Properties

Label 507.2.j.e.316.2
Level $507$
Weight $2$
Character 507.316
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) 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: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 507.316
Dual form 507.2.j.e.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(-3.46410 + 2.00000i) q^{7} -3.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(-3.46410 + 2.00000i) q^{7} -3.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} +(-3.46410 - 2.00000i) q^{11} -1.00000 q^{12} -4.00000 q^{14} +(-1.73205 - 1.00000i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} -1.00000i q^{18} +(-1.73205 + 1.00000i) q^{20} +4.00000i q^{21} +(-2.00000 - 3.46410i) q^{22} +(-2.59808 - 1.50000i) q^{24} +1.00000 q^{25} -1.00000 q^{27} +(3.46410 + 2.00000i) q^{28} +(5.00000 - 8.66025i) q^{29} +(-1.00000 - 1.73205i) q^{30} -4.00000i q^{31} +(-4.33013 + 2.50000i) q^{32} +(-3.46410 + 2.00000i) q^{33} +2.00000i q^{34} +(4.00000 + 6.92820i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.73205 + 1.00000i) q^{37} -6.00000 q^{40} +(5.19615 + 3.00000i) q^{41} +(-2.00000 + 3.46410i) q^{42} +(-6.00000 - 10.3923i) q^{43} +4.00000i q^{44} +(-1.73205 + 1.00000i) q^{45} +(-0.500000 - 0.866025i) q^{48} +(4.50000 - 7.79423i) q^{49} +(0.866025 + 0.500000i) q^{50} +2.00000 q^{51} +6.00000 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-4.00000 + 6.92820i) q^{55} +(6.00000 + 10.3923i) q^{56} +(8.66025 - 5.00000i) q^{58} +(10.3923 - 6.00000i) q^{59} +2.00000i q^{60} +(1.00000 + 1.73205i) q^{61} +(2.00000 - 3.46410i) q^{62} +(3.46410 + 2.00000i) q^{63} -7.00000 q^{64} -4.00000 q^{66} +(-6.92820 - 4.00000i) q^{67} +(1.00000 - 1.73205i) q^{68} +8.00000i q^{70} +(-2.59808 + 1.50000i) q^{72} +2.00000i q^{73} +(1.00000 + 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} +16.0000 q^{77} +8.00000 q^{79} +(-1.73205 - 1.00000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} -4.00000i q^{83} +(3.46410 - 2.00000i) q^{84} +(3.46410 - 2.00000i) q^{85} -12.0000i q^{86} +(-5.00000 - 8.66025i) q^{87} +(-6.00000 + 10.3923i) q^{88} +(1.73205 + 1.00000i) q^{89} -2.00000 q^{90} +(-3.46410 - 2.00000i) q^{93} +5.00000i q^{96} +(-8.66025 + 5.00000i) q^{97} +(7.79423 - 4.50000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 16 q^{14} + 2 q^{16} + 4 q^{17} - 8 q^{22} + 4 q^{25} - 4 q^{27} + 20 q^{29} - 4 q^{30} + 16 q^{35} - 2 q^{36} - 24 q^{40} - 8 q^{42} - 24 q^{43} - 2 q^{48} + 18 q^{49} + 8 q^{51} + 24 q^{53} - 16 q^{55} + 24 q^{56} + 4 q^{61} + 8 q^{62} - 28 q^{64} - 16 q^{66} + 4 q^{68} + 4 q^{74} + 2 q^{75} + 64 q^{77} + 32 q^{79} - 2 q^{81} + 12 q^{82} - 20 q^{87} - 24 q^{88} - 8 q^{90}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i 0.773893 0.633316i \(-0.218307\pi\)
−0.161521 + 0.986869i \(0.551640\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.00000i 0.894427i −0.894427 0.447214i \(-0.852416\pi\)
0.894427 0.447214i \(-0.147584\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −3.46410 + 2.00000i −1.30931 + 0.755929i −0.981981 0.188982i \(-0.939481\pi\)
−0.327327 + 0.944911i \(0.606148\pi\)
\(8\) 3.00000i 1.06066i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 1.73205i 0.316228 0.547723i
\(11\) −3.46410 2.00000i −1.04447 0.603023i −0.123371 0.992361i \(-0.539370\pi\)
−0.921095 + 0.389338i \(0.872704\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −4.00000 −1.06904
\(15\) −1.73205 1.00000i −0.447214 0.258199i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) −1.73205 + 1.00000i −0.387298 + 0.223607i
\(21\) 4.00000i 0.872872i
\(22\) −2.00000 3.46410i −0.426401 0.738549i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −2.59808 1.50000i −0.530330 0.306186i
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 3.46410 + 2.00000i 0.654654 + 0.377964i
\(29\) 5.00000 8.66025i 0.928477 1.60817i 0.142605 0.989780i \(-0.454452\pi\)
0.785872 0.618389i \(-0.212214\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) 4.00000i 0.718421i −0.933257 0.359211i \(-0.883046\pi\)
0.933257 0.359211i \(-0.116954\pi\)
\(32\) −4.33013 + 2.50000i −0.765466 + 0.441942i
\(33\) −3.46410 + 2.00000i −0.603023 + 0.348155i
\(34\) 2.00000i 0.342997i
\(35\) 4.00000 + 6.92820i 0.676123 + 1.17108i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 1.73205 + 1.00000i 0.284747 + 0.164399i 0.635571 0.772043i \(-0.280765\pi\)
−0.350823 + 0.936442i \(0.614098\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −6.00000 −0.948683
\(41\) 5.19615 + 3.00000i 0.811503 + 0.468521i 0.847477 0.530831i \(-0.178120\pi\)
−0.0359748 + 0.999353i \(0.511454\pi\)
\(42\) −2.00000 + 3.46410i −0.308607 + 0.534522i
\(43\) −6.00000 10.3923i −0.914991 1.58481i −0.806914 0.590669i \(-0.798864\pi\)
−0.108078 0.994142i \(-0.534469\pi\)
\(44\) 4.00000i 0.603023i
\(45\) −1.73205 + 1.00000i −0.258199 + 0.149071i
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 4.50000 7.79423i 0.642857 1.11346i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 2.00000 0.280056
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −4.00000 + 6.92820i −0.539360 + 0.934199i
\(56\) 6.00000 + 10.3923i 0.801784 + 1.38873i
\(57\) 0 0
\(58\) 8.66025 5.00000i 1.13715 0.656532i
\(59\) 10.3923 6.00000i 1.35296 0.781133i 0.364299 0.931282i \(-0.381308\pi\)
0.988663 + 0.150148i \(0.0479752\pi\)
\(60\) 2.00000i 0.258199i
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 2.00000 3.46410i 0.254000 0.439941i
\(63\) 3.46410 + 2.00000i 0.436436 + 0.251976i
\(64\) −7.00000 −0.875000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) −6.92820 4.00000i −0.846415 0.488678i 0.0130248 0.999915i \(-0.495854\pi\)
−0.859440 + 0.511237i \(0.829187\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0 0
\(70\) 8.00000i 0.956183i
\(71\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(72\) −2.59808 + 1.50000i −0.306186 + 0.176777i
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) 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 \(0.351411\pi\)
\(80\) −1.73205 1.00000i −0.193649 0.111803i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 3.46410 2.00000i 0.377964 0.218218i
\(85\) 3.46410 2.00000i 0.375735 0.216930i
\(86\) 12.0000i 1.29399i
\(87\) −5.00000 8.66025i −0.536056 0.928477i
\(88\) −6.00000 + 10.3923i −0.639602 + 1.10782i
\(89\) 1.73205 + 1.00000i 0.183597 + 0.106000i 0.588982 0.808146i \(-0.299529\pi\)
−0.405385 + 0.914146i \(0.632862\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) 0 0
\(93\) −3.46410 2.00000i −0.359211 0.207390i
\(94\) 0 0
\(95\) 0 0
\(96\) 5.00000i 0.510310i
\(97\) −8.66025 + 5.00000i −0.879316 + 0.507673i −0.870433 0.492287i \(-0.836161\pi\)
−0.00888289 + 0.999961i \(0.502828\pi\)
\(98\) 7.79423 4.50000i 0.787336 0.454569i
\(99\) 4.00000i 0.402015i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) 1.73205 + 1.00000i 0.171499 + 0.0990148i
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 8.00000 0.780720
\(106\) 5.19615 + 3.00000i 0.504695 + 0.291386i
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 2.00000i 0.191565i 0.995402 + 0.0957826i \(0.0305354\pi\)
−0.995402 + 0.0957826i \(0.969465\pi\)
\(110\) −6.92820 + 4.00000i −0.660578 + 0.381385i
\(111\) 1.73205 1.00000i 0.164399 0.0949158i
\(112\) 4.00000i 0.377964i
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −10.0000 −0.928477
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) −6.92820 4.00000i −0.635107 0.366679i
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) 2.50000 + 4.33013i 0.227273 + 0.393648i
\(122\) 2.00000i 0.181071i
\(123\) 5.19615 3.00000i 0.468521 0.270501i
\(124\) −3.46410 + 2.00000i −0.311086 + 0.179605i
\(125\) 12.0000i 1.07331i
\(126\) 2.00000 + 3.46410i 0.178174 + 0.308607i
\(127\) −8.00000 + 13.8564i −0.709885 + 1.22956i 0.255014 + 0.966937i \(0.417920\pi\)
−0.964899 + 0.262620i \(0.915413\pi\)
\(128\) 2.59808 + 1.50000i 0.229640 + 0.132583i
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 3.46410 + 2.00000i 0.301511 + 0.174078i
\(133\) 0 0
\(134\) −4.00000 6.92820i −0.345547 0.598506i
\(135\) 2.00000i 0.172133i
\(136\) 5.19615 3.00000i 0.445566 0.257248i
\(137\) 5.19615 3.00000i 0.443937 0.256307i −0.261329 0.965250i \(-0.584161\pi\)
0.705266 + 0.708942i \(0.250827\pi\)
\(138\) 0 0
\(139\) −6.00000 10.3923i −0.508913 0.881464i −0.999947 0.0103230i \(-0.996714\pi\)
0.491033 0.871141i \(-0.336619\pi\)
\(140\) 4.00000 6.92820i 0.338062 0.585540i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) −17.3205 10.0000i −1.43839 0.830455i
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) −4.50000 7.79423i −0.371154 0.642857i
\(148\) 2.00000i 0.164399i
\(149\) 5.19615 3.00000i 0.425685 0.245770i −0.271821 0.962348i \(-0.587626\pi\)
0.697507 + 0.716578i \(0.254293\pi\)
\(150\) 0.866025 0.500000i 0.0707107 0.0408248i
\(151\) 4.00000i 0.325515i 0.986666 + 0.162758i \(0.0520389\pi\)
−0.986666 + 0.162758i \(0.947961\pi\)
\(152\) 0 0
\(153\) 1.00000 1.73205i 0.0808452 0.140028i
\(154\) 13.8564 + 8.00000i 1.11658 + 0.644658i
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 6.92820 + 4.00000i 0.551178 + 0.318223i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 5.00000 + 8.66025i 0.395285 + 0.684653i
\(161\) 0 0
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) 6.92820 4.00000i 0.542659 0.313304i −0.203497 0.979076i \(-0.565231\pi\)
0.746156 + 0.665771i \(0.231897\pi\)
\(164\) 6.00000i 0.468521i
\(165\) 4.00000 + 6.92820i 0.311400 + 0.539360i
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) 6.92820 + 4.00000i 0.536120 + 0.309529i 0.743505 0.668730i \(-0.233162\pi\)
−0.207385 + 0.978259i \(0.566495\pi\)
\(168\) 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 \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 10.0000i 0.758098i
\(175\) −3.46410 + 2.00000i −0.261861 + 0.151186i
\(176\) −3.46410 + 2.00000i −0.261116 + 0.150756i
\(177\) 12.0000i 0.901975i
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) 2.00000 3.46410i 0.149487 0.258919i −0.781551 0.623841i \(-0.785571\pi\)
0.931038 + 0.364922i \(0.118904\pi\)
\(180\) 1.73205 + 1.00000i 0.129099 + 0.0745356i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 8.00000i 0.585018i
\(188\) 0 0
\(189\) 3.46410 2.00000i 0.251976 0.145479i
\(190\) 0 0
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) −3.50000 + 6.06218i −0.252591 + 0.437500i
\(193\) −15.5885 9.00000i −1.12208 0.647834i −0.180150 0.983639i \(-0.557658\pi\)
−0.941932 + 0.335805i \(0.890992\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) −9.00000 −0.642857
\(197\) 15.5885 + 9.00000i 1.11063 + 0.641223i 0.938993 0.343937i \(-0.111761\pi\)
0.171639 + 0.985160i \(0.445094\pi\)
\(198\) −2.00000 + 3.46410i −0.142134 + 0.246183i
\(199\) 4.00000 + 6.92820i 0.283552 + 0.491127i 0.972257 0.233915i \(-0.0751537\pi\)
−0.688705 + 0.725042i \(0.741820\pi\)
\(200\) 3.00000i 0.212132i
\(201\) −6.92820 + 4.00000i −0.488678 + 0.282138i
\(202\) −15.5885 + 9.00000i −1.09680 + 0.633238i
\(203\) 40.0000i 2.80745i
\(204\) −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
\(210\) 6.92820 + 4.00000i 0.478091 + 0.276026i
\(211\) 10.0000 17.3205i 0.688428 1.19239i −0.283918 0.958849i \(-0.591634\pi\)
0.972346 0.233544i \(-0.0750324\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 0 0
\(214\) −10.3923 + 6.00000i −0.710403 + 0.410152i
\(215\) −20.7846 + 12.0000i −1.41750 + 0.818393i
\(216\) 3.00000i 0.204124i
\(217\) 8.00000 + 13.8564i 0.543075 + 0.940634i
\(218\) −1.00000 + 1.73205i −0.0677285 + 0.117309i
\(219\) 1.73205 + 1.00000i 0.117041 + 0.0675737i
\(220\) 8.00000 0.539360
\(221\) 0 0
\(222\) 2.00000 0.134231
\(223\) 3.46410 + 2.00000i 0.231973 + 0.133930i 0.611482 0.791258i \(-0.290574\pi\)
−0.379509 + 0.925188i \(0.623907\pi\)
\(224\) 10.0000 17.3205i 0.668153 1.15728i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) 6.00000i 0.399114i
\(227\) 17.3205 10.0000i 1.14960 0.663723i 0.200812 0.979630i \(-0.435642\pi\)
0.948790 + 0.315906i \(0.102309\pi\)
\(228\) 0 0
\(229\) 10.0000i 0.660819i −0.943838 0.330409i \(-0.892813\pi\)
0.943838 0.330409i \(-0.107187\pi\)
\(230\) 0 0
\(231\) 8.00000 13.8564i 0.526361 0.911685i
\(232\) −25.9808 15.0000i −1.70572 0.984798i
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −10.3923 6.00000i −0.676481 0.390567i
\(237\) 4.00000 6.92820i 0.259828 0.450035i
\(238\) −4.00000 6.92820i −0.259281 0.449089i
\(239\) 24.0000i 1.55243i 0.630468 + 0.776215i \(0.282863\pi\)
−0.630468 + 0.776215i \(0.717137\pi\)
\(240\) −1.73205 + 1.00000i −0.111803 + 0.0645497i
\(241\) 8.66025 5.00000i 0.557856 0.322078i −0.194429 0.980917i \(-0.562285\pi\)
0.752285 + 0.658838i \(0.228952\pi\)
\(242\) 5.00000i 0.321412i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 1.00000 1.73205i 0.0640184 0.110883i
\(245\) −15.5885 9.00000i −0.995910 0.574989i
\(246\) 6.00000 0.382546
\(247\) 0 0
\(248\) −12.0000 −0.762001
\(249\) −3.46410 2.00000i −0.219529 0.126745i
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −6.00000 10.3923i −0.378717 0.655956i 0.612159 0.790735i \(-0.290301\pi\)
−0.990876 + 0.134778i \(0.956968\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 0 0
\(254\) −13.8564 + 8.00000i −0.869428 + 0.501965i
\(255\) 4.00000i 0.250490i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 13.0000 22.5167i 0.810918 1.40455i −0.101305 0.994855i \(-0.532302\pi\)
0.912222 0.409695i \(-0.134365\pi\)
\(258\) −10.3923 6.00000i −0.646997 0.373544i
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) −10.0000 −0.618984
\(262\) 3.46410 + 2.00000i 0.214013 + 0.123560i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 6.00000 + 10.3923i 0.369274 + 0.639602i
\(265\) 12.0000i 0.737154i
\(266\) 0 0
\(267\) 1.73205 1.00000i 0.106000 0.0611990i
\(268\) 8.00000i 0.488678i
\(269\) −11.0000 19.0526i −0.670682 1.16166i −0.977711 0.209955i \(-0.932668\pi\)
0.307029 0.951700i \(-0.400665\pi\)
\(270\) −1.00000 + 1.73205i −0.0608581 + 0.105409i
\(271\) 10.3923 + 6.00000i 0.631288 + 0.364474i 0.781251 0.624218i \(-0.214582\pi\)
−0.149963 + 0.988692i \(0.547915\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −3.46410 2.00000i −0.208893 0.120605i
\(276\) 0 0
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) 12.0000i 0.719712i
\(279\) −3.46410 + 2.00000i −0.207390 + 0.119737i
\(280\) 20.7846 12.0000i 1.24212 0.717137i
\(281\) 10.0000i 0.596550i −0.954480 0.298275i \(-0.903589\pi\)
0.954480 0.298275i \(-0.0964112\pi\)
\(282\) 0 0
\(283\) 6.00000 10.3923i 0.356663 0.617758i −0.630738 0.775996i \(-0.717248\pi\)
0.987401 + 0.158237i \(0.0505811\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 4.33013 + 2.50000i 0.255155 + 0.147314i
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −10.0000 17.3205i −0.587220 1.01710i
\(291\) 10.0000i 0.586210i
\(292\) 1.73205 1.00000i 0.101361 0.0585206i
\(293\) −5.19615 + 3.00000i −0.303562 + 0.175262i −0.644042 0.764990i \(-0.722744\pi\)
0.340480 + 0.940252i \(0.389411\pi\)
\(294\) 9.00000i 0.524891i
\(295\) −12.0000 20.7846i −0.698667 1.21013i
\(296\) 3.00000 5.19615i 0.174371 0.302020i
\(297\) 3.46410 + 2.00000i 0.201008 + 0.116052i
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 41.5692 + 24.0000i 2.39601 + 1.38334i
\(302\) −2.00000 + 3.46410i −0.115087 + 0.199337i
\(303\) 9.00000 + 15.5885i 0.517036 + 0.895533i
\(304\) 0 0
\(305\) 3.46410 2.00000i 0.198354 0.114520i
\(306\) 1.73205 1.00000i 0.0990148 0.0571662i
\(307\) 16.0000i 0.913168i −0.889680 0.456584i \(-0.849073\pi\)
0.889680 0.456584i \(-0.150927\pi\)
\(308\) −8.00000 13.8564i −0.455842 0.789542i
\(309\) 0 0
\(310\) −6.92820 4.00000i −0.393496 0.227185i
\(311\) 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 \(0.554238\pi\)
\(314\) −15.5885 9.00000i −0.879708 0.507899i
\(315\) 4.00000 6.92820i 0.225374 0.390360i
\(316\) −4.00000 6.92820i −0.225018 0.389742i
\(317\) 26.0000i 1.46031i −0.683284 0.730153i \(-0.739449\pi\)
0.683284 0.730153i \(-0.260551\pi\)
\(318\) 5.19615 3.00000i 0.291386 0.168232i
\(319\) −34.6410 + 20.0000i −1.93952 + 1.11979i
\(320\) 14.0000i 0.782624i
\(321\) 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
\(327\) 1.73205 + 1.00000i 0.0957826 + 0.0553001i
\(328\) 9.00000 15.5885i 0.496942 0.860729i
\(329\) 0 0
\(330\) 8.00000i 0.440386i
\(331\) 13.8564 8.00000i 0.761617 0.439720i −0.0682590 0.997668i \(-0.521744\pi\)
0.829876 + 0.557948i \(0.188411\pi\)
\(332\) −3.46410 + 2.00000i −0.190117 + 0.109764i
\(333\) 2.00000i 0.109599i
\(334\) 4.00000 + 6.92820i 0.218870 + 0.379094i
\(335\) −8.00000 + 13.8564i −0.437087 + 0.757056i
\(336\) 3.46410 + 2.00000i 0.188982 + 0.109109i
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) −3.46410 2.00000i −0.187867 0.108465i
\(341\) −8.00000 + 13.8564i −0.433224 + 0.750366i
\(342\) 0 0
\(343\) 8.00000i 0.431959i
\(344\) −31.1769 + 18.0000i −1.68095 + 0.970495i
\(345\) 0 0
\(346\) 6.00000i 0.322562i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) −5.00000 + 8.66025i −0.268028 + 0.464238i
\(349\) 22.5167 + 13.0000i 1.20529 + 0.695874i 0.961727 0.274011i \(-0.0883505\pi\)
0.243563 + 0.969885i \(0.421684\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) −1.73205 1.00000i −0.0921878 0.0532246i 0.453197 0.891410i \(-0.350283\pi\)
−0.545385 + 0.838186i \(0.683617\pi\)
\(354\) 6.00000 10.3923i 0.318896 0.552345i
\(355\) 0 0
\(356\) 2.00000i 0.106000i
\(357\) −6.92820 + 4.00000i −0.366679 + 0.211702i
\(358\) 3.46410 2.00000i 0.183083 0.105703i
\(359\) 24.0000i 1.26667i 0.773877 + 0.633336i \(0.218315\pi\)
−0.773877 + 0.633336i \(0.781685\pi\)
\(360\) 3.00000 + 5.19615i 0.158114 + 0.273861i
\(361\) −9.50000 + 16.4545i −0.500000 + 0.866025i
\(362\) 8.66025 + 5.00000i 0.455173 + 0.262794i
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 4.00000 0.209370
\(366\) 1.73205 + 1.00000i 0.0905357 + 0.0522708i
\(367\) −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i \(-0.970461\pi\)
0.578101 + 0.815966i \(0.303794\pi\)
\(368\) 0 0
\(369\) 6.00000i 0.312348i
\(370\) 3.46410 2.00000i 0.180090 0.103975i
\(371\) −20.7846 + 12.0000i −1.07908 + 0.623009i
\(372\) 4.00000i 0.207390i
\(373\) 13.0000 + 22.5167i 0.673114 + 1.16587i 0.977016 + 0.213165i \(0.0683772\pi\)
−0.303902 + 0.952703i \(0.598289\pi\)
\(374\) 4.00000 6.92820i 0.206835 0.358249i
\(375\) −10.3923 6.00000i −0.536656 0.309839i
\(376\) 0 0
\(377\) 0 0
\(378\) 4.00000 0.205738
\(379\) −20.7846 12.0000i −1.06763 0.616399i −0.140100 0.990137i \(-0.544742\pi\)
−0.927534 + 0.373739i \(0.878076\pi\)
\(380\) 0 0
\(381\) 8.00000 + 13.8564i 0.409852 + 0.709885i
\(382\) 8.00000i 0.409316i
\(383\) 13.8564 8.00000i 0.708029 0.408781i −0.102302 0.994753i \(-0.532621\pi\)
0.810331 + 0.585973i \(0.199287\pi\)
\(384\) 2.59808 1.50000i 0.132583 0.0765466i
\(385\) 32.0000i 1.63087i
\(386\) −9.00000 15.5885i −0.458088 0.793432i
\(387\) −6.00000 + 10.3923i −0.304997 + 0.528271i
\(388\) 8.66025 + 5.00000i 0.439658 + 0.253837i
\(389\) −22.0000 −1.11544 −0.557722 0.830028i \(-0.688325\pi\)
−0.557722 + 0.830028i \(0.688325\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −23.3827 13.5000i −1.18100 0.681853i
\(393\) 2.00000 3.46410i 0.100887 0.174741i
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 16.0000i 0.805047i
\(396\) 3.46410 2.00000i 0.174078 0.100504i
\(397\) 32.9090 19.0000i 1.65165 0.953583i 0.675261 0.737579i \(-0.264031\pi\)
0.976392 0.216004i \(-0.0693024\pi\)
\(398\) 8.00000i 0.401004i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −19.0526 11.0000i −0.951439 0.549314i −0.0579116 0.998322i \(-0.518444\pi\)
−0.893528 + 0.449008i \(0.851777\pi\)
\(402\) −8.00000 −0.399004
\(403\) 0 0
\(404\) 18.0000 0.895533
\(405\) 1.73205 + 1.00000i 0.0860663 + 0.0496904i
\(406\) −20.0000 + 34.6410i −0.992583 + 1.71920i
\(407\) −4.00000 6.92820i −0.198273 0.343418i
\(408\) 6.00000i 0.297044i
\(409\) −29.4449 + 17.0000i −1.45595 + 0.840596i −0.998809 0.0487958i \(-0.984462\pi\)
−0.457146 + 0.889392i \(0.651128\pi\)
\(410\) 10.3923 6.00000i 0.513239 0.296319i
\(411\) 6.00000i 0.295958i
\(412\) 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 −0.910735 0.412991i \(-0.864484\pi\)
0.813029 + 0.582224i \(0.197817\pi\)
\(420\) −4.00000 6.92820i −0.195180 0.338062i
\(421\) 10.0000i 0.487370i 0.969854 + 0.243685i \(0.0783563\pi\)
−0.969854 + 0.243685i \(0.921644\pi\)
\(422\) 17.3205 10.0000i 0.843149 0.486792i
\(423\) 0 0
\(424\) 18.0000i 0.874157i
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) −6.92820 4.00000i −0.335279 0.193574i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −24.0000 −1.15738
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 17.0000 + 29.4449i 0.816968 + 1.41503i 0.907906 + 0.419173i \(0.137680\pi\)
−0.0909384 + 0.995857i \(0.528987\pi\)
\(434\) 16.0000i 0.768025i
\(435\) −17.3205 + 10.0000i −0.830455 + 0.479463i
\(436\) 1.73205 1.00000i 0.0829502 0.0478913i
\(437\) 0 0
\(438\) 1.00000 + 1.73205i 0.0477818 + 0.0827606i
\(439\) 16.0000 27.7128i 0.763638 1.32266i −0.177325 0.984152i \(-0.556744\pi\)
0.940963 0.338508i \(-0.109922\pi\)
\(440\) 20.7846 + 12.0000i 0.990867 + 0.572078i
\(441\) −9.00000 −0.428571
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −1.73205 1.00000i −0.0821995 0.0474579i
\(445\) 2.00000 3.46410i 0.0948091 0.164214i
\(446\) 2.00000 + 3.46410i 0.0947027 + 0.164030i
\(447\) 6.00000i 0.283790i
\(448\) 24.2487 14.0000i 1.14564 0.661438i
\(449\) 19.0526 11.0000i 0.899146 0.519122i 0.0222229 0.999753i \(-0.492926\pi\)
0.876923 + 0.480631i \(0.159592\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −12.0000 20.7846i −0.565058 0.978709i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 3.46410 + 2.00000i 0.162758 + 0.0939682i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 0 0
\(457\) 1.73205 + 1.00000i 0.0810219 + 0.0467780i 0.539964 0.841688i \(-0.318438\pi\)
−0.458942 + 0.888466i \(0.651771\pi\)
\(458\) 5.00000 8.66025i 0.233635 0.404667i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) 0 0
\(461\) 32.9090 19.0000i 1.53272 0.884918i 0.533488 0.845807i \(-0.320881\pi\)
0.999235 0.0391109i \(-0.0124526\pi\)
\(462\) 13.8564 8.00000i 0.644658 0.372194i
\(463\) 4.00000i 0.185896i 0.995671 + 0.0929479i \(0.0296290\pi\)
−0.995671 + 0.0929479i \(0.970371\pi\)
\(464\) −5.00000 8.66025i −0.232119 0.402042i
\(465\) −4.00000 + 6.92820i −0.185496 + 0.321288i
\(466\) 12.1244 + 7.00000i 0.561650 + 0.324269i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 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
\(473\) 48.0000i 2.20704i
\(474\) 6.92820 4.00000i 0.318223 0.183726i
\(475\) 0 0
\(476\) 8.00000i 0.366679i
\(477\) −3.00000 5.19615i −0.137361 0.237915i
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) 20.7846 + 12.0000i 0.949673 + 0.548294i 0.892979 0.450098i \(-0.148611\pi\)
0.0566937 + 0.998392i \(0.481944\pi\)
\(480\) 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
\(486\) 1.00000i 0.0453609i
\(487\) −10.3923 + 6.00000i −0.470920 + 0.271886i −0.716625 0.697459i \(-0.754314\pi\)
0.245705 + 0.969345i \(0.420981\pi\)
\(488\) 5.19615 3.00000i 0.235219 0.135804i
\(489\) 8.00000i 0.361773i
\(490\) −9.00000 15.5885i −0.406579 0.704215i
\(491\) −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) −5.19615 3.00000i −0.234261 0.135250i
\(493\) 20.0000 0.900755
\(494\) 0 0
\(495\) 8.00000 0.359573
\(496\) −3.46410 2.00000i −0.155543 0.0898027i
\(497\) 0 0
\(498\) −2.00000 3.46410i −0.0896221 0.155230i
\(499\) 24.0000i 1.07439i 0.843459 + 0.537194i \(0.180516\pi\)
−0.843459 + 0.537194i \(0.819484\pi\)
\(500\) −10.3923 + 6.00000i −0.464758 + 0.268328i
\(501\) 6.92820 4.00000i 0.309529 0.178707i
\(502\) 12.0000i 0.535586i
\(503\) 4.00000 + 6.92820i 0.178351 + 0.308913i 0.941316 0.337527i \(-0.109590\pi\)
−0.762965 + 0.646440i \(0.776257\pi\)
\(504\) 6.00000 10.3923i 0.267261 0.462910i
\(505\) 31.1769 + 18.0000i 1.38735 + 0.800989i
\(506\) 0 0
\(507\) 0 0
\(508\) 16.0000 0.709885
\(509\) 8.66025 + 5.00000i 0.383859 + 0.221621i 0.679496 0.733679i \(-0.262199\pi\)
−0.295637 + 0.955300i \(0.595532\pi\)
\(510\) 2.00000 3.46410i 0.0885615 0.153393i
\(511\) −4.00000 6.92820i −0.176950 0.306486i
\(512\) 11.0000i 0.486136i
\(513\) 0 0
\(514\) 22.5167 13.0000i 0.993167 0.573405i
\(515\) 0 0
\(516\) 6.00000 + 10.3923i 0.264135 + 0.457496i
\(517\) 0 0
\(518\) −6.92820 4.00000i −0.304408 0.175750i
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) −8.66025 5.00000i −0.379049 0.218844i
\(523\) −22.0000 + 38.1051i −0.961993 + 1.66622i −0.244507 + 0.969648i \(0.578626\pi\)
−0.717486 + 0.696573i \(0.754707\pi\)
\(524\) −2.00000 3.46410i −0.0873704 0.151330i
\(525\) 4.00000i 0.174574i
\(526\) −20.7846 + 12.0000i −0.906252 + 0.523225i
\(527\) 6.92820 4.00000i 0.301797 0.174243i
\(528\) 4.00000i 0.174078i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 6.00000 10.3923i 0.260623 0.451413i
\(531\) −10.3923 6.00000i −0.450988 0.260378i
\(532\) 0 0
\(533\) 0 0
\(534\) 2.00000 0.0865485
\(535\) 20.7846 + 12.0000i 0.898597 + 0.518805i
\(536\) −12.0000 + 20.7846i −0.518321 + 0.897758i
\(537\) −2.00000 3.46410i −0.0863064 0.149487i
\(538\) 22.0000i 0.948487i
\(539\) −31.1769 + 18.0000i −1.34288 + 0.775315i
\(540\) 1.73205 1.00000i 0.0745356 0.0430331i
\(541\) 30.0000i 1.28980i 0.764267 + 0.644900i \(0.223101\pi\)
−0.764267 + 0.644900i \(0.776899\pi\)
\(542\) 6.00000 + 10.3923i 0.257722 + 0.446388i
\(543\) 5.00000 8.66025i 0.214571 0.371647i
\(544\) −8.66025 5.00000i −0.371305 0.214373i
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −5.19615 3.00000i −0.221969 0.128154i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) 0 0
\(552\) 0 0
\(553\) −27.7128 + 16.0000i −1.17847 + 0.680389i
\(554\) 10.0000i 0.424859i
\(555\) −2.00000 3.46410i −0.0848953 0.147043i
\(556\) −6.00000 + 10.3923i −0.254457 + 0.440732i
\(557\) −15.5885 9.00000i −0.660504 0.381342i 0.131965 0.991254i \(-0.457871\pi\)
−0.792469 + 0.609912i \(0.791205\pi\)
\(558\) −4.00000 −0.169334
\(559\) 0 0
\(560\) 8.00000 0.338062
\(561\) −6.92820 4.00000i −0.292509 0.168880i
\(562\) 5.00000 8.66025i 0.210912 0.365311i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) 0 0
\(565\) 10.3923 6.00000i 0.437208 0.252422i
\(566\) 10.3923 6.00000i 0.436821 0.252199i
\(567\) 4.00000i 0.167984i
\(568\) 0 0
\(569\) 17.0000 29.4449i 0.712677 1.23439i −0.251172 0.967943i \(-0.580816\pi\)
0.963849 0.266450i \(-0.0858508\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) −8.00000 −0.334205
\(574\) −20.7846 12.0000i −0.867533 0.500870i
\(575\) 0 0
\(576\) 3.50000 + 6.06218i 0.145833 + 0.252591i
\(577\) 46.0000i 1.91501i 0.288425 + 0.957503i \(0.406868\pi\)
−0.288425 + 0.957503i \(0.593132\pi\)
\(578\) 11.2583 6.50000i 0.468285 0.270364i
\(579\) −15.5885 + 9.00000i −0.647834 + 0.374027i
\(580\) 20.0000i 0.830455i
\(581\) 8.00000 + 13.8564i 0.331896 + 0.574861i
\(582\) −5.00000 + 8.66025i −0.207257 + 0.358979i
\(583\) −20.7846 12.0000i −0.860811 0.496989i
\(584\) 6.00000 0.248282
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 24.2487 + 14.0000i 1.00085 + 0.577842i 0.908500 0.417885i \(-0.137228\pi\)
0.0923513 + 0.995726i \(0.470562\pi\)
\(588\) −4.50000 + 7.79423i −0.185577 + 0.321429i
\(589\) 0 0
\(590\) 24.0000i 0.988064i
\(591\) 15.5885 9.00000i 0.641223 0.370211i
\(592\) 1.73205 1.00000i 0.0711868 0.0410997i
\(593\) 26.0000i 1.06769i −0.845582 0.533846i \(-0.820746\pi\)
0.845582 0.533846i \(-0.179254\pi\)
\(594\) 2.00000 + 3.46410i 0.0820610 + 0.142134i
\(595\) −8.00000 + 13.8564i −0.327968 + 0.568057i
\(596\) −5.19615 3.00000i −0.212843 0.122885i
\(597\) 8.00000 0.327418
\(598\) 0 0
\(599\) −40.0000 −1.63436 −0.817178 0.576386i \(-0.804463\pi\)
−0.817178 + 0.576386i \(0.804463\pi\)
\(600\) −2.59808 1.50000i −0.106066 0.0612372i
\(601\) 19.0000 32.9090i 0.775026 1.34238i −0.159754 0.987157i \(-0.551070\pi\)
0.934780 0.355228i \(-0.115597\pi\)
\(602\) 24.0000 + 41.5692i 0.978167 + 1.69423i
\(603\) 8.00000i 0.325785i
\(604\) 3.46410 2.00000i 0.140952 0.0813788i
\(605\) 8.66025 5.00000i 0.352089 0.203279i
\(606\) 18.0000i 0.731200i
\(607\) 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i \(-0.0614000\pi\)
−0.656744 + 0.754114i \(0.728067\pi\)
\(608\) 0 0
\(609\) 34.6410 + 20.0000i 1.40372 + 0.810441i
\(610\) 4.00000 0.161955
\(611\) 0 0
\(612\) −2.00000 −0.0808452
\(613\) −1.73205 1.00000i −0.0699569 0.0403896i 0.464614 0.885514i \(-0.346193\pi\)
−0.534570 + 0.845124i \(0.679527\pi\)
\(614\) 8.00000 13.8564i 0.322854 0.559199i
\(615\) −6.00000 10.3923i −0.241943 0.419058i
\(616\) 48.0000i 1.93398i
\(617\) −19.0526 + 11.0000i −0.767027 + 0.442843i −0.831813 0.555056i \(-0.812697\pi\)
0.0647859 + 0.997899i \(0.479364\pi\)
\(618\) 0 0
\(619\) 24.0000i 0.964641i 0.875995 + 0.482321i \(0.160206\pi\)
−0.875995 + 0.482321i \(0.839794\pi\)
\(620\) 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
\(626\) −5.19615 3.00000i −0.207680 0.119904i
\(627\) 0 0
\(628\) 9.00000 + 15.5885i 0.359139 + 0.622047i
\(629\) 4.00000i 0.159490i
\(630\) 6.92820 4.00000i 0.276026 0.159364i
\(631\) 17.3205 10.0000i 0.689519 0.398094i −0.113913 0.993491i \(-0.536339\pi\)
0.803432 + 0.595397i \(0.203005\pi\)
\(632\) 24.0000i 0.954669i
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) 13.0000 22.5167i 0.516296 0.894251i
\(635\) 27.7128 + 16.0000i 1.09975 + 0.634941i
\(636\) −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 \(-0.154091\pi\)
−0.845601 + 0.533816i \(0.820758\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 34.6410 20.0000i 1.36611 0.788723i 0.375680 0.926750i \(-0.377409\pi\)
0.990429 + 0.138027i \(0.0440759\pi\)
\(644\) 0 0
\(645\) 24.0000i 0.944999i
\(646\) 0 0
\(647\) −4.00000 + 6.92820i −0.157256 + 0.272376i −0.933878 0.357591i \(-0.883598\pi\)
0.776622 + 0.629967i \(0.216932\pi\)
\(648\) 2.59808 + 1.50000i 0.102062 + 0.0589256i
\(649\) −48.0000 −1.88416
\(650\) 0 0
\(651\) 16.0000 0.627089
\(652\) −6.92820 4.00000i −0.271329 0.156652i
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 1.00000 + 1.73205i 0.0391031 + 0.0677285i
\(655\) 8.00000i 0.312586i
\(656\) 5.19615 3.00000i 0.202876 0.117130i
\(657\) 1.73205 1.00000i 0.0675737 0.0390137i
\(658\) 0 0
\(659\) −14.0000 24.2487i −0.545363 0.944596i −0.998584 0.0531977i \(-0.983059\pi\)
0.453221 0.891398i \(-0.350275\pi\)
\(660\) 4.00000 6.92820i 0.155700 0.269680i
\(661\) −25.9808 15.0000i −1.01053 0.583432i −0.0991864 0.995069i \(-0.531624\pi\)
−0.911348 + 0.411636i \(0.864957\pi\)
\(662\) 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
\(668\) 8.00000i 0.309529i
\(669\) 3.46410 2.00000i 0.133930 0.0773245i
\(670\) −13.8564 + 8.00000i −0.535320 + 0.309067i
\(671\) 8.00000i 0.308837i
\(672\) −10.0000 17.3205i −0.385758 0.668153i
\(673\) −7.00000 + 12.1244i −0.269830 + 0.467360i −0.968818 0.247774i \(-0.920301\pi\)
0.698988 + 0.715134i \(0.253634\pi\)
\(674\) −15.5885 9.00000i −0.600445 0.346667i
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 22.0000 0.845529 0.422764 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) 5.19615 + 3.00000i 0.199557 + 0.115214i
\(679\) 20.0000 34.6410i 0.767530 1.32940i
\(680\) −6.00000 10.3923i −0.230089 0.398527i
\(681\) 20.0000i 0.766402i
\(682\) −13.8564 + 8.00000i −0.530589 + 0.306336i
\(683\) −10.3923 + 6.00000i −0.397650 + 0.229584i −0.685470 0.728101i \(-0.740403\pi\)
0.287819 + 0.957685i \(0.407070\pi\)
\(684\) 0 0
\(685\) −6.00000 10.3923i −0.229248 0.397070i
\(686\) −4.00000 + 6.92820i −0.152721 + 0.264520i
\(687\) −8.66025 5.00000i −0.330409 0.190762i
\(688\) −12.0000 −0.457496
\(689\) 0 0
\(690\) 0 0
\(691\) −20.7846 12.0000i −0.790684 0.456502i 0.0495194 0.998773i \(-0.484231\pi\)
−0.840203 + 0.542272i \(0.817564\pi\)
\(692\) 3.00000 5.19615i 0.114043 0.197528i
\(693\) −8.00000 13.8564i −0.303895 0.526361i
\(694\) 12.0000i 0.455514i
\(695\) −20.7846 + 12.0000i −0.788405 + 0.455186i
\(696\) −25.9808 + 15.0000i −0.984798 + 0.568574i
\(697\) 12.0000i 0.454532i
\(698\) 13.0000 + 22.5167i 0.492057 + 0.852268i
\(699\) 7.00000 12.1244i 0.264764 0.458585i
\(700\) 3.46410 + 2.00000i 0.130931 + 0.0755929i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 24.2487 + 14.0000i 0.913908 + 0.527645i
\(705\) 0 0
\(706\) −1.00000 1.73205i −0.0376355 0.0651866i
\(707\) 72.0000i 2.70784i
\(708\) −10.3923 + 6.00000i −0.390567 + 0.225494i
\(709\) −22.5167 + 13.0000i −0.845631 + 0.488225i −0.859174 0.511683i \(-0.829022\pi\)
0.0135434 + 0.999908i \(0.495689\pi\)
\(710\) 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
\(717\) 20.7846 + 12.0000i 0.776215 + 0.448148i
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) −12.0000 20.7846i −0.447524 0.775135i 0.550700 0.834703i \(-0.314361\pi\)
−0.998224 + 0.0595683i \(0.981028\pi\)
\(720\) 2.00000i 0.0745356i
\(721\) 0 0
\(722\) −16.4545 + 9.50000i −0.612372 + 0.353553i
\(723\) 10.0000i 0.371904i
\(724\) −5.00000 8.66025i −0.185824 0.321856i
\(725\) 5.00000 8.66025i 0.185695 0.321634i
\(726\) 4.33013 + 2.50000i 0.160706 + 0.0927837i
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 3.46410 + 2.00000i 0.128212 + 0.0740233i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) 30.0000i 1.10808i −0.832492 0.554038i \(-0.813086\pi\)
0.832492 0.554038i \(-0.186914\pi\)
\(734\) −13.8564 + 8.00000i −0.511449 + 0.295285i
\(735\) −15.5885 + 9.00000i −0.574989 + 0.331970i
\(736\) 0 0
\(737\) 16.0000 + 27.7128i 0.589368 + 1.02081i
\(738\) 3.00000 5.19615i 0.110432 0.191273i
\(739\) −27.7128 16.0000i −1.01943 0.588570i −0.105493 0.994420i \(-0.533642\pi\)
−0.913939 + 0.405851i \(0.866975\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) −24.0000 −0.881068
\(743\) 41.5692 + 24.0000i 1.52503 + 0.880475i 0.999560 + 0.0296605i \(0.00944260\pi\)
0.525467 + 0.850814i \(0.323891\pi\)
\(744\) −6.00000 + 10.3923i −0.219971 + 0.381000i
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) 26.0000i 0.951928i
\(747\) −3.46410 + 2.00000i −0.126745 + 0.0731762i
\(748\) −6.92820 + 4.00000i −0.253320 + 0.146254i
\(749\) 48.0000i 1.75388i
\(750\) −6.00000 10.3923i −0.219089 0.379473i
\(751\) 4.00000 6.92820i 0.145962 0.252814i −0.783769 0.621052i \(-0.786706\pi\)
0.929731 + 0.368238i \(0.120039\pi\)
\(752\) 0 0
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) −3.46410 2.00000i −0.125988 0.0727393i
\(757\) −11.0000 + 19.0526i −0.399802 + 0.692477i −0.993701 0.112062i \(-0.964254\pi\)
0.593899 + 0.804539i \(0.297588\pi\)
\(758\) −12.0000 20.7846i −0.435860 0.754931i
\(759\) 0 0
\(760\) 0 0
\(761\) −8.66025 + 5.00000i −0.313934 + 0.181250i −0.648686 0.761057i \(-0.724681\pi\)
0.334752 + 0.942306i \(0.391348\pi\)
\(762\) 16.0000i 0.579619i
\(763\) −4.00000 6.92820i −0.144810 0.250818i
\(764\) −4.00000 + 6.92820i −0.144715 + 0.250654i
\(765\) −3.46410 2.00000i −0.125245 0.0723102i
\(766\) 16.0000 0.578103
\(767\) 0 0
\(768\) 17.0000 0.613435
\(769\) −25.9808 15.0000i −0.936890 0.540914i −0.0479061 0.998852i \(-0.515255\pi\)
−0.888984 + 0.457938i \(0.848588\pi\)
\(770\) 16.0000 27.7128i 0.576600 0.998700i
\(771\) −13.0000 22.5167i −0.468184 0.810918i
\(772\) 18.0000i 0.647834i
\(773\) −8.66025 + 5.00000i −0.311488 + 0.179838i −0.647592 0.761987i \(-0.724224\pi\)
0.336104 + 0.941825i \(0.390891\pi\)
\(774\) −10.3923 + 6.00000i −0.373544 + 0.215666i
\(775\) 4.00000i 0.143684i
\(776\) 15.0000 + 25.9808i 0.538469 + 0.932655i
\(777\) −4.00000 + 6.92820i −0.143499 + 0.248548i
\(778\) −19.0526 11.0000i −0.683067 0.394369i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −5.00000 + 8.66025i −0.178685 + 0.309492