i −0.371656 0.643726i
\(220\) −2.00000 −0.134840
\(221\) 0 0
\(222\) −1.00000 −0.0671156
\(223\) 8.00000 + 13.8564i 0.535720 + 0.927894i 0.999128 + 0.0417488i \(0.0132929\pi\)
−0.463409 + 0.886145i \(0.653374\pi\)
\(224\) −5.00000 8.66025i −0.334077 0.578638i
\(225\) 2.00000 3.46410i 0.133333 0.230940i
\(226\) 15.0000 0.997785
\(227\) −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) −3.00000 + 5.19615i −0.198680 + 0.344124i
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) −3.00000 + 5.19615i −0.197814 + 0.342624i
\(231\) −2.00000 3.46410i −0.131590 0.227921i
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) 0 0
\(237\) −2.00000 3.46410i −0.129914 0.225018i
\(238\) 7.00000 12.1244i 0.453743 0.785905i
\(239\) −30.0000 −1.94054 −0.970269 0.242028i \(-0.922188\pi\)
−0.970269 + 0.242028i \(0.922188\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) 7.00000 0.449977
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0.500000 + 0.866025i 0.0320092 + 0.0554416i
\(245\) 1.50000 + 2.59808i 0.0958315 + 0.165985i
\(246\) −9.00000 −0.573819
\(247\) 0 0
\(248\) −12.0000 −0.762001
\(249\) 7.00000 + 12.1244i 0.443607 + 0.768350i
\(250\) −4.50000 7.79423i −0.284605 0.492950i
\(251\) −6.00000 + 10.3923i −0.378717 + 0.655956i −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 2.00000 0.125988
\(253\) 6.00000 10.3923i 0.377217 0.653359i
\(254\) 10.0000 17.3205i 0.627456 1.08679i
\(255\) 7.00000 0.438357
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 3.50000 + 6.06218i 0.218324 + 0.378148i 0.954296 0.298864i \(-0.0966077\pi\)
−0.735972 + 0.677012i \(0.763274\pi\)
\(258\) −3.00000 5.19615i −0.186772 0.323498i
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) −4.00000 6.92820i −0.247121 0.428026i
\(263\) 15.0000 + 25.9808i 0.924940 + 1.60204i 0.791658 + 0.610964i \(0.209218\pi\)
0.133281 + 0.991078i \(0.457449\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) −9.00000 −0.552866
\(266\) −6.00000 + 10.3923i −0.367884 + 0.637193i
\(267\) 7.00000 12.1244i 0.428393 0.741999i
\(268\) −2.00000 −0.122169
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) 7.00000 0.424437
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) 4.00000 + 6.92820i 0.241209 + 0.417786i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) 15.5000 26.8468i 0.931305 1.61307i 0.150210 0.988654i \(-0.452005\pi\)
0.781094 0.624413i \(-0.214662\pi\)
\(278\) −12.0000 −0.719712
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) 3.00000 5.19615i 0.179284 0.310530i
\(281\) 19.0000 1.13344 0.566722 0.823909i \(-0.308211\pi\)
0.566722 + 0.823909i \(0.308211\pi\)
\(282\) 3.00000 5.19615i 0.178647 0.309426i
\(283\) 9.00000 + 15.5885i 0.534994 + 0.926638i 0.999164 + 0.0408910i \(0.0130196\pi\)
−0.464169 + 0.885747i \(0.653647\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) −6.00000 −0.355409
\(286\) 0 0
\(287\) 18.0000 1.06251
\(288\) 2.50000 + 4.33013i 0.147314 + 0.255155i
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) −0.500000 + 0.866025i −0.0293610 + 0.0508548i
\(291\) −2.00000 −0.117242
\(292\) −5.50000 + 9.52628i −0.321863 + 0.557483i
\(293\) −4.50000 + 7.79423i −0.262893 + 0.455344i −0.967009 0.254741i \(-0.918010\pi\)
0.704117 + 0.710084i \(0.251343\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) 1.50000 + 2.59808i 0.0871857 + 0.151010i
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) 3.00000 0.173785
\(299\) 0 0
\(300\) −4.00000 −0.230940
\(301\) 6.00000 + 10.3923i 0.345834 + 0.599002i
\(302\) 1.00000 + 1.73205i 0.0575435 + 0.0996683i
\(303\) 1.50000 2.59808i 0.0861727 0.149256i
\(304\) −6.00000 −0.344124
\(305\) −0.500000 + 0.866025i −0.0286299 + 0.0495885i
\(306\) −3.50000 + 6.06218i −0.200082 + 0.346552i
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) −2.00000 + 3.46410i −0.113961 + 0.197386i
\(309\) 3.00000 + 5.19615i 0.170664 + 0.295599i
\(310\) −2.00000 3.46410i −0.113592 0.196748i
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) −1.50000 2.59808i −0.0846499 0.146618i
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) −2.00000 + 3.46410i −0.112509 + 0.194871i
\(317\) 25.0000 1.40414 0.702070 0.712108i \(-0.252259\pi\)
0.702070 + 0.712108i \(0.252259\pi\)
\(318\) 4.50000 7.79423i 0.252347 0.437079i
\(319\) 1.00000 1.73205i 0.0559893 0.0969762i
\(320\) 7.00000 0.391312
\(321\) −3.00000 + 5.19615i −0.167444 + 0.290021i
\(322\) 6.00000 + 10.3923i 0.334367 + 0.579141i
\(323\) 21.0000 + 36.3731i 1.16847 + 2.02385i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −4.00000 −0.221540
\(327\) 1.00000 + 1.73205i 0.0553001 + 0.0957826i
\(328\) 13.5000 + 23.3827i 0.745413 + 1.29109i
\(329\) −6.00000 + 10.3923i −0.330791 + 0.572946i
\(330\) 2.00000 0.110096
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 7.00000 12.1244i 0.384175 0.665410i
\(333\) −1.00000 −0.0547997
\(334\) −8.00000 + 13.8564i −0.437741 + 0.758189i
\(335\) −1.00000 1.73205i −0.0546358 0.0946320i
\(336\) 1.00000 + 1.73205i 0.0545545 + 0.0944911i
\(337\) −33.0000 −1.79762 −0.898812 0.438334i \(-0.855569\pi\)
−0.898812 + 0.438334i \(0.855569\pi\)
\(338\) 0 0
\(339\) 15.0000 0.814688
\(340\) −3.50000 6.06218i −0.189814 0.328768i
\(341\) 4.00000 + 6.92820i 0.216612 + 0.375183i
\(342\) 3.00000 5.19615i 0.162221 0.280976i
\(343\) 20.0000 1.07990
\(344\) −9.00000 + 15.5885i −0.485247 + 0.840473i
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) 6.00000 0.322562
\(347\) −9.00000 + 15.5885i −0.483145 + 0.836832i −0.999813 0.0193540i \(-0.993839\pi\)
0.516667 + 0.856186i \(0.327172\pi\)
\(348\) 0.500000 + 0.866025i 0.0268028 + 0.0464238i
\(349\) −13.0000 22.5167i −0.695874 1.20529i −0.969885 0.243563i \(-0.921684\pi\)
0.274011 0.961727i \(-0.411649\pi\)
\(350\) −8.00000 −0.427618
\(351\) 0 0
\(352\) −10.0000 −0.533002
\(353\) −5.50000 9.52628i −0.292735 0.507033i 0.681720 0.731613i \(-0.261232\pi\)
−0.974456 + 0.224580i \(0.927899\pi\)
\(354\) 0 0
\(355\) 3.00000 5.19615i 0.159223 0.275783i
\(356\) −14.0000 −0.741999
\(357\) 7.00000 12.1244i 0.370479 0.641689i
\(358\) −1.00000 + 1.73205i −0.0528516 + 0.0915417i
\(359\) 18.0000 0.950004 0.475002 0.879985i \(-0.342447\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(360\) −1.50000 + 2.59808i −0.0790569 + 0.136931i
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −11.0000 −0.575766
\(366\) −0.500000 0.866025i −0.0261354 0.0452679i
\(367\) −5.00000 8.66025i −0.260998 0.452062i 0.705509 0.708700i \(-0.250718\pi\)
−0.966507 + 0.256639i \(0.917385\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) −9.00000 −0.468521
\(370\) −0.500000 + 0.866025i −0.0259938 + 0.0450225i
\(371\) −9.00000 + 15.5885i −0.467257 + 0.809312i
\(372\) −4.00000 −0.207390
\(373\) 5.50000 9.52628i 0.284779 0.493252i −0.687776 0.725923i \(-0.741413\pi\)
0.972556 + 0.232671i \(0.0747464\pi\)
\(374\) −7.00000 12.1244i −0.361961 0.626936i
\(375\) −4.50000 7.79423i −0.232379 0.402492i
\(376\) −18.0000 −0.928279
\(377\) 0 0
\(378\) −2.00000 −0.102869
\(379\) −18.0000 31.1769i −0.924598 1.60145i −0.792207 0.610253i \(-0.791068\pi\)
−0.132391 0.991198i \(-0.542266\pi\)
\(380\) 3.00000 + 5.19615i 0.153897 + 0.266557i
\(381\) 10.0000 17.3205i 0.512316 0.887357i
\(382\) 4.00000 0.204658
\(383\) 4.00000 6.92820i 0.204390 0.354015i −0.745548 0.666452i \(-0.767812\pi\)
0.949938 + 0.312437i \(0.101145\pi\)
\(384\) 1.50000 2.59808i 0.0765466 0.132583i
\(385\) −4.00000 −0.203859
\(386\) 4.50000 7.79423i 0.229044 0.396716i
\(387\) −3.00000 5.19615i −0.152499 0.264135i
\(388\) 1.00000 + 1.73205i 0.0507673 + 0.0879316i
\(389\) 19.0000 0.963338 0.481669 0.876353i \(-0.340031\pi\)
0.481669 + 0.876353i \(0.340031\pi\)
\(390\) 0 0
\(391\) 42.0000 2.12403
\(392\) 4.50000 + 7.79423i 0.227284 + 0.393668i
\(393\) −4.00000 6.92820i −0.201773 0.349482i
\(394\) −3.00000 + 5.19615i −0.151138 + 0.261778i
\(395\) −4.00000 −0.201262
\(396\) 1.00000 1.73205i 0.0502519 0.0870388i
\(397\) −17.0000 + 29.4449i −0.853206 + 1.47780i 0.0250943 + 0.999685i \(0.492011\pi\)
−0.878300 + 0.478110i \(0.841322\pi\)
\(398\) −14.0000 −0.701757
\(399\) −6.00000 + 10.3923i −0.300376 + 0.520266i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 0.500000 + 0.866025i 0.0249688 + 0.0432472i 0.878240 0.478220i \(-0.158718\pi\)
−0.853271 + 0.521468i \(0.825385\pi\)
\(402\) 2.00000 0.0997509
\(403\) 0 0
\(404\) −3.00000 −0.149256
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) 1.00000 + 1.73205i 0.0496292 + 0.0859602i
\(407\) 1.00000 1.73205i 0.0495682 0.0858546i
\(408\) 21.0000 1.03965
\(409\) 3.50000 6.06218i 0.173064 0.299755i −0.766426 0.642333i \(-0.777967\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) −4.50000 + 7.79423i −0.222239 + 0.384930i
\(411\) −3.00000 −0.147979
\(412\) 3.00000 5.19615i 0.147799 0.255996i
\(413\) 0 0
\(414\) −3.00000 5.19615i −0.147442 0.255377i
\(415\) 14.0000 0.687233
\(416\) 0 0
\(417\) −12.0000 −0.587643
\(418\) 6.00000 + 10.3923i 0.293470 + 0.508304i
\(419\) −8.00000 13.8564i −0.390826 0.676930i 0.601733 0.798697i \(-0.294477\pi\)
−0.992559 + 0.121768i \(0.961144\pi\)
\(420\) 1.00000 1.73205i 0.0487950 0.0845154i
\(421\) 19.0000 0.926003 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(422\) −4.00000 + 6.92820i −0.194717 + 0.337260i
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) −27.0000 −1.31124
\(425\) −14.0000 + 24.2487i −0.679100 + 1.17624i
\(426\) 3.00000 + 5.19615i 0.145350 + 0.251754i
\(427\) 1.00000 + 1.73205i 0.0483934 + 0.0838198i
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) −6.00000 −0.289346
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −9.50000 + 16.4545i −0.456541 + 0.790752i −0.998775 0.0494752i \(-0.984245\pi\)
0.542234 + 0.840227i \(0.317578\pi\)
\(434\) −8.00000 −0.384012
\(435\) −0.500000 + 0.866025i −0.0239732 + 0.0415227i
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) −36.0000 −1.72211
\(438\) 5.50000 9.52628i 0.262800 0.455183i
\(439\) −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i \(-0.275096\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(440\) −3.00000 5.19615i −0.143019 0.247717i
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 0.500000 + 0.866025i 0.0237289 + 0.0410997i
\(445\) −7.00000 12.1244i −0.331832 0.574750i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 3.00000 0.141895
\(448\) 7.00000 12.1244i 0.330719 0.572822i
\(449\) 17.0000 29.4449i 0.802280 1.38959i −0.115833 0.993269i \(-0.536954\pi\)
0.918112 0.396320i \(-0.129713\pi\)
\(450\) 4.00000 0.188562
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) −7.50000 12.9904i −0.352770 0.611016i
\(453\) 1.00000 + 1.73205i 0.0469841 + 0.0813788i
\(454\) −14.0000 −0.657053
\(455\) 0 0
\(456\) −18.0000 −0.842927
\(457\) −6.50000 11.2583i −0.304057 0.526642i 0.672994 0.739648i \(-0.265008\pi\)
−0.977051 + 0.213006i \(0.931675\pi\)
\(458\) 11.0000 + 19.0526i 0.513996 + 0.890268i
\(459\) −3.50000 + 6.06218i −0.163366 + 0.282958i
\(460\) 6.00000 0.279751
\(461\) 9.50000 16.4545i 0.442459 0.766362i −0.555412 0.831575i \(-0.687440\pi\)
0.997871 + 0.0652135i \(0.0207728\pi\)
\(462\) 2.00000 3.46410i 0.0930484 0.161165i
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) −2.00000 3.46410i −0.0927478 0.160644i
\(466\) 5.00000 + 8.66025i 0.231621 + 0.401179i
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) −3.00000 5.19615i −0.138380 0.239681i
\(471\) −1.50000 2.59808i −0.0691164 0.119713i
\(472\) 0 0
\(473\) 12.0000 0.551761
\(474\) 2.00000 3.46410i 0.0918630 0.159111i
\(475\) 12.0000 20.7846i 0.550598 0.953663i
\(476\) −14.0000 −0.641689
\(477\) 4.50000 7.79423i 0.206041 0.356873i
\(478\) −15.0000 25.9808i −0.686084 1.18833i
\(479\) 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i \(0.0180558\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(480\) 5.00000 0.228218
\(481\) 0 0
\(482\) 7.00000 0.318841
\(483\) 6.00000 + 10.3923i 0.273009 + 0.472866i
\(484\) −3.50000 6.06218i −0.159091 0.275554i
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 1.00000 0.0453609
\(487\) 9.00000 15.5885i 0.407829 0.706380i −0.586817 0.809719i \(-0.699619\pi\)
0.994646 + 0.103339i \(0.0329526\pi\)
\(488\) −1.50000 + 2.59808i −0.0679018 + 0.117609i
\(489\) −4.00000 −0.180886
\(490\) −1.50000 + 2.59808i −0.0677631 + 0.117369i
\(491\) −3.00000 5.19615i −0.135388 0.234499i 0.790358 0.612646i \(-0.209895\pi\)
−0.925746 + 0.378147i \(0.876561\pi\)
\(492\) 4.50000 + 7.79423i 0.202876 + 0.351391i
\(493\) 7.00000 0.315264
\(494\) 0 0
\(495\) 2.00000 0.0898933
\(496\) −2.00000 3.46410i −0.0898027 0.155543i
\(497\) −6.00000 10.3923i −0.269137 0.466159i
\(498\) −7.00000 + 12.1244i −0.313678 + 0.543305i
\(499\) −24.0000 −1.07439 −0.537194 0.843459i \(-0.680516\pi\)
−0.537194 + 0.843459i \(0.680516\pi\)
\(500\) −4.50000 + 7.79423i −0.201246 + 0.348569i
\(501\) −8.00000 + 13.8564i −0.357414 + 0.619059i
\(502\) −12.0000 −0.535586
\(503\) 1.00000 1.73205i 0.0445878 0.0772283i −0.842870 0.538117i \(-0.819136\pi\)
0.887458 + 0.460889i \(0.152469\pi\)
\(504\) 3.00000 + 5.19615i 0.133631 + 0.231455i
\(505\) −1.50000 2.59808i −0.0667491 0.115613i
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) −20.0000 −0.887357
\(509\) 3.50000 + 6.06218i 0.155135 + 0.268701i 0.933108 0.359596i \(-0.117085\pi\)
−0.777973 + 0.628297i \(0.783752\pi\)
\(510\) 3.50000 + 6.06218i 0.154983 + 0.268438i
\(511\) −11.0000 + 19.0526i −0.486611 + 0.842836i
\(512\) 11.0000 0.486136
\(513\) 3.00000 5.19615i 0.132453 0.229416i
\(514\) −3.50000 + 6.06218i −0.154378 + 0.267391i
\(515\) 6.00000 0.264392
\(516\) −3.00000 + 5.19615i −0.132068 + 0.228748i
\(517\) 6.00000 + 10.3923i 0.263880 + 0.457053i
\(518\) 1.00000 + 1.73205i 0.0439375 + 0.0761019i
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) −0.500000 0.866025i −0.0218844 0.0379049i
\(523\) −7.00000 12.1244i −0.306089 0.530161i 0.671414 0.741082i \(-0.265687\pi\)
−0.977503 + 0.210921i \(0.932354\pi\)
\(524\) −4.00000 + 6.92820i −0.174741 + 0.302660i
\(525\) −8.00000 −0.349149
\(526\) −15.0000 + 25.9808i −0.654031 + 1.13282i
\(527\) −14.0000 + 24.2487i −0.609850 + 1.05629i
\(528\) 2.00000 0.0870388
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −4.50000 7.79423i −0.195468 0.338560i
\(531\) 0 0
\(532\) 12.0000 0.520266
\(533\) 0 0
\(534\) 14.0000 0.605839
\(535\) 3.00000 + 5.19615i 0.129701 + 0.224649i
\(536\) −3.00000 5.19615i −0.129580 0.224440i
\(537\) −1.00000 + 1.73205i −0.0431532 + 0.0747435i
\(538\) 14.0000 0.603583
\(539\) 3.00000 5.19615i 0.129219 0.223814i
\(540\) −0.500000 + 0.866025i −0.0215166 + 0.0372678i
\(541\) −45.0000 −1.93470 −0.967351 0.253442i \(-0.918437\pi\)
−0.967351 + 0.253442i \(0.918437\pi\)
\(542\) 0 0
\(543\) −3.50000 6.06218i −0.150199 0.260153i
\(544\) −17.5000 30.3109i −0.750306 1.29957i
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −26.0000 −1.11168 −0.555840 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) 1.50000 + 2.59808i 0.0640768 + 0.110984i
\(549\) −0.500000 0.866025i −0.0213395 0.0369611i
\(550\) −4.00000 + 6.92820i −0.170561 + 0.295420i
\(551\) −6.00000 −0.255609
\(552\) −9.00000 + 15.5885i −0.383065 + 0.663489i
\(553\) −4.00000 + 6.92820i −0.170097 + 0.294617i
\(554\) 31.0000 1.31706
\(555\) −0.500000 + 0.866025i −0.0212238 + 0.0367607i
\(556\) 6.00000 + 10.3923i 0.254457 + 0.440732i
\(557\) −4.50000 7.79423i −0.190671 0.330252i 0.754802 0.655953i \(-0.227733\pi\)
−0.945473 + 0.325701i \(0.894400\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) 2.00000 0.0845154
\(561\) −7.00000 12.1244i −0.295540 0.511891i
\(562\) 9.50000 + 16.4545i 0.400733 + 0.694090i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) −6.00000 −0.252646
\(565\) 7.50000 12.9904i 0.315527 0.546509i
\(566\) −9.00000 + 15.5885i −0.378298 + 0.655232i
\(567\) −2.00000 −0.0839921
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) −11.0000 19.0526i −0.461144 0.798725i 0.537874 0.843025i \(-0.319228\pi\)
−0.999018 + 0.0443003i \(0.985894\pi\)
\(570\) −3.00000 5.19615i −0.125656 0.217643i
\(571\) 26.0000 1.08807 0.544033 0.839064i \(-0.316897\pi\)
0.544033 + 0.839064i \(0.316897\pi\)
\(572\) 0 0
\(573\) 4.00000 0.167102
\(574\) 9.00000 + 15.5885i 0.375653 + 0.650650i
\(575\) −12.0000 20.7846i −0.500435 0.866778i
\(576\) −3.50000 + 6.06218i −0.145833 + 0.252591i
\(577\) −11.0000 −0.457936 −0.228968 0.973434i \(-0.573535\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) 16.0000 27.7128i 0.665512 1.15270i
\(579\) 4.50000 7.79423i 0.187014 0.323917i
\(580\) 1.00000 0.0415227
\(581\) 14.0000 24.2487i 0.580818 1.00601i
\(582\) −1.00000 1.73205i −0.0414513 0.0717958i
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) −33.0000 −1.36555
\(585\) 0 0
\(586\) −9.00000 −0.371787
\(587\) 8.00000 + 13.8564i 0.330195 + 0.571915i 0.982550 0.185999i \(-0.0595520\pi\)
−0.652355 + 0.757914i \(0.726219\pi\)
\(588\) 1.50000 + 2.59808i 0.0618590 + 0.107143i
\(589\) 12.0000 20.7846i 0.494451 0.856415i
\(590\) 0 0
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) −0.500000 + 0.866025i −0.0205499 + 0.0355934i
\(593\) −13.0000 −0.533846 −0.266923 0.963718i \(-0.586007\pi\)
−0.266923 + 0.963718i \(0.586007\pi\)
\(594\) −1.00000 + 1.73205i −0.0410305 + 0.0710669i
\(595\) −7.00000 12.1244i −0.286972 0.497050i
\(596\) −1.50000 2.59808i −0.0614424 0.106421i
\(597\) −14.0000 −0.572982
\(598\) 0 0
\(599\) −16.0000 −0.653742 −0.326871 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(600\) −6.00000 10.3923i −0.244949 0.424264i
\(601\) 2.50000 + 4.33013i 0.101977 + 0.176630i 0.912499 0.409079i \(-0.134150\pi\)
−0.810522 + 0.585708i \(0.800816\pi\)
\(602\) −6.00000 + 10.3923i −0.244542 + 0.423559i
\(603\) 2.00000 0.0814463
\(604\) 1.00000 1.73205i 0.0406894 0.0704761i
\(605\) 3.50000 6.06218i 0.142295 0.246463i
\(606\) 3.00000 0.121867
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 15.0000 + 25.9808i 0.608330 + 1.05366i
\(609\) 1.00000 + 1.73205i 0.0405220 + 0.0701862i
\(610\) −1.00000 −0.0404888
\(611\) 0 0
\(612\) 7.00000 0.282958
\(613\) −11.5000 19.9186i −0.464481 0.804504i 0.534697 0.845044i \(-0.320426\pi\)
−0.999178 + 0.0405396i \(0.987092\pi\)
\(614\) −7.00000 12.1244i −0.282497 0.489299i
\(615\) −4.50000 + 7.79423i −0.181458 + 0.314294i
\(616\) −12.0000 −0.483494
\(617\) 6.50000 11.2583i 0.261680 0.453243i −0.705008 0.709199i \(-0.749057\pi\)
0.966689 + 0.255956i \(0.0823901\pi\)
\(618\) −3.00000 + 5.19615i −0.120678 + 0.209020i
\(619\) 24.0000 0.964641 0.482321 0.875995i \(-0.339794\pi\)
0.482321 + 0.875995i \(0.339794\pi\)
\(620\) −2.00000 + 3.46410i −0.0803219 + 0.139122i
\(621\) −3.00000 5.19615i −0.120386 0.208514i
\(622\) 9.00000 + 15.5885i 0.360867 + 0.625040i
\(623\) −28.0000 −1.12180
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 6.00000 + 10.3923i 0.239617 + 0.415029i
\(628\) −1.50000 + 2.59808i −0.0598565 + 0.103675i
\(629\) 7.00000 0.279108
\(630\) −1.00000 + 1.73205i −0.0398410 + 0.0690066i
\(631\) 10.0000 17.3205i 0.398094 0.689519i −0.595397 0.803432i \(-0.703005\pi\)
0.993491 + 0.113913i \(0.0363385\pi\)
\(632\) −12.0000 −0.477334
\(633\) −4.00000 + 6.92820i −0.158986 + 0.275371i
\(634\) 12.5000 + 21.6506i 0.496438 + 0.859857i
\(635\) −10.0000 17.3205i −0.396838 0.687343i
\(636\) −9.00000 −0.356873
\(637\) 0 0
\(638\) 2.00000 0.0791808
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) 15.5000 26.8468i 0.612213 1.06038i −0.378653 0.925539i \(-0.623613\pi\)
0.990867 0.134846i \(-0.0430539\pi\)
\(642\) −6.00000 −0.236801
\(643\) −8.00000 + 13.8564i −0.315489 + 0.546443i −0.979541 0.201243i \(-0.935502\pi\)
0.664052 + 0.747686i \(0.268835\pi\)
\(644\) 6.00000 10.3923i 0.236433 0.409514i
\(645\) −6.00000 −0.236250
\(646\) −21.0000 + 36.3731i −0.826234 + 1.43108i
\(647\) 16.0000 + 27.7128i 0.629025 + 1.08950i 0.987748 + 0.156059i \(0.0498790\pi\)
−0.358723 + 0.933444i \(0.616788\pi\)
\(648\) −1.50000 2.59808i −0.0589256 0.102062i
\(649\) 0 0
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) −1.00000 + 1.73205i −0.0391031 + 0.0677285i
\(655\) −8.00000 −0.312586
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) 5.50000 9.52628i 0.214575 0.371656i
\(658\) −12.0000 −0.467809
\(659\) 4.00000 6.92820i 0.155818 0.269884i −0.777539 0.628835i \(-0.783532\pi\)
0.933357 + 0.358951i \(0.116865\pi\)
\(660\) −1.00000 1.73205i −0.0389249 0.0674200i
\(661\) 22.5000 + 38.9711i 0.875149 + 1.51580i 0.856604 + 0.515974i \(0.172570\pi\)
0.0185442 + 0.999828i \(0.494097\pi\)
\(662\) −4.00000 −0.155464
\(663\) 0 0
\(664\) 42.0000 1.62992
\(665\) 6.00000 + 10.3923i 0.232670 + 0.402996i
\(666\) −0.500000 0.866025i −0.0193746 0.0335578i
\(667\) −3.00000 + 5.19615i −0.116160 + 0.201196i
\(668\) 16.0000 0.619059
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) 1.00000 1.73205i 0.0386334 0.0669150i
\(671\) 2.00000 0.0772091
\(672\) 5.00000 8.66025i 0.192879 0.334077i
\(673\) 14.5000 + 25.1147i 0.558934 + 0.968102i 0.997586 + 0.0694449i \(0.0221228\pi\)
−0.438652 + 0.898657i \(0.644544\pi\)
\(674\) −16.5000 28.5788i −0.635556 1.10082i
\(675\) 4.00000 0.153960
\(676\) 0 0
\(677\) 34.0000 1.30673 0.653363 0.757045i \(-0.273358\pi\)
0.653363 + 0.757045i \(0.273358\pi\)
\(678\) 7.50000 + 12.9904i 0.288036 + 0.498893i
\(679\) 2.00000 + 3.46410i 0.0767530 + 0.132940i
\(680\) 10.5000 18.1865i 0.402657 0.697422i
\(681\) −14.0000 −0.536481
\(682\) −4.00000 + 6.92820i −0.153168 + 0.265295i
\(683\) −12.0000 + 20.7846i −0.459167 + 0.795301i −0.998917 0.0465244i \(-0.985185\pi\)
0.539750 + 0.841825i \(0.318519\pi\)
\(684\) −6.00000 −0.229416
\(685\) −1.50000 + 2.59808i −0.0573121 + 0.0992674i
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 11.0000 + 19.0526i 0.419676 + 0.726900i
\(688\) −6.00000 −0.228748
\(689\) 0 0
\(690\) −6.00000 −0.228416
\(691\) 21.0000 + 36.3731i 0.798878 + 1.38370i 0.920348 + 0.391102i \(0.127906\pi\)
−0.121470 + 0.992595i \(0.538761\pi\)
\(692\) −3.00000 5.19615i −0.114043 0.197528i
\(693\) 2.00000 3.46410i 0.0759737 0.131590i
\(694\) −18.0000 −0.683271
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) −1.50000 + 2.59808i −0.0568574 + 0.0984798i
\(697\) 63.0000 2.38630
\(698\) 13.0000 22.5167i 0.492057 0.852268i
\(699\) 5.00000 + 8.66025i 0.189117 + 0.327561i
\(700\) 4.00000 + 6.92820i 0.151186 + 0.261861i
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) −7.00000 12.1244i −0.263822 0.456954i
\(705\) −3.00000 5.19615i −0.112987 0.195698i
\(706\) 5.50000 9.52628i 0.206995 0.358526i
\(707\) −6.00000 −0.225653
\(708\) 0 0
\(709\) −5.50000 + 9.52628i −0.206557 + 0.357767i −0.950628 0.310334i \(-0.899559\pi\)
0.744071 + 0.668101i \(0.232892\pi\)
\(710\) 6.00000 0.225176
\(711\) 2.00000 3.46410i 0.0750059 0.129914i
\(712\) −21.0000 36.3731i −0.787008 1.36314i
\(713\) −12.0000 20.7846i −0.449404 0.778390i
\(714\) 14.0000 0.523937
\(715\) 0 0
\(716\) 2.00000 0.0747435
\(717\) −15.0000 25.9808i −0.560185 0.970269i
\(718\) 9.00000 + 15.5885i 0.335877 + 0.581756i
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 6.00000 10.3923i 0.223452 0.387030i
\(722\) 8.50000 14.7224i 0.316337 0.547912i
\(723\) 7.00000 0.260333
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) −2.00000 3.46410i −0.0742781 0.128654i
\(726\) 3.50000 + 6.06218i 0.129897 + 0.224989i
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −5.50000 9.52628i −0.203564 0.352583i
\(731\) 21.0000 + 36.3731i 0.776713 + 1.34531i
\(732\) −0.500000 + 0.866025i −0.0184805 + 0.0320092i
\(733\) 15.0000 0.554038 0.277019 0.960864i \(-0.410654\pi\)
0.277019 + 0.960864i \(0.410654\pi\)
\(734\) 5.00000 8.66025i 0.184553 0.319656i
\(735\) −1.50000 + 2.59808i −0.0553283 + 0.0958315i
\(736\) 30.0000 1.10581
\(737\) −2.00000 + 3.46410i −0.0736709 + 0.127602i
\(738\) −4.50000 7.79423i −0.165647 0.286910i
\(739\) −8.00000 13.8564i −0.294285 0.509716i 0.680534 0.732717i \(-0.261748\pi\)
−0.974818 + 0.223001i \(0.928415\pi\)
\(740\) 1.00000 0.0367607
\(741\) 0 0
\(742\) −18.0000 −0.660801
\(743\) −18.0000 31.1769i −0.660356 1.14377i −0.980522 0.196409i \(-0.937072\pi\)
0.320166 0.947361i \(-0.396261\pi\)
\(744\) −6.00000 10.3923i −0.219971 0.381000i
\(745\) 1.50000 2.59808i 0.0549557 0.0951861i
\(746\) 11.0000 0.402739
\(747\) −7.00000 + 12.1244i −0.256117 + 0.443607i
\(748\) −7.00000 + 12.1244i −0.255945 + 0.443310i
\(749\) 12.0000 0.438470
\(750\) 4.50000 7.79423i 0.164317 0.284605i
\(751\) 17.0000 + 29.4449i 0.620339 + 1.07446i 0.989423 + 0.145062i \(0.0463382\pi\)
−0.369084 + 0.929396i \(0.620328\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) 2.00000 0.0727875
\(756\) 1.00000 + 1.73205i 0.0363696 + 0.0629941i
\(757\) 25.0000 + 43.3013i 0.908640 + 1.57381i 0.815955 + 0.578116i \(0.196212\pi\)
0.0926859 + 0.995695i \(0.470455\pi\)
\(758\) 18.0000 31.1769i 0.653789 1.13240i
\(759\) 12.0000 0.435572
\(760\) −9.00000 + 15.5885i −0.326464 + 0.565453i
\(761\) 25.0000 43.3013i 0.906249 1.56967i 0.0870179 0.996207i \(-0.472266\pi\)
0.819231 0.573463i \(-0.194400\pi\)
\(762\) 20.0000 0.724524
\(763\) 2.00000 3.46410i 0.0724049 0.125409i
\(764\) −2.00000 3.46410i −0.0723575 0.125327i
\(765\) 3.50000 + 6.06218i 0.126543 + 0.219179i
\(766\) 8.00000 0.289052
\(767\) 0 0
\(768\) 17.0000 0.613435
\(769\) 15.0000 + 25.9808i 0.540914 + 0.936890i 0.998852 + 0.0479061i \(0.0152548\pi\)
−0.457938 + 0.888984i \(0.651412\pi\)
\(770\) −2.00000 3.46410i −0.0720750 0.124838i
\(771\) −3.50000 + 6.06218i −0.126049 + 0.218324i
\(772\) −9.00000 −0.323917
\(773\) −7.00000 + 12.1244i −0.251773 + 0.436083i −0.964014 0.265852i \(-0.914347\pi\)
0.712241 + 0.701935i \(0.247680\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) 16.0000 0.574737
\(776\) −3.00000 + 5.19615i −0.107694 + 0.186531i
\(777\) 1.00000 + 1.73205i 0.0358748 + 0.0621370i
\(778\) 9.50000 + 16.4545i 0.340592 + 0.589922i
\(779\) −54.0000