Properties

Label 507.2.j.e.361.2
Level $507$
Weight $2$
Character 507.361
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 361.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 507.361
Dual form 507.2.j.e.316.2

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 −0.161521 0.986869i \(-0.551640\pi\)
0.773893 + 0.633316i \(0.218307\pi\)
\(3\) 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 \(0.147584\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) −3.46410 2.00000i −1.30931 0.755929i −0.327327 0.944911i \(-0.606148\pi\)
−0.981981 + 0.188982i \(0.939481\pi\)
\(8\) 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 −0.921095 0.389338i \(-0.872704\pi\)
−0.123371 + 0.992361i \(0.539370\pi\)
\(12\) −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 −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) −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 0.785872 + 0.618389i \(0.212214\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) 4.00000i 0.718421i 0.933257 + 0.359211i \(0.116954\pi\)
−0.933257 + 0.359211i \(0.883046\pi\)
\(32\) −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 −0.350823 0.936442i \(-0.614098\pi\)
0.635571 + 0.772043i \(0.280765\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −6.00000 −0.948683
\(41\) 5.19615 3.00000i 0.811503 0.468521i −0.0359748 0.999353i \(-0.511454\pi\)
0.847477 + 0.530831i \(0.178120\pi\)
\(42\) −2.00000 3.46410i −0.308607 0.534522i
\(43\) −6.00000 + 10.3923i −0.914991 + 1.58481i −0.108078 + 0.994142i \(0.534469\pi\)
−0.806914 + 0.590669i \(0.798864\pi\)
\(44\) 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 0.988663 0.150148i \(-0.0479752\pi\)
0.364299 + 0.931282i \(0.381308\pi\)
\(60\) 2.00000i 0.258199i
\(61\) 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
\(63\) 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 −0.859440 0.511237i \(-0.829187\pi\)
0.0130248 + 0.999915i \(0.495854\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 0 0
\(70\) 8.00000i 0.956183i
\(71\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) −2.59808 1.50000i −0.306186 0.176777i
\(73\) 2.00000i 0.234082i −0.993127 0.117041i \(-0.962659\pi\)
0.993127 0.117041i \(-0.0373409\pi\)
\(74\) 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 \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 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 −0.405385 0.914146i \(-0.632862\pi\)
0.588982 + 0.808146i \(0.299529\pi\)
\(90\) −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 −0.00888289 0.999961i \(-0.502828\pi\)
−0.870433 + 0.492287i \(0.836161\pi\)
\(98\) 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 −0.833143 0.553058i \(-0.813461\pi\)
−0.0623905 0.998052i \(-0.519872\pi\)
\(102\) 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 −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) −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 −0.689714 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
\(119\) −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 −0.964899 0.262620i \(-0.915413\pi\)
0.255014 0.966937i \(-0.417920\pi\)
\(128\) 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 0.705266 0.708942i \(-0.250827\pi\)
−0.261329 + 0.965250i \(0.584161\pi\)
\(138\) 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
\(145\) −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 0.697507 0.716578i \(-0.254293\pi\)
−0.271821 + 0.962348i \(0.587626\pi\)
\(150\) 0.866025 + 0.500000i 0.0707107 + 0.0408248i
\(151\) 4.00000i 0.325515i −0.986666 0.162758i \(-0.947961\pi\)
0.986666 0.162758i \(-0.0520389\pi\)
\(152\) 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 0.746156 0.665771i \(-0.231897\pi\)
−0.203497 + 0.979076i \(0.565231\pi\)
\(164\) 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 −0.207385 0.978259i \(-0.566495\pi\)
0.743505 + 0.668730i \(0.233162\pi\)
\(168\) 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 −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 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 0.931038 0.364922i \(-0.118904\pi\)
−0.781551 + 0.623841i \(0.785571\pi\)
\(180\) 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 −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) −3.50000 6.06218i −0.252591 0.437500i
\(193\) −15.5885 + 9.00000i −1.12208 + 0.647834i −0.941932 0.335805i \(-0.890992\pi\)
−0.180150 + 0.983639i \(0.557658\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) −9.00000 −0.642857
\(197\) 15.5885 9.00000i 1.11063 0.641223i 0.171639 0.985160i \(-0.445094\pi\)
0.938993 + 0.343937i \(0.111761\pi\)
\(198\) −2.00000 3.46410i −0.142134 0.246183i
\(199\) 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) 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 0.972346 + 0.233544i \(0.0750324\pi\)
−0.283918 + 0.958849i \(0.591634\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) −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 −0.379509 0.925188i \(-0.623907\pi\)
0.611482 + 0.791258i \(0.290574\pi\)
\(224\) 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 0.948790 0.315906i \(-0.102309\pi\)
0.200812 + 0.979630i \(0.435642\pi\)
\(228\) 0 0
\(229\) 10.0000i 0.660819i 0.943838 + 0.330409i \(0.107187\pi\)
−0.943838 + 0.330409i \(0.892813\pi\)
\(230\) 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 \(-0.717137\pi\)
0.630468 0.776215i \(-0.282863\pi\)
\(240\) −1.73205 1.00000i −0.111803 0.0645497i
\(241\) 8.66025 + 5.00000i 0.557856 + 0.322078i 0.752285 0.658838i \(-0.228952\pi\)
−0.194429 + 0.980917i \(0.562285\pi\)
\(242\) 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 −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) 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 0.912222 + 0.409695i \(0.134365\pi\)
−0.101305 + 0.994855i \(0.532302\pi\)
\(258\) −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 −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 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 0.307029 + 0.951700i \(0.400665\pi\)
−0.977711 + 0.209955i \(0.932668\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) 10.3923 6.00000i 0.631288 0.364474i −0.149963 0.988692i \(-0.547915\pi\)
0.781251 + 0.624218i \(0.214582\pi\)
\(272\) 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 −0.976231 0.216731i \(-0.930460\pi\)
0.675810 + 0.737075i \(0.263794\pi\)
\(278\) 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 \(0.0964112\pi\)
−0.954480 + 0.298275i \(0.903589\pi\)
\(282\) 0 0
\(283\) 6.00000 + 10.3923i 0.356663 + 0.617758i 0.987401 0.158237i \(-0.0505811\pi\)
−0.630738 + 0.775996i \(0.717248\pi\)
\(284\) 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 0.340480 0.940252i \(-0.389411\pi\)
−0.644042 + 0.764990i \(0.722744\pi\)
\(294\) 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 \(0.150927\pi\)
−0.889680 + 0.456584i \(0.849073\pi\)
\(308\) −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 \(0.260551\pi\)
−0.683284 + 0.730153i \(0.739449\pi\)
\(318\) 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 0.829876 0.557948i \(-0.188411\pi\)
−0.0682590 + 0.997668i \(0.521744\pi\)
\(332\) −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 −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) −5.00000 8.66025i −0.268028 0.464238i
\(349\) 22.5167 13.0000i 1.20529 0.695874i 0.243563 0.969885i \(-0.421684\pi\)
0.961727 + 0.274011i \(0.0883505\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) −1.73205 + 1.00000i −0.0921878 + 0.0532246i −0.545385 0.838186i \(-0.683617\pi\)
0.453197 + 0.891410i \(0.350283\pi\)
\(354\) 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 \(-0.781685\pi\)
0.773877 0.633336i \(-0.218315\pi\)
\(360\) 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 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) 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 −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) 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 −0.927534 0.373739i \(-0.878076\pi\)
−0.140100 + 0.990137i \(0.544742\pi\)
\(380\) 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 0.810331 0.585973i \(-0.199287\pi\)
−0.102302 + 0.994753i \(0.532621\pi\)
\(384\) 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 0.976392 + 0.216004i \(0.0693024\pi\)
0.675261 + 0.737579i \(0.264031\pi\)
\(398\) 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 −0.893528 0.449008i \(-0.851777\pi\)
−0.0579116 + 0.998322i \(0.518444\pi\)
\(402\) −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 −0.457146 0.889392i \(-0.651128\pi\)
−0.998809 + 0.0487958i \(0.984462\pi\)
\(410\) 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 0.813029 0.582224i \(-0.197817\pi\)
−0.910735 + 0.412991i \(0.864484\pi\)
\(420\) −4.00000 + 6.92820i −0.195180 + 0.338062i
\(421\) 10.0000i 0.487370i −0.969854 0.243685i \(-0.921644\pi\)
0.969854 0.243685i \(-0.0783563\pi\)
\(422\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 17.0000 29.4449i 0.816968 1.41503i −0.0909384 0.995857i \(-0.528987\pi\)
0.907906 0.419173i \(-0.137680\pi\)
\(434\) 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 0.940963 + 0.338508i \(0.109922\pi\)
−0.177325 + 0.984152i \(0.556744\pi\)
\(440\) 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 0.876923 0.480631i \(-0.159592\pi\)
0.0222229 + 0.999753i \(0.492926\pi\)
\(450\) 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 −0.458942 0.888466i \(-0.651771\pi\)
0.539964 + 0.841688i \(0.318438\pi\)
\(458\) 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 0.999235 + 0.0391109i \(0.0124526\pi\)
0.533488 + 0.845807i \(0.320881\pi\)
\(462\) 13.8564 + 8.00000i 0.644658 + 0.372194i
\(463\) 4.00000i 0.185896i −0.995671 0.0929479i \(-0.970371\pi\)
0.995671 0.0929479i \(-0.0296290\pi\)
\(464\) −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 0.0566937 0.998392i \(-0.481944\pi\)
0.892979 + 0.450098i \(0.148611\pi\)
\(480\) 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 0.245705 0.969345i \(-0.420981\pi\)
−0.716625 + 0.697459i \(0.754314\pi\)
\(488\) 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 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) −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 \(-0.819484\pi\)
0.843459 0.537194i \(-0.180516\pi\)
\(500\) −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 −0.762965 0.646440i \(-0.776257\pi\)
0.941316 + 0.337527i \(0.109590\pi\)
\(504\) 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 −0.295637 0.955300i \(-0.595532\pi\)
0.679496 + 0.733679i \(0.262199\pi\)
\(510\) 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 −0.717486 0.696573i \(-0.754707\pi\)
−0.244507 0.969648i \(-0.578626\pi\)
\(524\) −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 \(-0.776899\pi\)
0.764267 0.644900i \(-0.223101\pi\)
\(542\) 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 −0.792469 0.609912i \(-0.791205\pi\)
0.131965 + 0.991254i \(0.457871\pi\)
\(558\) −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 −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) 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 0.963849 + 0.266450i \(0.0858508\pi\)
−0.251172 + 0.967943i \(0.580816\pi\)
\(570\) 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 \(-0.593132\pi\)
0.288425 0.957503i \(-0.406868\pi\)
\(578\) 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 0.0923513 0.995726i \(-0.470562\pi\)
0.908500 + 0.417885i \(0.137228\pi\)
\(588\) −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 \(0.179254\pi\)
−0.845582 + 0.533846i \(0.820746\pi\)
\(594\) 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 0.934780 + 0.355228i \(0.115597\pi\)
−0.159754 + 0.987157i \(0.551070\pi\)
\(602\) 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 −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) 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 −0.534570 0.845124i \(-0.679527\pi\)
0.464614 + 0.885514i \(0.346193\pi\)
\(614\) 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 0.0647859 0.997899i \(-0.479364\pi\)
−0.831813 + 0.555056i \(0.812697\pi\)
\(618\) 0 0
\(619\) 24.0000i 0.964641i −0.875995 0.482321i \(-0.839794\pi\)
0.875995 0.482321i \(-0.160206\pi\)
\(620\) 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 0.803432 0.595397i \(-0.203005\pi\)
−0.113913 + 0.993491i \(0.536339\pi\)
\(632\) 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 −0.845601 0.533816i \(-0.820758\pi\)
0.885098 + 0.465404i \(0.154091\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 34.6410 + 20.0000i 1.36611 + 0.788723i 0.990429 0.138027i \(-0.0440759\pi\)
0.375680 + 0.926750i \(0.377409\pi\)
\(644\) 0 0
\(645\) 24.0000i 0.944999i
\(646\) 0 0
\(647\) −4.00000 6.92820i −0.157256 0.272376i 0.776622 0.629967i \(-0.216932\pi\)
−0.933878 + 0.357591i \(0.883598\pi\)
\(648\) 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 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 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 0.453221 + 0.891398i \(0.350275\pi\)
−0.998584 + 0.0531977i \(0.983059\pi\)
\(660\) 4.00000 + 6.92820i 0.155700 + 0.269680i
\(661\) −25.9808 + 15.0000i −1.01053 + 0.583432i −0.911348 0.411636i \(-0.864957\pi\)
−0.0991864 + 0.995069i \(0.531624\pi\)
\(662\) 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 0.698988 0.715134i \(-0.253634\pi\)
−0.968818 + 0.247774i \(0.920301\pi\)
\(674\) −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 0.287819 0.957685i \(-0.407070\pi\)
−0.685470 + 0.728101i \(0.740403\pi\)
\(684\) 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 −0.840203 0.542272i \(-0.817564\pi\)
0.0495194 + 0.998773i \(0.484231\pi\)
\(692\) 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 0.0135434 0.999908i \(-0.495689\pi\)
−0.859174 + 0.511683i \(0.829022\pi\)
\(710\) 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 −0.998224 0.0595683i \(-0.981028\pi\)
0.550700 + 0.834703i \(0.314361\pi\)
\(720\) 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 \(0.186914\pi\)
−0.832492 + 0.554038i \(0.813086\pi\)
\(734\) −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 −0.913939 0.405851i \(-0.866975\pi\)
−0.105493 + 0.994420i \(0.533642\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) −24.0000 −0.881068
\(743\) 41.5692 24.0000i 1.52503 0.880475i 0.525467 0.850814i \(-0.323891\pi\)
0.999560 0.0296605i \(-0.00944260\pi\)
\(744\) −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 0.929731 0.368238i \(-0.120039\pi\)
−0.783769 + 0.621052i \(0.786706\pi\)
\(752\) 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 0.593899 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
\(761\) −8.66025 5.00000i −0.313934 0.181250i 0.334752 0.942306i \(-0.391348\pi\)
−0.648686 + 0.761057i \(0.724681\pi\)
\(762\) 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 −0.888984 0.457938i \(-0.848588\pi\)
−0.0479061 + 0.998852i \(0.515255\pi\)
\(770\) 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 0.336104 0.941825i \(-0.390891\pi\)
−0.647592 + 0.761987i \(0.724224\pi\)
\(774\) −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 0.309492i