Properties

Label 507.2.e.c.22.1
Level $507$
Weight $2$
Character 507.22
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 22.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.c.484.1

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i −0.633316 0.773893i \(-0.718307\pi\)
0.986869 + 0.161521i \(0.0516399\pi\)
\(3\) 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 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 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 −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 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 0.882213 + 0.470850i \(0.156053\pi\)
−0.0333386 + 0.999444i \(0.510614\pi\)
\(18\) −1.00000 −0.235702
\(19\) −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i \(-0.925047\pi\)
0.284157 0.958778i \(-0.408286\pi\)
\(20\) 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 −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 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 −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) −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 −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i \(-0.585274\pi\)
0.967486 0.252924i \(-0.0813924\pi\)
\(42\) 1.00000 1.73205i 0.154303 0.267261i
\(43\) −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i \(-0.317920\pi\)
−0.998828 + 0.0484030i \(0.984587\pi\)
\(44\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 1.00000 0.129099
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −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 −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) −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 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) −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 0.209585 + 0.977790i \(0.432789\pi\)
−0.951584 + 0.307389i \(0.900545\pi\)
\(90\) −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 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) −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 −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 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 −0.683793 0.729676i \(-0.739671\pi\)
0.973814 + 0.227345i \(0.0730044\pi\)
\(108\) −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 0.966496 + 0.256681i \(0.0826291\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(114\) −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 −0.0443678 + 0.999015i \(0.514127\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) −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 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) −6.00000 −0.510754
\(139\) −6.00000 10.3923i −0.508913 0.881464i −0.999947 0.0103230i \(-0.996714\pi\)
0.491033 0.871141i \(-0.336619\pi\)
\(140\) −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 0.920904 0.389789i \(-0.127452\pi\)
−0.798019 + 0.602632i \(0.794119\pi\)
\(150\) 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 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) 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 −0.370599 0.928793i \(-0.620848\pi\)
0.989658 0.143448i \(-0.0458190\pi\)
\(168\) 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 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) −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 −0.826231 0.563331i \(-0.809520\pi\)
0.900975 + 0.433872i \(0.142853\pi\)
\(180\) 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 0.929267 0.369410i \(-0.120440\pi\)
−0.784552 + 0.620063i \(0.787107\pi\)
\(192\) 3.50000 6.06218i 0.252591 0.437500i
\(193\) −4.50000 + 7.79423i −0.323917 + 0.561041i −0.981293 0.192522i \(-0.938333\pi\)
0.657376 + 0.753563i \(0.271667\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) 3.00000 5.19615i 0.213741 0.370211i −0.739141 0.673550i \(-0.764768\pi\)
0.952882 + 0.303340i \(0.0981018\pi\)
\(198\) 1.00000 1.73205i 0.0710669 0.123091i
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) −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 −0.694857 0.719148i \(-0.744533\pi\)
0.970229 + 0.242190i \(0.0778659\pi\)
\(212\) −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 −0.463409 0.886145i \(-0.653374\pi\)
0.999128 0.0417488i \(-0.0132929\pi\)
\(224\) −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 0.534577 0.845120i \(-0.320471\pi\)
−0.999184 + 0.0403978i \(0.987137\pi\)
\(228\) −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 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 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 0.612159 0.790735i \(-0.290301\pi\)
−0.990876 + 0.134778i \(0.956968\pi\)
\(252\) 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 −0.735972 0.677012i \(-0.763274\pi\)
0.954296 + 0.298864i \(0.0966077\pi\)
\(258\) −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 0.133281 0.991078i \(-0.457449\pi\)
0.791658 0.610964i \(-0.209218\pi\)
\(264\) 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 0.996586 0.0825561i \(-0.0263084\pi\)
−0.569789 + 0.821791i \(0.692975\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) 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 0.781094 + 0.624413i \(0.214662\pi\)
0.150210 + 0.988654i \(0.452005\pi\)
\(278\) −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 −0.464169 0.885747i \(-0.653647\pi\)
0.999164 0.0408910i \(-0.0130196\pi\)
\(284\) −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 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) −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 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) 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 0.516667 0.856186i \(-0.327172\pi\)
−0.999813 + 0.0193540i \(0.993839\pi\)
\(348\) 0.500000 0.866025i 0.0268028 0.0464238i
\(349\) −13.0000 + 22.5167i −0.695874 + 1.20529i 0.274011 + 0.961727i \(0.411649\pi\)
−0.969885 + 0.243563i \(0.921684\pi\)
\(350\) −8.00000 −0.427618
\(351\) 0 0
\(352\) −10.0000 −0.533002
\(353\) −5.50000 + 9.52628i −0.292735 + 0.507033i −0.974456 0.224580i \(-0.927899\pi\)
0.681720 + 0.731613i \(0.261232\pi\)
\(354\) 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 −0.966507 0.256639i \(-0.917385\pi\)
0.705509 + 0.708700i \(0.250718\pi\)
\(368\) −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 0.972556 0.232671i \(-0.0747464\pi\)
−0.687776 + 0.725923i \(0.741413\pi\)
\(374\) −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 −0.132391 + 0.991198i \(0.542266\pi\)
−0.792207 + 0.610253i \(0.791068\pi\)
\(380\) 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 0.949938 0.312437i \(-0.101145\pi\)
−0.745548 + 0.666452i \(0.767812\pi\)
\(384\) 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 −0.878300 0.478110i \(-0.841322\pi\)
0.0250943 0.999685i \(-0.492011\pi\)
\(398\) −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 −0.853271 0.521468i \(-0.825385\pi\)
0.878240 + 0.478220i \(0.158718\pi\)
\(402\) 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 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) −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 −0.992559 0.121768i \(-0.961144\pi\)
0.601733 + 0.798697i \(0.294477\pi\)
\(420\) 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 0.237460 + 0.971397i \(0.423685\pi\)
−0.959985 + 0.280052i \(0.909648\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −9.50000 16.4545i −0.456541 0.790752i 0.542234 0.840227i \(-0.317578\pi\)
−0.998775 + 0.0494752i \(0.984245\pi\)
\(434\) −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 −0.983310 0.181938i \(-0.941763\pi\)
0.649218 + 0.760602i \(0.275096\pi\)
\(440\) −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 0.918112 + 0.396320i \(0.129713\pi\)
−0.115833 + 0.993269i \(0.536954\pi\)
\(450\) 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 −0.977051 0.213006i \(-0.931675\pi\)
0.672994 + 0.739648i \(0.265008\pi\)
\(458\) 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 0.997871 0.0652135i \(-0.0207728\pi\)
−0.555412 + 0.831575i \(0.687440\pi\)
\(462\) 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 −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 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 0.994646 0.103339i \(-0.0329526\pi\)
−0.586817 + 0.809719i \(0.699619\pi\)
\(488\) −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 −0.925746 0.378147i \(-0.876561\pi\)
0.790358 + 0.612646i \(0.209895\pi\)
\(492\) 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 0.887458 0.460889i \(-0.152469\pi\)
−0.842870 + 0.538117i \(0.819136\pi\)
\(504\) 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 −0.777973 0.628297i \(-0.783752\pi\)
0.933108 + 0.359596i \(0.117085\pi\)
\(510\) 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 −0.977503 0.210921i \(-0.932354\pi\)
0.671414 + 0.741082i \(0.265687\pi\)
\(524\) −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 −0.945473 0.325701i \(-0.894400\pi\)
0.754802 + 0.655953i \(0.227733\pi\)
\(558\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) −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 −0.999018 0.0443003i \(-0.985894\pi\)
0.537874 + 0.843025i \(0.319228\pi\)
\(570\) −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 −0.652355 0.757914i \(-0.726219\pi\)
0.982550 + 0.185999i \(0.0595520\pi\)
\(588\) 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 −0.810522 0.585708i \(-0.800816\pi\)
0.912499 + 0.409079i \(0.134150\pi\)
\(602\) −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 0.773358 0.633970i \(-0.218576\pi\)
−0.935713 + 0.352763i \(0.885242\pi\)
\(608\) 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 −0.999178 0.0405396i \(-0.987092\pi\)
0.534697 + 0.845044i \(0.320426\pi\)
\(614\) −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 0.966689 0.255956i \(-0.0823901\pi\)
−0.705008 + 0.709199i \(0.749057\pi\)
\(618\) −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 0.993491 0.113913i \(-0.0363385\pi\)
−0.595397 + 0.803432i \(0.703005\pi\)
\(632\) −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 0.990867 + 0.134846i \(0.0430539\pi\)
−0.378653 + 0.925539i \(0.623613\pi\)
\(642\) −6.00000 −0.236801
\(643\) −8.00000 13.8564i −0.315489 0.546443i 0.664052 0.747686i \(-0.268835\pi\)
−0.979541 + 0.201243i \(0.935502\pi\)
\(644\) 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 −0.358723 0.933444i \(-0.616788\pi\)
0.987748 0.156059i \(-0.0498790\pi\)
\(648\) −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 −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) −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 0.933357 0.358951i \(-0.116865\pi\)
−0.777539 + 0.628835i \(0.783532\pi\)
\(660\) −1.00000 + 1.73205i −0.0389249 + 0.0674200i
\(661\) 22.5000 38.9711i 0.875149 1.51580i 0.0185442 0.999828i \(-0.494097\pi\)
0.856604 0.515974i \(-0.172570\pi\)
\(662\) −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 −0.438652 0.898657i \(-0.644544\pi\)
0.997586 0.0694449i \(-0.0221228\pi\)
\(674\) −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 0.539750 0.841825i \(-0.318519\pi\)
−0.998917 + 0.0465244i \(0.985185\pi\)
\(684\) −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 −0.121470 0.992595i \(-0.538761\pi\)
0.920348 0.391102i \(-0.127906\pi\)
\(692\) −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 0.744071 0.668101i \(-0.232892\pi\)
−0.950628 + 0.310334i \(0.899559\pi\)
\(710\) 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 0.833744 + 0.552151i \(0.186193\pi\)
0.0613050 + 0.998119i \(0.480474\pi\)
\(720\) −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 −0.974818 0.223001i \(-0.928415\pi\)
0.680534 + 0.732717i \(0.261748\pi\)
\(740\) 1.00000 0.0367607
\(741\) 0 0
\(742\) −18.0000 −0.660801
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) −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 −0.369084 0.929396i \(-0.620328\pi\)
0.989423 0.145062i \(-0.0463382\pi\)
\(752\) −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 0.0926859 0.995695i \(-0.470455\pi\)
0.815955 0.578116i \(-0.196212\pi\)
\(758\) 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 0.819231 + 0.573463i \(0.194400\pi\)
0.0870179 + 0.996207i \(0.472266\pi\)
\(762\) 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 −0.457938 0.888984i \(-0.651412\pi\)
0.998852 0.0479061i \(-0.0152548\pi\)
\(770\) −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 0.712241 0.701935i \(-0.247680\pi\)
−0.964014 + 0.265852i \(0.914347\pi\)
\(774\) 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