Properties

Label 507.2.e.b.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.b.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(2.00000 + 3.46410i) q^{11} +1.00000 q^{12} -4.00000 q^{14} +(-1.00000 - 1.73205i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(-1.00000 + 1.73205i) q^{20} -4.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(1.50000 + 2.59808i) q^{24} -1.00000 q^{25} -1.00000 q^{27} +(2.00000 + 3.46410i) q^{28} +(5.00000 + 8.66025i) q^{29} +(1.00000 - 1.73205i) q^{30} -4.00000 q^{31} +(2.50000 - 4.33013i) q^{32} +(-2.00000 + 3.46410i) q^{33} -2.00000 q^{34} +(4.00000 - 6.92820i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-1.00000 - 1.73205i) q^{37} -6.00000 q^{40} +(3.00000 + 5.19615i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(6.00000 - 10.3923i) q^{43} +4.00000 q^{44} +(1.00000 - 1.73205i) q^{45} +(-0.500000 + 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +6.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(-6.00000 + 10.3923i) q^{56} +(-5.00000 + 8.66025i) q^{58} +(6.00000 - 10.3923i) q^{59} -2.00000 q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-2.00000 - 3.46410i) q^{63} +7.00000 q^{64} -4.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(1.00000 + 1.73205i) q^{68} +8.00000 q^{70} +(-1.50000 + 2.59808i) q^{72} -2.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} -16.0000 q^{77} +8.00000 q^{79} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} -4.00000 q^{83} +(-2.00000 + 3.46410i) q^{84} +(2.00000 - 3.46410i) q^{85} +12.0000 q^{86} +(-5.00000 + 8.66025i) q^{87} +(6.00000 + 10.3923i) q^{88} +(-1.00000 - 1.73205i) q^{89} +2.00000 q^{90} +(-2.00000 - 3.46410i) q^{93} +5.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(4.50000 - 7.79423i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} + q^{4} - 4 q^{5} - q^{6} - 4 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} + q^{4} - 4 q^{5} - q^{6} - 4 q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{12} - 8 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{20} - 8 q^{21} - 4 q^{22} + 3 q^{24} - 2 q^{25} - 2 q^{27} + 4 q^{28} + 10 q^{29} + 2 q^{30} - 8 q^{31} + 5 q^{32} - 4 q^{33} - 4 q^{34} + 8 q^{35} + q^{36} - 2 q^{37} - 12 q^{40} + 6 q^{41} - 4 q^{42} + 12 q^{43} + 8 q^{44} + 2 q^{45} - q^{48} - 9 q^{49} - q^{50} - 4 q^{51} + 12 q^{53} - q^{54} - 8 q^{55} - 12 q^{56} - 10 q^{58} + 12 q^{59} - 4 q^{60} + 2 q^{61} - 4 q^{62} - 4 q^{63} + 14 q^{64} - 8 q^{66} - 8 q^{67} + 2 q^{68} + 16 q^{70} - 3 q^{72} - 4 q^{73} + 2 q^{74} - q^{75} - 32 q^{77} + 16 q^{79} - 2 q^{80} - q^{81} - 6 q^{82} - 8 q^{83} - 4 q^{84} + 4 q^{85} + 24 q^{86} - 10 q^{87} + 12 q^{88} - 2 q^{89} + 4 q^{90} - 4 q^{93} + 10 q^{96} + 10 q^{97} + 9 q^{98} - 8 q^{99}+O(q^{100}) \) 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
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −2.00000 + 3.46410i −0.755929 + 1.30931i 0.188982 + 0.981981i \(0.439481\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 3.00000 1.06066
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.00000 1.73205i −0.316228 0.547723i
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) −4.00000 −1.06904
\(15\) −1.00000 1.73205i −0.258199 0.447214i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) −4.00000 −0.872872
\(22\) −2.00000 + 3.46410i −0.426401 + 0.738549i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 1.50000 + 2.59808i 0.306186 + 0.530330i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 2.00000 + 3.46410i 0.377964 + 0.654654i
\(29\) 5.00000 + 8.66025i 0.928477 + 1.60817i 0.785872 + 0.618389i \(0.212214\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(30\) 1.00000 1.73205i 0.182574 0.316228i
\(31\) −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
\(33\) −2.00000 + 3.46410i −0.348155 + 0.603023i
\(34\) −2.00000 −0.342997
\(35\) 4.00000 6.92820i 0.676123 1.17108i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −6.00000 −0.948683
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) −2.00000 3.46410i −0.308607 0.534522i
\(43\) 6.00000 10.3923i 0.914991 1.58481i 0.108078 0.994142i \(-0.465531\pi\)
0.806914 0.590669i \(-0.201136\pi\)
\(44\) 4.00000 0.603023
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −4.50000 7.79423i −0.642857 1.11346i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) −2.00000 −0.280056
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −4.00000 6.92820i −0.539360 0.934199i
\(56\) −6.00000 + 10.3923i −0.801784 + 1.38873i
\(57\) 0 0
\(58\) −5.00000 + 8.66025i −0.656532 + 1.13715i
\(59\) 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i \(-0.547975\pi\)
0.931282 0.364299i \(-0.118692\pi\)
\(60\) −2.00000 −0.258199
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) −2.00000 3.46410i −0.251976 0.436436i
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 0 0
\(70\) 8.00000 0.956183
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 0 0
\(77\) −16.0000 −1.82337
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −1.00000 1.73205i −0.111803 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.00000 + 5.19615i −0.331295 + 0.573819i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) −2.00000 + 3.46410i −0.218218 + 0.377964i
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) 12.0000 1.29399
\(87\) −5.00000 + 8.66025i −0.536056 + 0.928477i
\(88\) 6.00000 + 10.3923i 0.639602 + 1.10782i
\(89\) −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i \(-0.200471\pi\)
−0.914146 + 0.405385i \(0.867138\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 0 0
\(93\) −2.00000 3.46410i −0.207390 0.359211i
\(94\) 0 0
\(95\) 0 0
\(96\) 5.00000 0.510310
\(97\) 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i \(-0.663839\pi\)
0.999961 0.00888289i \(-0.00282755\pi\)
\(98\) 4.50000 7.79423i 0.454569 0.787336i
\(99\) −4.00000 −0.402015
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) −1.00000 1.73205i −0.0990148 0.171499i
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 8.00000 0.780720
\(106\) 3.00000 + 5.19615i 0.291386 + 0.504695i
\(107\) −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
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 4.00000 6.92820i 0.381385 0.660578i
\(111\) 1.00000 1.73205i 0.0949158 0.164399i
\(112\) −4.00000 −0.377964
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) −4.00000 6.92820i −0.366679 0.635107i
\(120\) −3.00000 5.19615i −0.273861 0.474342i
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 2.00000 0.181071
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) 12.0000 1.07331
\(126\) 2.00000 3.46410i 0.178174 0.308607i
\(127\) 8.00000 + 13.8564i 0.709885 + 1.22956i 0.964899 + 0.262620i \(0.0845865\pi\)
−0.255014 + 0.966937i \(0.582080\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 12.0000 1.05654
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 2.00000 + 3.46410i 0.174078 + 0.301511i
\(133\) 0 0
\(134\) 4.00000 6.92820i 0.345547 0.598506i
\(135\) 2.00000 0.172133
\(136\) −3.00000 + 5.19615i −0.257248 + 0.445566i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) −4.00000 6.92820i −0.338062 0.585540i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) −10.0000 17.3205i −0.830455 1.43839i
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 4.50000 7.79423i 0.371154 0.642857i
\(148\) −2.00000 −0.164399
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −4.00000 −0.325515 −0.162758 0.986666i \(-0.552039\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) 0 0
\(153\) −1.00000 1.73205i −0.0808452 0.140028i
\(154\) −8.00000 13.8564i −0.644658 1.11658i
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 4.00000 + 6.92820i 0.318223 + 0.551178i
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) −5.00000 + 8.66025i −0.395285 + 0.684653i
\(161\) 0 0
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 4.00000 6.92820i 0.313304 0.542659i −0.665771 0.746156i \(-0.731897\pi\)
0.979076 + 0.203497i \(0.0652307\pi\)
\(164\) 6.00000 0.468521
\(165\) 4.00000 6.92820i 0.311400 0.539360i
\(166\) −2.00000 3.46410i −0.155230 0.268866i
\(167\) −4.00000 6.92820i −0.309529 0.536120i 0.668730 0.743505i \(-0.266838\pi\)
−0.978259 + 0.207385i \(0.933505\pi\)
\(168\) −12.0000 −0.925820
\(169\) 0 0
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) −6.00000 10.3923i −0.457496 0.792406i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) −10.0000 −0.758098
\(175\) 2.00000 3.46410i 0.151186 0.261861i
\(176\) −2.00000 + 3.46410i −0.150756 + 0.261116i
\(177\) 12.0000 0.901975
\(178\) 1.00000 1.73205i 0.0749532 0.129823i
\(179\) −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) −1.00000 1.73205i −0.0745356 0.129099i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) −8.00000 −0.585018
\(188\) 0 0
\(189\) 2.00000 3.46410i 0.145479 0.251976i
\(190\) 0 0
\(191\) −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) 3.50000 + 6.06218i 0.252591 + 0.437500i
\(193\) 9.00000 + 15.5885i 0.647834 + 1.12208i 0.983639 + 0.180150i \(0.0576584\pi\)
−0.335805 + 0.941932i \(0.609008\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) −9.00000 −0.642857
\(197\) 9.00000 + 15.5885i 0.641223 + 1.11063i 0.985160 + 0.171639i \(0.0549062\pi\)
−0.343937 + 0.938993i \(0.611761\pi\)
\(198\) −2.00000 3.46410i −0.142134 0.246183i
\(199\) −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i \(-0.924846\pi\)
0.688705 + 0.725042i \(0.258180\pi\)
\(200\) −3.00000 −0.212132
\(201\) 4.00000 6.92820i 0.282138 0.488678i
\(202\) −9.00000 + 15.5885i −0.633238 + 1.09680i
\(203\) −40.0000 −2.80745
\(204\) −1.00000 + 1.73205i −0.0700140 + 0.121268i
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 4.00000 + 6.92820i 0.276026 + 0.478091i
\(211\) 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
\(213\) 0 0
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) −12.0000 + 20.7846i −0.818393 + 1.41750i
\(216\) −3.00000 −0.204124
\(217\) 8.00000 13.8564i 0.543075 0.940634i
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) −8.00000 −0.539360
\(221\) 0 0
\(222\) 2.00000 0.134231
\(223\) 2.00000 + 3.46410i 0.133930 + 0.231973i 0.925188 0.379509i \(-0.123907\pi\)
−0.791258 + 0.611482i \(0.790574\pi\)
\(224\) 10.0000 + 17.3205i 0.668153 + 1.15728i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 6.00000 0.399114
\(227\) −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −8.00000 13.8564i −0.526361 0.911685i
\(232\) 15.0000 + 25.9808i 0.984798 + 1.70572i
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 4.00000 + 6.92820i 0.259828 + 0.450035i
\(238\) 4.00000 6.92820i 0.259281 0.449089i
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 1.00000 1.73205i 0.0645497 0.111803i
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −1.00000 1.73205i −0.0640184 0.110883i
\(245\) 9.00000 + 15.5885i 0.574989 + 0.995910i
\(246\) −6.00000 −0.382546
\(247\) 0 0
\(248\) −12.0000 −0.762001
\(249\) −2.00000 3.46410i −0.126745 0.219529i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) −4.00000 −0.251976
\(253\) 0 0
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) 4.00000 0.250490
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −13.0000 22.5167i −0.810918 1.40455i −0.912222 0.409695i \(-0.865635\pi\)
0.101305 0.994855i \(-0.467698\pi\)
\(258\) 6.00000 + 10.3923i 0.373544 + 0.646997i
\(259\) 8.00000 0.497096
\(260\) 0 0
\(261\) −10.0000 −0.618984
\(262\) 2.00000 + 3.46410i 0.123560 + 0.214013i
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) −6.00000 + 10.3923i −0.369274 + 0.639602i
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 1.00000 1.73205i 0.0611990 0.106000i
\(268\) −8.00000 −0.488678
\(269\) −11.0000 + 19.0526i −0.670682 + 1.16166i 0.307029 + 0.951700i \(0.400665\pi\)
−0.977711 + 0.209955i \(0.932668\pi\)
\(270\) 1.00000 + 1.73205i 0.0608581 + 0.105409i
\(271\) −6.00000 10.3923i −0.364474 0.631288i 0.624218 0.781251i \(-0.285418\pi\)
−0.988692 + 0.149963i \(0.952085\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −12.0000 −0.719712
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) 12.0000 20.7846i 0.717137 1.24212i
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −6.00000 10.3923i −0.356663 0.617758i 0.630738 0.775996i \(-0.282752\pi\)
−0.987401 + 0.158237i \(0.949419\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 2.50000 + 4.33013i 0.147314 + 0.255155i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 10.0000 17.3205i 0.587220 1.01710i
\(291\) 10.0000 0.586210
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) −3.00000 + 5.19615i −0.175262 + 0.303562i −0.940252 0.340480i \(-0.889411\pi\)
0.764990 + 0.644042i \(0.222744\pi\)
\(294\) 9.00000 0.524891
\(295\) −12.0000 + 20.7846i −0.698667 + 1.21013i
\(296\) −3.00000 5.19615i −0.174371 0.302020i
\(297\) −2.00000 3.46410i −0.116052 0.201008i
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 24.0000 + 41.5692i 1.38334 + 2.39601i
\(302\) −2.00000 3.46410i −0.115087 0.199337i
\(303\) −9.00000 + 15.5885i −0.517036 + 0.895533i
\(304\) 0 0
\(305\) −2.00000 + 3.46410i −0.114520 + 0.198354i
\(306\) 1.00000 1.73205i 0.0571662 0.0990148i
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) −8.00000 + 13.8564i −0.455842 + 0.789542i
\(309\) 0 0
\(310\) 4.00000 + 6.92820i 0.227185 + 0.393496i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −9.00000 15.5885i −0.507899 0.879708i
\(315\) 4.00000 + 6.92820i 0.225374 + 0.390360i
\(316\) 4.00000 6.92820i 0.225018 0.389742i
\(317\) −26.0000 −1.46031 −0.730153 0.683284i \(-0.760551\pi\)
−0.730153 + 0.683284i \(0.760551\pi\)
\(318\) −3.00000 + 5.19615i −0.168232 + 0.291386i
\(319\) −20.0000 + 34.6410i −1.11979 + 1.93952i
\(320\) −14.0000 −0.782624
\(321\) 6.00000 10.3923i 0.334887 0.580042i
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 8.00000 0.443079
\(327\) 1.00000 + 1.73205i 0.0553001 + 0.0957826i
\(328\) 9.00000 + 15.5885i 0.496942 + 0.860729i
\(329\) 0 0
\(330\) 8.00000 0.440386
\(331\) −8.00000 + 13.8564i −0.439720 + 0.761617i −0.997668 0.0682590i \(-0.978256\pi\)
0.557948 + 0.829876i \(0.311589\pi\)
\(332\) −2.00000 + 3.46410i −0.109764 + 0.190117i
\(333\) 2.00000 0.109599
\(334\) 4.00000 6.92820i 0.218870 0.379094i
\(335\) 8.00000 + 13.8564i 0.437087 + 0.757056i
\(336\) −2.00000 3.46410i −0.109109 0.188982i
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) −2.00000 3.46410i −0.108465 0.187867i
\(341\) −8.00000 13.8564i −0.433224 0.750366i
\(342\) 0 0
\(343\) 8.00000 0.431959
\(344\) 18.0000 31.1769i 0.970495 1.68095i
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 5.00000 + 8.66025i 0.268028 + 0.464238i
\(349\) −13.0000 22.5167i −0.695874 1.20529i −0.969885 0.243563i \(-0.921684\pi\)
0.274011 0.961727i \(-0.411649\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) −1.00000 1.73205i −0.0532246 0.0921878i 0.838186 0.545385i \(-0.183617\pi\)
−0.891410 + 0.453197i \(0.850283\pi\)
\(354\) 6.00000 + 10.3923i 0.318896 + 0.552345i
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) 4.00000 6.92820i 0.211702 0.366679i
\(358\) 2.00000 3.46410i 0.105703 0.183083i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 3.00000 5.19615i 0.158114 0.273861i
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) −5.00000 8.66025i −0.262794 0.455173i
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) 4.00000 0.209370
\(366\) 1.00000 + 1.73205i 0.0522708 + 0.0905357i
\(367\) −8.00000 13.8564i −0.417597 0.723299i 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) −2.00000 + 3.46410i −0.103975 + 0.180090i
\(371\) −12.0000 + 20.7846i −0.623009 + 1.07908i
\(372\) −4.00000 −0.207390
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) −4.00000 6.92820i −0.206835 0.358249i
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) 0 0
\(377\) 0 0
\(378\) 4.00000 0.205738
\(379\) −12.0000 20.7846i −0.616399 1.06763i −0.990137 0.140100i \(-0.955258\pi\)
0.373739 0.927534i \(-0.378076\pi\)
\(380\) 0 0
\(381\) −8.00000 + 13.8564i −0.409852 + 0.709885i
\(382\) −8.00000 −0.409316
\(383\) −8.00000 + 13.8564i −0.408781 + 0.708029i −0.994753 0.102302i \(-0.967379\pi\)
0.585973 + 0.810331i \(0.300713\pi\)
\(384\) 1.50000 2.59808i 0.0765466 0.132583i
\(385\) 32.0000 1.63087
\(386\) −9.00000 + 15.5885i −0.458088 + 0.793432i
\(387\) 6.00000 + 10.3923i 0.304997 + 0.528271i
\(388\) −5.00000 8.66025i −0.253837 0.439658i
\(389\) 22.0000 1.11544 0.557722 0.830028i \(-0.311675\pi\)
0.557722 + 0.830028i \(0.311675\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −13.5000 23.3827i −0.681853 1.18100i
\(393\) 2.00000 + 3.46410i 0.100887 + 0.174741i
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) −16.0000 −0.805047
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) 19.0000 32.9090i 0.953583 1.65165i 0.216004 0.976392i \(-0.430698\pi\)
0.737579 0.675261i \(-0.235969\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 11.0000 + 19.0526i 0.549314 + 0.951439i 0.998322 + 0.0579116i \(0.0184442\pi\)
−0.449008 + 0.893528i \(0.648223\pi\)
\(402\) 8.00000 0.399004
\(403\) 0 0
\(404\) 18.0000 0.895533
\(405\) 1.00000 + 1.73205i 0.0496904 + 0.0860663i
\(406\) −20.0000 34.6410i −0.992583 1.71920i
\(407\) 4.00000 6.92820i 0.198273 0.343418i
\(408\) −6.00000 −0.297044
\(409\) 17.0000 29.4449i 0.840596 1.45595i −0.0487958 0.998809i \(-0.515538\pi\)
0.889392 0.457146i \(-0.151128\pi\)
\(410\) 6.00000 10.3923i 0.296319 0.513239i
\(411\) 6.00000 0.295958
\(412\) 0 0
\(413\) 24.0000 + 41.5692i 1.18096 + 2.04549i
\(414\) 0 0
\(415\) 8.00000 0.392705
\(416\) 0 0
\(417\) −12.0000 −0.587643
\(418\) 0 0
\(419\) −2.00000 3.46410i −0.0977064 0.169232i 0.813029 0.582224i \(-0.197817\pi\)
−0.910735 + 0.412991i \(0.864484\pi\)
\(420\) 4.00000 6.92820i 0.195180 0.338062i
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −10.0000 + 17.3205i −0.486792 + 0.843149i
\(423\) 0 0
\(424\) 18.0000 0.874157
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) 4.00000 + 6.92820i 0.193574 + 0.335279i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) −24.0000 −1.15738
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −17.0000 + 29.4449i −0.816968 + 1.41503i 0.0909384 + 0.995857i \(0.471013\pi\)
−0.907906 + 0.419173i \(0.862320\pi\)
\(434\) 16.0000 0.768025
\(435\) 10.0000 17.3205i 0.479463 0.830455i
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 0 0
\(438\) 1.00000 1.73205i 0.0477818 0.0827606i
\(439\) −16.0000 27.7128i −0.763638 1.32266i −0.940963 0.338508i \(-0.890078\pi\)
0.177325 0.984152i \(-0.443256\pi\)
\(440\) −12.0000 20.7846i −0.572078 0.990867i
\(441\) 9.00000 0.428571
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −1.00000 1.73205i −0.0474579 0.0821995i
\(445\) 2.00000 + 3.46410i 0.0948091 + 0.164214i
\(446\) −2.00000 + 3.46410i −0.0947027 + 0.164030i
\(447\) −6.00000 −0.283790
\(448\) −14.0000 + 24.2487i −0.661438 + 1.14564i
\(449\) 11.0000 19.0526i 0.519122 0.899146i −0.480631 0.876923i \(-0.659592\pi\)
0.999753 0.0222229i \(-0.00707434\pi\)
\(450\) 1.00000 0.0471405
\(451\) −12.0000 + 20.7846i −0.565058 + 0.978709i
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) −2.00000 3.46410i −0.0939682 0.162758i
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) 0 0
\(457\) 1.00000 + 1.73205i 0.0467780 + 0.0810219i 0.888466 0.458942i \(-0.151771\pi\)
−0.841688 + 0.539964i \(0.818438\pi\)
\(458\) 5.00000 + 8.66025i 0.233635 + 0.404667i
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 0 0
\(461\) −19.0000 + 32.9090i −0.884918 + 1.53272i −0.0391109 + 0.999235i \(0.512453\pi\)
−0.845807 + 0.533488i \(0.820881\pi\)
\(462\) 8.00000 13.8564i 0.372194 0.644658i
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) −5.00000 + 8.66025i −0.232119 + 0.402042i
\(465\) 4.00000 + 6.92820i 0.185496 + 0.321288i
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 32.0000 1.47762
\(470\) 0 0
\(471\) −9.00000 15.5885i −0.414698 0.718278i
\(472\) 18.0000 31.1769i 0.828517 1.43503i
\(473\) 48.0000 2.20704
\(474\) −4.00000 + 6.92820i −0.183726 + 0.318223i
\(475\) 0 0
\(476\) −8.00000 −0.366679
\(477\) −3.00000 + 5.19615i −0.137361 + 0.237915i
\(478\) 12.0000 + 20.7846i 0.548867 + 0.950666i
\(479\) −12.0000 20.7846i −0.548294 0.949673i −0.998392 0.0566937i \(-0.981944\pi\)
0.450098 0.892979i \(-0.351389\pi\)
\(480\) −10.0000 −0.456435
\(481\) 0 0
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 2.50000 + 4.33013i 0.113636 + 0.196824i
\(485\) −10.0000 + 17.3205i −0.454077 + 0.786484i
\(486\) 1.00000 0.0453609
\(487\) 6.00000 10.3923i 0.271886 0.470920i −0.697459 0.716625i \(-0.745686\pi\)
0.969345 + 0.245705i \(0.0790193\pi\)
\(488\) 3.00000 5.19615i 0.135804 0.235219i
\(489\) 8.00000 0.361773
\(490\) −9.00000 + 15.5885i −0.406579 + 0.704215i
\(491\) 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) 3.00000 + 5.19615i 0.135250 + 0.234261i
\(493\) −20.0000 −0.900755
\(494\) 0 0
\(495\) 8.00000 0.359573
\(496\) −2.00000 3.46410i −0.0898027 0.155543i
\(497\) 0 0
\(498\) 2.00000 3.46410i 0.0896221 0.155230i
\(499\) 24.0000 1.07439 0.537194 0.843459i \(-0.319484\pi\)
0.537194 + 0.843459i \(0.319484\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 4.00000 6.92820i 0.178707 0.309529i
\(502\) 12.0000 0.535586
\(503\) 4.00000 6.92820i 0.178351 0.308913i −0.762965 0.646440i \(-0.776257\pi\)
0.941316 + 0.337527i \(0.109590\pi\)
\(504\) −6.00000 10.3923i −0.267261 0.462910i
\(505\) −18.0000 31.1769i −0.800989 1.38735i
\(506\) 0 0
\(507\) 0 0
\(508\) 16.0000 0.709885
\(509\) 5.00000 + 8.66025i 0.221621 + 0.383859i 0.955300 0.295637i \(-0.0955319\pi\)
−0.733679 + 0.679496i \(0.762199\pi\)
\(510\) 2.00000 + 3.46410i 0.0885615 + 0.153393i
\(511\) 4.00000 6.92820i 0.176950 0.306486i
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) 13.0000 22.5167i 0.573405 0.993167i
\(515\) 0 0
\(516\) 6.00000 10.3923i 0.264135 0.457496i
\(517\) 0 0
\(518\) 4.00000 + 6.92820i 0.175750 + 0.304408i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) −5.00000 8.66025i −0.218844 0.379049i
\(523\) −22.0000 38.1051i −0.961993 1.66622i −0.717486 0.696573i \(-0.754707\pi\)
−0.244507 0.969648i \(-0.578626\pi\)
\(524\) 2.00000 3.46410i 0.0873704 0.151330i
\(525\) 4.00000 0.174574
\(526\) 12.0000 20.7846i 0.523225 0.906252i
\(527\) 4.00000 6.92820i 0.174243 0.301797i
\(528\) −4.00000 −0.174078
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −6.00000 10.3923i −0.260623 0.451413i
\(531\) 6.00000 + 10.3923i 0.260378 + 0.450988i
\(532\) 0 0
\(533\) 0 0
\(534\) 2.00000 0.0865485
\(535\) 12.0000 + 20.7846i 0.518805 + 0.898597i
\(536\) −12.0000 20.7846i −0.518321 0.897758i
\(537\) 2.00000 3.46410i 0.0863064 0.149487i
\(538\) −22.0000 −0.948487
\(539\) 18.0000 31.1769i 0.775315 1.34288i
\(540\) 1.00000 1.73205i 0.0430331 0.0745356i
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 6.00000 10.3923i 0.257722 0.446388i
\(543\) −5.00000 8.66025i −0.214571 0.371647i
\(544\) 5.00000 + 8.66025i 0.214373 + 0.371305i
\(545\) −4.00000 −0.171341
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −3.00000 5.19615i −0.128154 0.221969i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 2.00000 3.46410i 0.0852803 0.147710i
\(551\) 0 0
\(552\) 0 0
\(553\) −16.0000 + 27.7128i −0.680389 + 1.17847i
\(554\) 10.0000 0.424859
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) 6.00000 + 10.3923i 0.254457 + 0.440732i
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) 8.00000 0.338062
\(561\) −4.00000 6.92820i −0.168880 0.292509i
\(562\) 5.00000 + 8.66025i 0.210912 + 0.365311i
\(563\) 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) 0 0
\(565\) −6.00000 + 10.3923i −0.252422 + 0.437208i
\(566\) 6.00000 10.3923i 0.252199 0.436821i
\(567\) 4.00000 0.167984
\(568\) 0 0
\(569\) −17.0000 29.4449i −0.712677 1.23439i −0.963849 0.266450i \(-0.914149\pi\)
0.251172 0.967943i \(-0.419184\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −8.00000 −0.334205
\(574\) −12.0000 20.7846i −0.500870 0.867533i
\(575\) 0 0
\(576\) −3.50000 + 6.06218i −0.145833 + 0.252591i
\(577\) 46.0000 1.91501 0.957503 0.288425i \(-0.0931316\pi\)
0.957503 + 0.288425i \(0.0931316\pi\)
\(578\) −6.50000 + 11.2583i −0.270364 + 0.468285i
\(579\) −9.00000 + 15.5885i −0.374027 + 0.647834i
\(580\) −20.0000 −0.830455
\(581\) 8.00000 13.8564i 0.331896 0.574861i
\(582\) 5.00000 + 8.66025i 0.207257 + 0.358979i
\(583\) 12.0000 + 20.7846i 0.496989 + 0.860811i
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 14.0000 + 24.2487i 0.577842 + 1.00085i 0.995726 + 0.0923513i \(0.0294383\pi\)
−0.417885 + 0.908500i \(0.637228\pi\)
\(588\) −4.50000 7.79423i −0.185577 0.321429i
\(589\) 0 0
\(590\) −24.0000 −0.988064
\(591\) −9.00000 + 15.5885i −0.370211 + 0.641223i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) 26.0000 1.06769 0.533846 0.845582i \(-0.320746\pi\)
0.533846 + 0.845582i \(0.320746\pi\)
\(594\) 2.00000 3.46410i 0.0820610 0.142134i
\(595\) 8.00000 + 13.8564i 0.327968 + 0.568057i
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) −8.00000 −0.327418
\(598\) 0 0
\(599\) −40.0000 −1.63436 −0.817178 0.576386i \(-0.804463\pi\)
−0.817178 + 0.576386i \(0.804463\pi\)
\(600\) −1.50000 2.59808i −0.0612372 0.106066i
\(601\) 19.0000 + 32.9090i 0.775026 + 1.34238i 0.934780 + 0.355228i \(0.115597\pi\)
−0.159754 + 0.987157i \(0.551070\pi\)
\(602\) −24.0000 + 41.5692i −0.978167 + 1.69423i
\(603\) 8.00000 0.325785
\(604\) −2.00000 + 3.46410i −0.0813788 + 0.140952i
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) −18.0000 −0.731200
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) 0 0
\(609\) −20.0000 34.6410i −0.810441 1.40372i
\(610\) −4.00000 −0.161955
\(611\) 0 0
\(612\) −2.00000 −0.0808452
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 8.00000 + 13.8564i 0.322854 + 0.559199i
\(615\) 6.00000 10.3923i 0.241943 0.419058i
\(616\) −48.0000 −1.93398
\(617\) 11.0000 19.0526i 0.442843 0.767027i −0.555056 0.831813i \(-0.687303\pi\)
0.997899 + 0.0647859i \(0.0206365\pi\)
\(618\) 0 0
\(619\) −24.0000 −0.964641 −0.482321 0.875995i \(-0.660206\pi\)
−0.482321 + 0.875995i \(0.660206\pi\)
\(620\) 4.00000 6.92820i 0.160644 0.278243i
\(621\) 0 0
\(622\) 0 0
\(623\) 8.00000 0.320513
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) −3.00000 5.19615i −0.119904 0.207680i
\(627\) 0 0
\(628\) −9.00000 + 15.5885i −0.359139 + 0.622047i
\(629\) 4.00000 0.159490
\(630\) −4.00000 + 6.92820i −0.159364 + 0.276026i
\(631\) 10.0000 17.3205i 0.398094 0.689519i −0.595397 0.803432i \(-0.703005\pi\)
0.993491 + 0.113913i \(0.0363385\pi\)
\(632\) 24.0000 0.954669
\(633\) −10.0000 + 17.3205i −0.397464 + 0.688428i
\(634\) −13.0000 22.5167i −0.516296 0.894251i
\(635\) −16.0000 27.7128i −0.634941 1.09975i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) −40.0000 −1.58362
\(639\) 0 0
\(640\) 3.00000 + 5.19615i 0.118585 + 0.205396i
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 12.0000 0.473602
\(643\) −20.0000 + 34.6410i −0.788723 + 1.36611i 0.138027 + 0.990429i \(0.455924\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 0 0
\(645\) −24.0000 −0.944999
\(646\) 0 0
\(647\) 4.00000 + 6.92820i 0.157256 + 0.272376i 0.933878 0.357591i \(-0.116402\pi\)
−0.776622 + 0.629967i \(0.783068\pi\)
\(648\) −1.50000 2.59808i −0.0589256 0.102062i
\(649\) 48.0000 1.88416
\(650\) 0 0
\(651\) 16.0000 0.627089
\(652\) −4.00000 6.92820i −0.156652 0.271329i
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) −1.00000 + 1.73205i −0.0391031 + 0.0677285i
\(655\) −8.00000 −0.312586
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 1.00000 1.73205i 0.0390137 0.0675737i
\(658\) 0 0
\(659\) −14.0000 + 24.2487i −0.545363 + 0.944596i 0.453221 + 0.891398i \(0.350275\pi\)
−0.998584 + 0.0531977i \(0.983059\pi\)
\(660\) −4.00000 6.92820i −0.155700 0.269680i
\(661\) 15.0000 + 25.9808i 0.583432 + 1.01053i 0.995069 + 0.0991864i \(0.0316240\pi\)
−0.411636 + 0.911348i \(0.635043\pi\)
\(662\) −16.0000 −0.621858
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 1.00000 + 1.73205i 0.0387492 + 0.0671156i
\(667\) 0 0
\(668\) −8.00000 −0.309529
\(669\) −2.00000 + 3.46410i −0.0773245 + 0.133930i
\(670\) −8.00000 + 13.8564i −0.309067 + 0.535320i
\(671\) 8.00000 0.308837
\(672\) −10.0000 + 17.3205i −0.385758 + 0.668153i
\(673\) 7.00000 + 12.1244i 0.269830 + 0.467360i 0.968818 0.247774i \(-0.0796991\pi\)
−0.698988 + 0.715134i \(0.746366\pi\)
\(674\) 9.00000 + 15.5885i 0.346667 + 0.600445i
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 22.0000 0.845529 0.422764 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) 3.00000 + 5.19615i 0.115214 + 0.199557i
\(679\) 20.0000 + 34.6410i 0.767530 + 1.32940i
\(680\) 6.00000 10.3923i 0.230089 0.398527i
\(681\) −20.0000 −0.766402
\(682\) 8.00000 13.8564i 0.306336 0.530589i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 0 0
\(685\) −6.00000 + 10.3923i −0.229248 + 0.397070i
\(686\) 4.00000 + 6.92820i 0.152721 + 0.264520i
\(687\) 5.00000 + 8.66025i 0.190762 + 0.330409i
\(688\) 12.0000 0.457496
\(689\) 0 0
\(690\) 0 0
\(691\) −12.0000 20.7846i −0.456502 0.790684i 0.542272 0.840203i \(-0.317564\pi\)
−0.998773 + 0.0495194i \(0.984231\pi\)
\(692\) 3.00000 + 5.19615i 0.114043 + 0.197528i
\(693\) 8.00000 13.8564i 0.303895 0.526361i
\(694\) 12.0000 0.455514
\(695\) 12.0000 20.7846i 0.455186 0.788405i
\(696\) −15.0000 + 25.9808i −0.568574 + 0.984798i
\(697\) −12.0000 −0.454532
\(698\) 13.0000 22.5167i 0.492057 0.852268i
\(699\) −7.00000 12.1244i −0.264764 0.458585i
\(700\) −2.00000 3.46410i −0.0755929 0.130931i
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 14.0000 + 24.2487i 0.527645 + 0.913908i
\(705\) 0 0
\(706\) 1.00000 1.73205i 0.0376355 0.0651866i
\(707\) −72.0000 −2.70784
\(708\) 6.00000 10.3923i 0.225494 0.390567i
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 0 0
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) 0 0
\(714\) 8.00000 0.299392
\(715\) 0 0
\(716\) −4.00000 −0.149487
\(717\) 12.0000 + 20.7846i 0.448148 + 0.776215i
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) 12.0000 20.7846i 0.447524 0.775135i −0.550700 0.834703i \(-0.685639\pi\)
0.998224 + 0.0595683i \(0.0189724\pi\)
\(720\) 2.00000 0.0745356
\(721\) 0 0
\(722\) −9.50000 + 16.4545i −0.353553 + 0.612372i
\(723\) 10.0000 0.371904
\(724\) −5.00000 + 8.66025i −0.185824 + 0.321856i
\(725\) −5.00000 8.66025i −0.185695 0.321634i
\(726\) −2.50000 4.33013i −0.0927837 0.160706i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 2.00000 + 3.46410i 0.0740233 + 0.128212i
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) 1.00000 1.73205i 0.0369611 0.0640184i
\(733\) −30.0000 −1.10808 −0.554038 0.832492i \(-0.686914\pi\)
−0.554038 + 0.832492i \(0.686914\pi\)
\(734\) 8.00000 13.8564i 0.295285 0.511449i
\(735\) −9.00000 + 15.5885i −0.331970 + 0.574989i
\(736\) 0 0
\(737\) 16.0000 27.7128i 0.589368 1.02081i
\(738\) −3.00000 5.19615i −0.110432 0.191273i
\(739\) 16.0000 + 27.7128i 0.588570 + 1.01943i 0.994420 + 0.105493i \(0.0336420\pi\)
−0.405851 + 0.913939i \(0.633025\pi\)
\(740\) 4.00000 0.147043
\(741\) 0 0
\(742\) −24.0000 −0.881068
\(743\) 24.0000 + 41.5692i 0.880475 + 1.52503i 0.850814 + 0.525467i \(0.176109\pi\)
0.0296605 + 0.999560i \(0.490557\pi\)
\(744\) −6.00000 10.3923i −0.219971 0.381000i
\(745\) 6.00000 10.3923i 0.219823 0.380745i
\(746\) 26.0000 0.951928
\(747\) 2.00000 3.46410i 0.0731762 0.126745i
\(748\) −4.00000 + 6.92820i −0.146254 + 0.253320i
\(749\) 48.0000 1.75388
\(750\) −6.00000 + 10.3923i −0.219089 + 0.379473i
\(751\) −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i \(-0.213294\pi\)
−0.929731 + 0.368238i \(0.879961\pi\)
\(752\) 0 0
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) −2.00000 3.46410i −0.0727393 0.125988i
\(757\) −11.0000 19.0526i −0.399802 0.692477i 0.593899 0.804539i \(-0.297588\pi\)
−0.993701 + 0.112062i \(0.964254\pi\)
\(758\) 12.0000 20.7846i 0.435860 0.754931i
\(759\) 0 0
\(760\) 0 0
\(761\) −5.00000 + 8.66025i −0.181250 + 0.313934i −0.942306 0.334752i \(-0.891348\pi\)
0.761057 + 0.648686i \(0.224681\pi\)
\(762\) −16.0000 −0.579619
\(763\) −4.00000 + 6.92820i −0.144810 + 0.250818i
\(764\) 4.00000 + 6.92820i 0.144715 + 0.250654i
\(765\) 2.00000 + 3.46410i 0.0723102 + 0.125245i
\(766\) −16.0000 −0.578103
\(767\) 0 0
\(768\) 17.0000 0.613435
\(769\) −15.0000 25.9808i −0.540914 0.936890i −0.998852 0.0479061i \(-0.984745\pi\)
0.457938 0.888984i \(-0.348588\pi\)
\(770\) 16.0000 + 27.7128i 0.576600 + 0.998700i
\(771\) 13.0000 22.5167i 0.468184 0.810918i
\(772\) 18.0000 0.647834
\(773\) 5.00000 8.66025i 0.179838 0.311488i −0.761987 0.647592i \(-0.775776\pi\)
0.941825 + 0.336104i \(0.109109\pi\)
\(774\) −6.00000 + 10.3923i −0.215666 + 0.373544i
\(775\) 4.00000 0.143684
\(776\) 15.0000 25.9808i 0.538469 0.932655i
\(777\) 4.00000 + 6.92820i 0.143499 + 0.248548i
\(778\) 11.0000 + 19.0526i 0.394369 + 0.683067i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −5.00000 8.66025i