Properties

Label 390.2.s.a.77.3
Level $390$
Weight $2$
Character 390.77
Analytic conductor $3.114$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.s (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.40960000.1
Defining polynomial: \( x^{8} + 7x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.3
Root \(1.14412 + 1.14412i\) of defining polynomial
Character \(\chi\) \(=\) 390.77
Dual form 390.2.s.a.233.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.618034 - 1.61803i) q^{3} +1.00000i q^{4} +(0.707107 + 2.12132i) q^{5} +(0.707107 - 1.58114i) q^{6} +(-3.16228 + 3.16228i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.618034 - 1.61803i) q^{3} +1.00000i q^{4} +(0.707107 + 2.12132i) q^{5} +(0.707107 - 1.58114i) q^{6} +(-3.16228 + 3.16228i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.23607 + 2.00000i) q^{9} +(-1.00000 + 2.00000i) q^{10} -5.65685 q^{11} +(1.61803 - 0.618034i) q^{12} +(3.58114 - 0.418861i) q^{13} -4.47214 q^{14} +(2.99535 - 2.45517i) q^{15} -1.00000 q^{16} +(-2.23607 + 2.23607i) q^{17} +(-2.99535 - 0.166925i) q^{18} +6.32456 q^{19} +(-2.12132 + 0.707107i) q^{20} +(7.07107 + 3.16228i) q^{21} +(-4.00000 - 4.00000i) q^{22} +(1.58114 + 0.707107i) q^{24} +(-4.00000 + 3.00000i) q^{25} +(2.82843 + 2.23607i) q^{26} +(4.61803 + 2.38197i) q^{27} +(-3.16228 - 3.16228i) q^{28} +4.47214 q^{29} +(3.85410 + 0.381966i) q^{30} -3.16228i q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.49613 + 9.15298i) q^{33} -3.16228 q^{34} +(-8.94427 - 4.47214i) q^{35} +(-2.00000 - 2.23607i) q^{36} +(-3.16228 + 3.16228i) q^{37} +(4.47214 + 4.47214i) q^{38} +(-2.89100 - 5.53553i) q^{39} +(-2.00000 - 1.00000i) q^{40} +5.65685 q^{41} +(2.76393 + 7.23607i) q^{42} +(-5.00000 + 5.00000i) q^{43} -5.65685i q^{44} +(-5.82378 - 3.32920i) q^{45} +(1.41421 + 1.41421i) q^{47} +(0.618034 + 1.61803i) q^{48} -13.0000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(5.00000 + 2.23607i) q^{51} +(0.418861 + 3.58114i) q^{52} +(4.47214 + 4.47214i) q^{53} +(1.58114 + 4.94975i) q^{54} +(-4.00000 - 12.0000i) q^{55} -4.47214i q^{56} +(-3.90879 - 10.2333i) q^{57} +(3.16228 + 3.16228i) q^{58} -2.82843i q^{59} +(2.45517 + 2.99535i) q^{60} +10.0000 q^{61} +(2.23607 - 2.23607i) q^{62} +(0.746512 - 13.3956i) q^{63} -1.00000i q^{64} +(3.42079 + 7.30056i) q^{65} +(-4.00000 + 8.94427i) q^{66} +(-2.23607 - 2.23607i) q^{68} +(-3.16228 - 9.48683i) q^{70} -1.41421 q^{71} +(0.166925 - 2.99535i) q^{72} +(-3.16228 - 3.16228i) q^{73} -4.47214 q^{74} +(7.32624 + 4.61803i) q^{75} +6.32456i q^{76} +(17.8885 - 17.8885i) q^{77} +(1.86997 - 5.95846i) q^{78} +(-0.707107 - 2.12132i) q^{80} +(1.00000 - 8.94427i) q^{81} +(4.00000 + 4.00000i) q^{82} +(-2.82843 + 2.82843i) q^{83} +(-3.16228 + 7.07107i) q^{84} +(-6.32456 - 3.16228i) q^{85} -7.07107 q^{86} +(-2.76393 - 7.23607i) q^{87} +(4.00000 - 4.00000i) q^{88} +2.82843i q^{89} +(-1.76393 - 6.47214i) q^{90} +(-10.0000 + 12.6491i) q^{91} +(-5.11667 + 1.95440i) q^{93} +2.00000i q^{94} +(4.47214 + 13.4164i) q^{95} +(-0.707107 + 1.58114i) q^{96} +(-9.48683 + 9.48683i) q^{97} +(9.19239 - 9.19239i) q^{98} +(12.6491 - 11.3137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} - 8 q^{10} + 4 q^{12} + 16 q^{13} - 8 q^{16} - 32 q^{22} - 32 q^{25} + 28 q^{27} + 4 q^{30} - 16 q^{36} - 16 q^{40} + 40 q^{42} - 40 q^{43} - 4 q^{48} + 40 q^{51} + 16 q^{52} - 32 q^{55} + 80 q^{61} - 32 q^{66} - 4 q^{75} + 20 q^{78} + 8 q^{81} + 32 q^{82} - 40 q^{87} + 32 q^{88} - 32 q^{90} - 80 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −0.618034 1.61803i −0.356822 0.934172i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 + 2.12132i 0.316228 + 0.948683i
\(6\) 0.707107 1.58114i 0.288675 0.645497i
\(7\) −3.16228 + 3.16228i −1.19523 + 1.19523i −0.219650 + 0.975579i \(0.570491\pi\)
−0.975579 + 0.219650i \(0.929509\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −2.23607 + 2.00000i −0.745356 + 0.666667i
\(10\) −1.00000 + 2.00000i −0.316228 + 0.632456i
\(11\) −5.65685 −1.70561 −0.852803 0.522233i \(-0.825099\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) 1.61803 0.618034i 0.467086 0.178411i
\(13\) 3.58114 0.418861i 0.993229 0.116171i
\(14\) −4.47214 −1.19523
\(15\) 2.99535 2.45517i 0.773397 0.633922i
\(16\) −1.00000 −0.250000
\(17\) −2.23607 + 2.23607i −0.542326 + 0.542326i −0.924210 0.381884i \(-0.875275\pi\)
0.381884 + 0.924210i \(0.375275\pi\)
\(18\) −2.99535 0.166925i −0.706011 0.0393447i
\(19\) 6.32456 1.45095 0.725476 0.688247i \(-0.241620\pi\)
0.725476 + 0.688247i \(0.241620\pi\)
\(20\) −2.12132 + 0.707107i −0.474342 + 0.158114i
\(21\) 7.07107 + 3.16228i 1.54303 + 0.690066i
\(22\) −4.00000 4.00000i −0.852803 0.852803i
\(23\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(24\) 1.58114 + 0.707107i 0.322749 + 0.144338i
\(25\) −4.00000 + 3.00000i −0.800000 + 0.600000i
\(26\) 2.82843 + 2.23607i 0.554700 + 0.438529i
\(27\) 4.61803 + 2.38197i 0.888741 + 0.458410i
\(28\) −3.16228 3.16228i −0.597614 0.597614i
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) 3.85410 + 0.381966i 0.703660 + 0.0697371i
\(31\) 3.16228i 0.567962i −0.958830 0.283981i \(-0.908345\pi\)
0.958830 0.283981i \(-0.0916552\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 3.49613 + 9.15298i 0.608598 + 1.59333i
\(34\) −3.16228 −0.542326
\(35\) −8.94427 4.47214i −1.51186 0.755929i
\(36\) −2.00000 2.23607i −0.333333 0.372678i
\(37\) −3.16228 + 3.16228i −0.519875 + 0.519875i −0.917534 0.397658i \(-0.869823\pi\)
0.397658 + 0.917534i \(0.369823\pi\)
\(38\) 4.47214 + 4.47214i 0.725476 + 0.725476i
\(39\) −2.89100 5.53553i −0.462930 0.886395i
\(40\) −2.00000 1.00000i −0.316228 0.158114i
\(41\) 5.65685 0.883452 0.441726 0.897150i \(-0.354366\pi\)
0.441726 + 0.897150i \(0.354366\pi\)
\(42\) 2.76393 + 7.23607i 0.426484 + 1.11655i
\(43\) −5.00000 + 5.00000i −0.762493 + 0.762493i −0.976772 0.214280i \(-0.931260\pi\)
0.214280 + 0.976772i \(0.431260\pi\)
\(44\) 5.65685i 0.852803i
\(45\) −5.82378 3.32920i −0.868158 0.496288i
\(46\) 0 0
\(47\) 1.41421 + 1.41421i 0.206284 + 0.206284i 0.802686 0.596402i \(-0.203403\pi\)
−0.596402 + 0.802686i \(0.703403\pi\)
\(48\) 0.618034 + 1.61803i 0.0892055 + 0.233543i
\(49\) 13.0000i 1.85714i
\(50\) −4.94975 0.707107i −0.700000 0.100000i
\(51\) 5.00000 + 2.23607i 0.700140 + 0.313112i
\(52\) 0.418861 + 3.58114i 0.0580856 + 0.496615i
\(53\) 4.47214 + 4.47214i 0.614295 + 0.614295i 0.944062 0.329767i \(-0.106970\pi\)
−0.329767 + 0.944062i \(0.606970\pi\)
\(54\) 1.58114 + 4.94975i 0.215166 + 0.673575i
\(55\) −4.00000 12.0000i −0.539360 1.61808i
\(56\) 4.47214i 0.597614i
\(57\) −3.90879 10.2333i −0.517732 1.35544i
\(58\) 3.16228 + 3.16228i 0.415227 + 0.415227i
\(59\) 2.82843i 0.368230i −0.982905 0.184115i \(-0.941058\pi\)
0.982905 0.184115i \(-0.0589419\pi\)
\(60\) 2.45517 + 2.99535i 0.316961 + 0.386698i
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 2.23607 2.23607i 0.283981 0.283981i
\(63\) 0.746512 13.3956i 0.0940517 1.68769i
\(64\) 1.00000i 0.125000i
\(65\) 3.42079 + 7.30056i 0.424296 + 0.905523i
\(66\) −4.00000 + 8.94427i −0.492366 + 1.10096i
\(67\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) −2.23607 2.23607i −0.271163 0.271163i
\(69\) 0 0
\(70\) −3.16228 9.48683i −0.377964 1.13389i
\(71\) −1.41421 −0.167836 −0.0839181 0.996473i \(-0.526743\pi\)
−0.0839181 + 0.996473i \(0.526743\pi\)
\(72\) 0.166925 2.99535i 0.0196723 0.353006i
\(73\) −3.16228 3.16228i −0.370117 0.370117i 0.497403 0.867520i \(-0.334287\pi\)
−0.867520 + 0.497403i \(0.834287\pi\)
\(74\) −4.47214 −0.519875
\(75\) 7.32624 + 4.61803i 0.845961 + 0.533245i
\(76\) 6.32456i 0.725476i
\(77\) 17.8885 17.8885i 2.03859 2.03859i
\(78\) 1.86997 5.95846i 0.211732 0.674662i
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.707107 2.12132i −0.0790569 0.237171i
\(81\) 1.00000 8.94427i 0.111111 0.993808i
\(82\) 4.00000 + 4.00000i 0.441726 + 0.441726i
\(83\) −2.82843 + 2.82843i −0.310460 + 0.310460i −0.845088 0.534628i \(-0.820452\pi\)
0.534628 + 0.845088i \(0.320452\pi\)
\(84\) −3.16228 + 7.07107i −0.345033 + 0.771517i
\(85\) −6.32456 3.16228i −0.685994 0.342997i
\(86\) −7.07107 −0.762493
\(87\) −2.76393 7.23607i −0.296325 0.775788i
\(88\) 4.00000 4.00000i 0.426401 0.426401i
\(89\) 2.82843i 0.299813i 0.988700 + 0.149906i \(0.0478972\pi\)
−0.988700 + 0.149906i \(0.952103\pi\)
\(90\) −1.76393 6.47214i −0.185935 0.682223i
\(91\) −10.0000 + 12.6491i −1.04828 + 1.32599i
\(92\) 0 0
\(93\) −5.11667 + 1.95440i −0.530574 + 0.202661i
\(94\) 2.00000i 0.206284i
\(95\) 4.47214 + 13.4164i 0.458831 + 1.37649i
\(96\) −0.707107 + 1.58114i −0.0721688 + 0.161374i
\(97\) −9.48683 + 9.48683i −0.963242 + 0.963242i −0.999348 0.0361060i \(-0.988505\pi\)
0.0361060 + 0.999348i \(0.488505\pi\)
\(98\) 9.19239 9.19239i 0.928571 0.928571i
\(99\) 12.6491 11.3137i 1.27128 1.13707i
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 4.47214i 0.444994i −0.974933 0.222497i \(-0.928579\pi\)
0.974933 0.222497i \(-0.0714208\pi\)
\(102\) 1.95440 + 5.11667i 0.193514 + 0.506626i
\(103\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(104\) −2.23607 + 2.82843i −0.219265 + 0.277350i
\(105\) −1.70820 + 17.2361i −0.166704 + 1.68207i
\(106\) 6.32456i 0.614295i
\(107\) 2.23607 2.23607i 0.216169 0.216169i −0.590713 0.806882i \(-0.701153\pi\)
0.806882 + 0.590713i \(0.201153\pi\)
\(108\) −2.38197 + 4.61803i −0.229205 + 0.444371i
\(109\) −3.16228 −0.302891 −0.151446 0.988466i \(-0.548393\pi\)
−0.151446 + 0.988466i \(0.548393\pi\)
\(110\) 5.65685 11.3137i 0.539360 1.07872i
\(111\) 7.07107 + 3.16228i 0.671156 + 0.300150i
\(112\) 3.16228 3.16228i 0.298807 0.298807i
\(113\) 6.70820 + 6.70820i 0.631055 + 0.631055i 0.948333 0.317278i \(-0.102769\pi\)
−0.317278 + 0.948333i \(0.602769\pi\)
\(114\) 4.47214 10.0000i 0.418854 0.936586i
\(115\) 0 0
\(116\) 4.47214i 0.415227i
\(117\) −7.16995 + 8.09888i −0.662862 + 0.748742i
\(118\) 2.00000 2.00000i 0.184115 0.184115i
\(119\) 14.1421i 1.29641i
\(120\) −0.381966 + 3.85410i −0.0348686 + 0.351830i
\(121\) 21.0000 1.90909
\(122\) 7.07107 + 7.07107i 0.640184 + 0.640184i
\(123\) −3.49613 9.15298i −0.315235 0.825297i
\(124\) 3.16228 0.283981
\(125\) −9.19239 6.36396i −0.822192 0.569210i
\(126\) 10.0000 8.94427i 0.890871 0.796819i
\(127\) −2.00000 2.00000i −0.177471 0.177471i 0.612781 0.790253i \(-0.290051\pi\)
−0.790253 + 0.612781i \(0.790051\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 11.1803 + 5.00000i 0.984374 + 0.440225i
\(130\) −2.74342 + 7.58114i −0.240614 + 0.664910i
\(131\) 17.8885i 1.56293i 0.623949 + 0.781465i \(0.285527\pi\)
−0.623949 + 0.781465i \(0.714473\pi\)
\(132\) −9.15298 + 3.49613i −0.796665 + 0.304299i
\(133\) −20.0000 + 20.0000i −1.73422 + 1.73422i
\(134\) 0 0
\(135\) −1.78747 + 11.4806i −0.153841 + 0.988096i
\(136\) 3.16228i 0.271163i
\(137\) 12.7279 + 12.7279i 1.08742 + 1.08742i 0.995793 + 0.0916263i \(0.0292065\pi\)
0.0916263 + 0.995793i \(0.470793\pi\)
\(138\) 0 0
\(139\) 4.00000i 0.339276i −0.985506 0.169638i \(-0.945740\pi\)
0.985506 0.169638i \(-0.0542598\pi\)
\(140\) 4.47214 8.94427i 0.377964 0.755929i
\(141\) 1.41421 3.16228i 0.119098 0.266312i
\(142\) −1.00000 1.00000i −0.0839181 0.0839181i
\(143\) −20.2580 + 2.36944i −1.69406 + 0.198142i
\(144\) 2.23607 2.00000i 0.186339 0.166667i
\(145\) 3.16228 + 9.48683i 0.262613 + 0.787839i
\(146\) 4.47214i 0.370117i
\(147\) −21.0344 + 8.03444i −1.73489 + 0.662670i
\(148\) −3.16228 3.16228i −0.259938 0.259938i
\(149\) 4.24264i 0.347571i 0.984784 + 0.173785i \(0.0555999\pi\)
−0.984784 + 0.173785i \(0.944400\pi\)
\(150\) 1.91499 + 8.44588i 0.156358 + 0.689603i
\(151\) 22.1359i 1.80140i −0.434444 0.900699i \(-0.643055\pi\)
0.434444 0.900699i \(-0.356945\pi\)
\(152\) −4.47214 + 4.47214i −0.362738 + 0.362738i
\(153\) 0.527864 9.47214i 0.0426753 0.765777i
\(154\) 25.2982 2.03859
\(155\) 6.70820 2.23607i 0.538816 0.179605i
\(156\) 5.53553 2.89100i 0.443197 0.231465i
\(157\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) 0 0
\(159\) 4.47214 10.0000i 0.354663 0.793052i
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) 0 0
\(162\) 7.03166 5.61745i 0.552460 0.441348i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 5.65685i 0.441726i
\(165\) −16.9443 + 13.8885i −1.31911 + 1.08122i
\(166\) −4.00000 −0.310460
\(167\) 12.7279 + 12.7279i 0.984916 + 0.984916i 0.999888 0.0149717i \(-0.00476583\pi\)
−0.0149717 + 0.999888i \(0.504766\pi\)
\(168\) −7.23607 + 2.76393i −0.558275 + 0.213242i
\(169\) 12.6491 3.00000i 0.973009 0.230769i
\(170\) −2.23607 6.70820i −0.171499 0.514496i
\(171\) −14.1421 + 12.6491i −1.08148 + 0.967302i
\(172\) −5.00000 5.00000i −0.381246 0.381246i
\(173\) −13.4164 13.4164i −1.02003 1.02003i −0.999795 0.0202354i \(-0.993558\pi\)
−0.0202354 0.999795i \(-0.506442\pi\)
\(174\) 3.16228 7.07107i 0.239732 0.536056i
\(175\) 3.16228 22.1359i 0.239046 1.67332i
\(176\) 5.65685 0.426401
\(177\) −4.57649 + 1.74806i −0.343990 + 0.131393i
\(178\) −2.00000 + 2.00000i −0.149906 + 0.149906i
\(179\) 17.8885 1.33705 0.668526 0.743689i \(-0.266925\pi\)
0.668526 + 0.743689i \(0.266925\pi\)
\(180\) 3.32920 5.82378i 0.248144 0.434079i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −16.0153 + 1.87320i −1.18714 + 0.138851i
\(183\) −6.18034 16.1803i −0.456864 1.19609i
\(184\) 0 0
\(185\) −8.94427 4.47214i −0.657596 0.328798i
\(186\) −5.00000 2.23607i −0.366618 0.163956i
\(187\) 12.6491 12.6491i 0.924995 0.924995i
\(188\) −1.41421 + 1.41421i −0.103142 + 0.103142i
\(189\) −22.1359 + 7.07107i −1.61015 + 0.514344i
\(190\) −6.32456 + 12.6491i −0.458831 + 0.917663i
\(191\) 8.94427i 0.647185i −0.946197 0.323592i \(-0.895109\pi\)
0.946197 0.323592i \(-0.104891\pi\)
\(192\) −1.61803 + 0.618034i −0.116772 + 0.0446028i
\(193\) −9.48683 9.48683i −0.682877 0.682877i 0.277770 0.960648i \(-0.410405\pi\)
−0.960648 + 0.277770i \(0.910405\pi\)
\(194\) −13.4164 −0.963242
\(195\) 9.69840 10.0469i 0.694517 0.719477i
\(196\) 13.0000 0.928571
\(197\) 1.41421 + 1.41421i 0.100759 + 0.100759i 0.755689 0.654931i \(-0.227302\pi\)
−0.654931 + 0.755689i \(0.727302\pi\)
\(198\) 16.9443 + 0.944272i 1.20418 + 0.0671065i
\(199\) 20.0000i 1.41776i 0.705328 + 0.708881i \(0.250800\pi\)
−0.705328 + 0.708881i \(0.749200\pi\)
\(200\) 0.707107 4.94975i 0.0500000 0.350000i
\(201\) 0 0
\(202\) 3.16228 3.16228i 0.222497 0.222497i
\(203\) −14.1421 + 14.1421i −0.992583 + 0.992583i
\(204\) −2.23607 + 5.00000i −0.156556 + 0.350070i
\(205\) 4.00000 + 12.0000i 0.279372 + 0.838116i
\(206\) 0 0
\(207\) 0 0
\(208\) −3.58114 + 0.418861i −0.248307 + 0.0290428i
\(209\) −35.7771 −2.47475
\(210\) −13.3956 + 10.9799i −0.924386 + 0.757682i
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −4.47214 + 4.47214i −0.307148 + 0.307148i
\(213\) 0.874032 + 2.28825i 0.0598877 + 0.156788i
\(214\) 3.16228 0.216169
\(215\) −14.1421 7.07107i −0.964486 0.482243i
\(216\) −4.94975 + 1.58114i −0.336788 + 0.107583i
\(217\) 10.0000 + 10.0000i 0.678844 + 0.678844i
\(218\) −2.23607 2.23607i −0.151446 0.151446i
\(219\) −3.16228 + 7.07107i −0.213687 + 0.477818i
\(220\) 12.0000 4.00000i 0.809040 0.269680i
\(221\) −7.07107 + 8.94427i −0.475651 + 0.601657i
\(222\) 2.76393 + 7.23607i 0.185503 + 0.485653i
\(223\) 18.9737 + 18.9737i 1.27057 + 1.27057i 0.945789 + 0.324782i \(0.105291\pi\)
0.324782 + 0.945789i \(0.394709\pi\)
\(224\) 4.47214 0.298807
\(225\) 2.94427 14.7082i 0.196285 0.980547i
\(226\) 9.48683i 0.631055i
\(227\) −8.48528 8.48528i −0.563188 0.563188i 0.367024 0.930212i \(-0.380377\pi\)
−0.930212 + 0.367024i \(0.880377\pi\)
\(228\) 10.2333 3.90879i 0.677720 0.258866i
\(229\) −9.48683 −0.626908 −0.313454 0.949603i \(-0.601486\pi\)
−0.313454 + 0.949603i \(0.601486\pi\)
\(230\) 0 0
\(231\) −40.0000 17.8885i −2.63181 1.17698i
\(232\) −3.16228 + 3.16228i −0.207614 + 0.207614i
\(233\) −2.23607 2.23607i −0.146490 0.146490i 0.630058 0.776548i \(-0.283031\pi\)
−0.776548 + 0.630058i \(0.783031\pi\)
\(234\) −10.7967 + 0.656854i −0.705802 + 0.0429399i
\(235\) −2.00000 + 4.00000i −0.130466 + 0.260931i
\(236\) 2.82843 0.184115
\(237\) 0 0
\(238\) 10.0000 10.0000i 0.648204 0.648204i
\(239\) 4.24264i 0.274434i 0.990541 + 0.137217i \(0.0438157\pi\)
−0.990541 + 0.137217i \(0.956184\pi\)
\(240\) −2.99535 + 2.45517i −0.193349 + 0.158481i
\(241\) 12.6491i 0.814801i 0.913250 + 0.407400i \(0.133565\pi\)
−0.913250 + 0.407400i \(0.866435\pi\)
\(242\) 14.8492 + 14.8492i 0.954545 + 0.954545i
\(243\) −15.0902 + 3.90983i −0.968035 + 0.250816i
\(244\) 10.0000i 0.640184i
\(245\) 27.5772 9.19239i 1.76184 0.587280i
\(246\) 4.00000 8.94427i 0.255031 0.570266i
\(247\) 22.6491 2.64911i 1.44113 0.168559i
\(248\) 2.23607 + 2.23607i 0.141990 + 0.141990i
\(249\) 6.32456 + 2.82843i 0.400802 + 0.179244i
\(250\) −2.00000 11.0000i −0.126491 0.695701i
\(251\) 17.8885i 1.12911i 0.825394 + 0.564557i \(0.190953\pi\)
−0.825394 + 0.564557i \(0.809047\pi\)
\(252\) 13.3956 + 0.746512i 0.843845 + 0.0470259i
\(253\) 0 0
\(254\) 2.82843i 0.177471i
\(255\) −1.20788 + 12.1877i −0.0756405 + 0.763226i
\(256\) 1.00000 0.0625000
\(257\) 20.1246 20.1246i 1.25534 1.25534i 0.302045 0.953294i \(-0.402331\pi\)
0.953294 0.302045i \(-0.0976694\pi\)
\(258\) 4.37016 + 11.4412i 0.272074 + 0.712300i
\(259\) 20.0000i 1.24274i
\(260\) −7.30056 + 3.42079i −0.452762 + 0.212148i
\(261\) −10.0000 + 8.94427i −0.618984 + 0.553637i
\(262\) −12.6491 + 12.6491i −0.781465 + 0.781465i
\(263\) 8.94427 + 8.94427i 0.551527 + 0.551527i 0.926882 0.375354i \(-0.122479\pi\)
−0.375354 + 0.926882i \(0.622479\pi\)
\(264\) −8.94427 4.00000i −0.550482 0.246183i
\(265\) −6.32456 + 12.6491i −0.388514 + 0.777029i
\(266\) −28.2843 −1.73422
\(267\) 4.57649 1.74806i 0.280077 0.106980i
\(268\) 0 0
\(269\) 22.3607 1.36335 0.681677 0.731653i \(-0.261251\pi\)
0.681677 + 0.731653i \(0.261251\pi\)
\(270\) −9.38197 + 6.85410i −0.570968 + 0.417127i
\(271\) 9.48683i 0.576284i −0.957588 0.288142i \(-0.906962\pi\)
0.957588 0.288142i \(-0.0930375\pi\)
\(272\) 2.23607 2.23607i 0.135582 0.135582i
\(273\) 26.6470 + 8.36276i 1.61275 + 0.506137i
\(274\) 18.0000i 1.08742i
\(275\) 22.6274 16.9706i 1.36448 1.02336i
\(276\) 0 0
\(277\) 10.0000 + 10.0000i 0.600842 + 0.600842i 0.940536 0.339694i \(-0.110324\pi\)
−0.339694 + 0.940536i \(0.610324\pi\)
\(278\) 2.82843 2.82843i 0.169638 0.169638i
\(279\) 6.32456 + 7.07107i 0.378641 + 0.423334i
\(280\) 9.48683 3.16228i 0.566947 0.188982i
\(281\) 8.48528 0.506189 0.253095 0.967442i \(-0.418552\pi\)
0.253095 + 0.967442i \(0.418552\pi\)
\(282\) 3.23607 1.23607i 0.192705 0.0736068i
\(283\) 9.00000 9.00000i 0.534994 0.534994i −0.387060 0.922055i \(-0.626509\pi\)
0.922055 + 0.387060i \(0.126509\pi\)
\(284\) 1.41421i 0.0839181i
\(285\) 18.9443 15.5279i 1.12216 0.919791i
\(286\) −16.0000 12.6491i −0.946100 0.747958i
\(287\) −17.8885 + 17.8885i −1.05593 + 1.05593i
\(288\) 2.99535 + 0.166925i 0.176503 + 0.00983617i
\(289\) 7.00000i 0.411765i
\(290\) −4.47214 + 8.94427i −0.262613 + 0.525226i
\(291\) 21.2132 + 9.48683i 1.24354 + 0.556128i
\(292\) 3.16228 3.16228i 0.185058 0.185058i
\(293\) −11.3137 + 11.3137i −0.660954 + 0.660954i −0.955605 0.294651i \(-0.904797\pi\)
0.294651 + 0.955605i \(0.404797\pi\)
\(294\) −20.5548 9.19239i −1.19878 0.536111i
\(295\) 6.00000 2.00000i 0.349334 0.116445i
\(296\) 4.47214i 0.259938i
\(297\) −26.1235 13.4744i −1.51584 0.781866i
\(298\) −3.00000 + 3.00000i −0.173785 + 0.173785i
\(299\) 0 0
\(300\) −4.61803 + 7.32624i −0.266622 + 0.422981i
\(301\) 31.6228i 1.82271i
\(302\) 15.6525 15.6525i 0.900699 0.900699i
\(303\) −7.23607 + 2.76393i −0.415701 + 0.158784i
\(304\) −6.32456 −0.362738
\(305\) 7.07107 + 21.2132i 0.404888 + 1.21466i
\(306\) 7.07107 6.32456i 0.404226 0.361551i
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 17.8885 + 17.8885i 1.01929 + 1.01929i
\(309\) 0 0
\(310\) 6.32456 + 3.16228i 0.359211 + 0.179605i
\(311\) 8.94427i 0.507183i −0.967311 0.253592i \(-0.918388\pi\)
0.967311 0.253592i \(-0.0816119\pi\)
\(312\) 5.95846 + 1.86997i 0.337331 + 0.105866i
\(313\) −1.00000 + 1.00000i −0.0565233 + 0.0565233i −0.734803 0.678280i \(-0.762726\pi\)
0.678280 + 0.734803i \(0.262726\pi\)
\(314\) 0 0
\(315\) 28.9443 7.88854i 1.63082 0.444469i
\(316\) 0 0
\(317\) −19.7990 19.7990i −1.11202 1.11202i −0.992877 0.119145i \(-0.961985\pi\)
−0.119145 0.992877i \(-0.538015\pi\)
\(318\) 10.2333 3.90879i 0.573858 0.219194i
\(319\) −25.2982 −1.41643
\(320\) 2.12132 0.707107i 0.118585 0.0395285i
\(321\) −5.00000 2.23607i −0.279073 0.124805i
\(322\) 0 0
\(323\) −14.1421 + 14.1421i −0.786889 + 0.786889i
\(324\) 8.94427 + 1.00000i 0.496904 + 0.0555556i
\(325\) −13.0680 + 12.4189i −0.724881 + 0.688874i
\(326\) 0 0
\(327\) 1.95440 + 5.11667i 0.108078 + 0.282953i
\(328\) −4.00000 + 4.00000i −0.220863 + 0.220863i
\(329\) −8.94427 −0.493114
\(330\) −21.8021 2.16073i −1.20017 0.118944i
\(331\) 12.6491i 0.695258i 0.937632 + 0.347629i \(0.113013\pi\)
−0.937632 + 0.347629i \(0.886987\pi\)
\(332\) −2.82843 2.82843i −0.155230 0.155230i
\(333\) 0.746512 13.3956i 0.0409086 0.734076i
\(334\) 18.0000i 0.984916i
\(335\) 0 0
\(336\) −7.07107 3.16228i −0.385758 0.172516i
\(337\) −13.0000 13.0000i −0.708155 0.708155i 0.257992 0.966147i \(-0.416939\pi\)
−0.966147 + 0.257992i \(0.916939\pi\)
\(338\) 11.0656 + 6.82295i 0.601889 + 0.371120i
\(339\) 6.70820 15.0000i 0.364340 0.814688i
\(340\) 3.16228 6.32456i 0.171499 0.342997i
\(341\) 17.8885i 0.968719i
\(342\) −18.9443 1.05573i −1.02439 0.0570872i
\(343\) 18.9737 + 18.9737i 1.02448 + 1.02448i
\(344\) 7.07107i 0.381246i
\(345\) 0 0
\(346\) 18.9737i 1.02003i
\(347\) −20.1246 + 20.1246i −1.08035 + 1.08035i −0.0838690 + 0.996477i \(0.526728\pi\)
−0.996477 + 0.0838690i \(0.973272\pi\)
\(348\) 7.23607 2.76393i 0.387894 0.148162i
\(349\) −3.16228 −0.169273 −0.0846364 0.996412i \(-0.526973\pi\)
−0.0846364 + 0.996412i \(0.526973\pi\)
\(350\) 17.8885 13.4164i 0.956183 0.717137i
\(351\) 17.5355 + 6.59584i 0.935978 + 0.352060i
\(352\) 4.00000 + 4.00000i 0.213201 + 0.213201i
\(353\) 9.89949 9.89949i 0.526897 0.526897i −0.392749 0.919646i \(-0.628476\pi\)
0.919646 + 0.392749i \(0.128476\pi\)
\(354\) −4.47214 2.00000i −0.237691 0.106299i
\(355\) −1.00000 3.00000i −0.0530745 0.159223i
\(356\) −2.82843 −0.149906
\(357\) −22.8825 + 8.74032i −1.21107 + 0.462587i
\(358\) 12.6491 + 12.6491i 0.668526 + 0.668526i
\(359\) 32.5269i 1.71670i −0.513061 0.858352i \(-0.671488\pi\)
0.513061 0.858352i \(-0.328512\pi\)
\(360\) 6.47214 1.76393i 0.341112 0.0929674i
\(361\) 21.0000 1.10526
\(362\) −15.5563 15.5563i −0.817624 0.817624i
\(363\) −12.9787 33.9787i −0.681206 1.78342i
\(364\) −12.6491 10.0000i −0.662994 0.524142i
\(365\) 4.47214 8.94427i 0.234082 0.468165i
\(366\) 7.07107 15.8114i 0.369611 0.826475i
\(367\) −20.0000 20.0000i −1.04399 1.04399i −0.998987 0.0450047i \(-0.985670\pi\)
−0.0450047 0.998987i \(-0.514330\pi\)
\(368\) 0 0
\(369\) −12.6491 + 11.3137i −0.658486 + 0.588968i
\(370\) −3.16228 9.48683i −0.164399 0.493197i
\(371\) −28.2843 −1.46845
\(372\) −1.95440 5.11667i −0.101331 0.265287i
\(373\) 16.0000 16.0000i 0.828449 0.828449i −0.158854 0.987302i \(-0.550780\pi\)
0.987302 + 0.158854i \(0.0507798\pi\)
\(374\) 17.8885 0.924995
\(375\) −4.61590 + 18.8067i −0.238364 + 0.971176i
\(376\) −2.00000 −0.103142
\(377\) 16.0153 1.87320i 0.824832 0.0964749i
\(378\) −20.6525 10.6525i −1.06225 0.547904i
\(379\) −6.32456 −0.324871 −0.162435 0.986719i \(-0.551935\pi\)
−0.162435 + 0.986719i \(0.551935\pi\)
\(380\) −13.4164 + 4.47214i −0.688247 + 0.229416i
\(381\) −2.00000 + 4.47214i −0.102463 + 0.229114i
\(382\) 6.32456 6.32456i 0.323592 0.323592i
\(383\) 11.3137 11.3137i 0.578103 0.578103i −0.356277 0.934380i \(-0.615954\pi\)
0.934380 + 0.356277i \(0.115954\pi\)
\(384\) −1.58114 0.707107i −0.0806872 0.0360844i
\(385\) 50.5964 + 25.2982i 2.57863 + 1.28932i
\(386\) 13.4164i 0.682877i
\(387\) 1.18034 21.1803i 0.0600000 1.07666i
\(388\) −9.48683 9.48683i −0.481621 0.481621i
\(389\) −13.4164 −0.680239 −0.340119 0.940382i \(-0.610468\pi\)
−0.340119 + 0.940382i \(0.610468\pi\)
\(390\) 13.9621 0.246460i 0.706997 0.0124800i
\(391\) 0 0
\(392\) 9.19239 + 9.19239i 0.464286 + 0.464286i
\(393\) 28.9443 11.0557i 1.46005 0.557688i
\(394\) 2.00000i 0.100759i
\(395\) 0 0
\(396\) 11.3137 + 12.6491i 0.568535 + 0.635642i
\(397\) 25.2982 25.2982i 1.26968 1.26968i 0.323429 0.946252i \(-0.395164\pi\)
0.946252 0.323429i \(-0.104836\pi\)
\(398\) −14.1421 + 14.1421i −0.708881 + 0.708881i
\(399\) 44.7214 + 20.0000i 2.23887 + 1.00125i
\(400\) 4.00000 3.00000i 0.200000 0.150000i
\(401\) −8.48528 −0.423735 −0.211867 0.977298i \(-0.567954\pi\)
−0.211867 + 0.977298i \(0.567954\pi\)
\(402\) 0 0
\(403\) −1.32456 11.3246i −0.0659808 0.564116i
\(404\) 4.47214 0.222497
\(405\) 19.6808 4.20323i 0.977945 0.208860i
\(406\) −20.0000 −0.992583
\(407\) 17.8885 17.8885i 0.886702 0.886702i
\(408\) −5.11667 + 1.95440i −0.253313 + 0.0967570i
\(409\) −18.9737 −0.938187 −0.469094 0.883148i \(-0.655419\pi\)
−0.469094 + 0.883148i \(0.655419\pi\)
\(410\) −5.65685 + 11.3137i −0.279372 + 0.558744i
\(411\) 12.7279 28.4605i 0.627822 1.40385i
\(412\) 0 0
\(413\) 8.94427 + 8.94427i 0.440119 + 0.440119i
\(414\) 0 0
\(415\) −8.00000 4.00000i −0.392705 0.196352i
\(416\) −2.82843 2.23607i −0.138675 0.109632i
\(417\) −6.47214 + 2.47214i −0.316942 + 0.121061i
\(418\) −25.2982 25.2982i −1.23738 1.23738i
\(419\) 13.4164 0.655434 0.327717 0.944776i \(-0.393721\pi\)
0.327717 + 0.944776i \(0.393721\pi\)
\(420\) −17.2361 1.70820i −0.841034 0.0833518i
\(421\) 3.16228i 0.154120i −0.997026 0.0770600i \(-0.975447\pi\)
0.997026 0.0770600i \(-0.0245533\pi\)
\(422\) 14.1421 + 14.1421i 0.688428 + 0.688428i
\(423\) −5.99070 0.333851i −0.291278 0.0162324i
\(424\) −6.32456 −0.307148
\(425\) 2.23607 15.6525i 0.108465 0.759257i
\(426\) −1.00000 + 2.23607i −0.0484502 + 0.108338i
\(427\) −31.6228 + 31.6228i −1.53033 + 1.53033i
\(428\) 2.23607 + 2.23607i 0.108084 + 0.108084i
\(429\) 16.3539 + 31.3137i 0.789576 + 1.51184i
\(430\) −5.00000 15.0000i −0.241121 0.723364i
\(431\) 1.41421 0.0681203 0.0340601 0.999420i \(-0.489156\pi\)
0.0340601 + 0.999420i \(0.489156\pi\)
\(432\) −4.61803 2.38197i −0.222185 0.114602i
\(433\) 21.0000 21.0000i 1.00920 1.00920i 0.00923827 0.999957i \(-0.497059\pi\)
0.999957 0.00923827i \(-0.00294067\pi\)
\(434\) 14.1421i 0.678844i
\(435\) 13.3956 10.9799i 0.642271 0.526444i
\(436\) 3.16228i 0.151446i
\(437\) 0 0
\(438\) −7.23607 + 2.76393i −0.345753 + 0.132066i
\(439\) 16.0000i 0.763638i 0.924237 + 0.381819i \(0.124702\pi\)
−0.924237 + 0.381819i \(0.875298\pi\)
\(440\) 11.3137 + 5.65685i 0.539360 + 0.269680i
\(441\) 26.0000 + 29.0689i 1.23810 + 1.38423i
\(442\) −11.3246 + 1.32456i −0.538654 + 0.0630027i
\(443\) 11.1803 + 11.1803i 0.531194 + 0.531194i 0.920928 0.389734i \(-0.127433\pi\)
−0.389734 + 0.920928i \(0.627433\pi\)
\(444\) −3.16228 + 7.07107i −0.150075 + 0.335578i
\(445\) −6.00000 + 2.00000i −0.284427 + 0.0948091i
\(446\) 26.8328i 1.27057i
\(447\) 6.86474 2.62210i 0.324691 0.124021i
\(448\) 3.16228 + 3.16228i 0.149404 + 0.149404i
\(449\) 31.1127i 1.46830i −0.678988 0.734150i \(-0.737581\pi\)
0.678988 0.734150i \(-0.262419\pi\)
\(450\) 12.4822 8.31836i 0.588416 0.392131i
\(451\) −32.0000 −1.50682
\(452\) −6.70820 + 6.70820i −0.315527 + 0.315527i
\(453\) −35.8167 + 13.6808i −1.68282 + 0.642778i
\(454\) 12.0000i 0.563188i
\(455\) −33.9039 12.2689i −1.58944 0.575176i
\(456\) 10.0000 + 4.47214i 0.468293 + 0.209427i
\(457\) 22.1359 22.1359i 1.03548 1.03548i 0.0361286 0.999347i \(-0.488497\pi\)
0.999347 0.0361286i \(-0.0115026\pi\)
\(458\) −6.70820 6.70820i −0.313454 0.313454i
\(459\) −15.6525 + 5.00000i −0.730595 + 0.233380i
\(460\) 0 0
\(461\) 1.41421 0.0658665 0.0329332 0.999458i \(-0.489515\pi\)
0.0329332 + 0.999458i \(0.489515\pi\)
\(462\) −15.6352 40.9334i −0.727414 1.90439i
\(463\) 18.9737 + 18.9737i 0.881781 + 0.881781i 0.993716 0.111935i \(-0.0357047\pi\)
−0.111935 + 0.993716i \(0.535705\pi\)
\(464\) −4.47214 −0.207614
\(465\) −7.76393 9.47214i −0.360044 0.439260i
\(466\) 3.16228i 0.146490i
\(467\) −6.70820 + 6.70820i −0.310419 + 0.310419i −0.845072 0.534653i \(-0.820442\pi\)
0.534653 + 0.845072i \(0.320442\pi\)
\(468\) −8.09888 7.16995i −0.374371 0.331431i
\(469\) 0 0
\(470\) −4.24264 + 1.41421i −0.195698 + 0.0652328i
\(471\) 0 0
\(472\) 2.00000 + 2.00000i 0.0920575 + 0.0920575i
\(473\) 28.2843 28.2843i 1.30051 1.30051i
\(474\) 0 0
\(475\) −25.2982 + 18.9737i −1.16076 + 0.870572i
\(476\) 14.1421 0.648204
\(477\) −18.9443 1.05573i −0.867399 0.0483385i
\(478\) −3.00000 + 3.00000i −0.137217 + 0.137217i
\(479\) 18.3848i 0.840022i −0.907519 0.420011i \(-0.862026\pi\)
0.907519 0.420011i \(-0.137974\pi\)
\(480\) −3.85410 0.381966i −0.175915 0.0174343i
\(481\) −10.0000 + 12.6491i −0.455961 + 0.576750i
\(482\) −8.94427 + 8.94427i −0.407400 + 0.407400i
\(483\) 0 0
\(484\) 21.0000i 0.954545i
\(485\) −26.8328 13.4164i −1.21842 0.609208i
\(486\) −13.4350 7.90569i −0.609425 0.358610i
\(487\) 3.16228 3.16228i 0.143296 0.143296i −0.631819 0.775116i \(-0.717692\pi\)
0.775116 + 0.631819i \(0.217692\pi\)
\(488\) −7.07107 + 7.07107i −0.320092 + 0.320092i
\(489\) 0 0
\(490\) 26.0000 + 13.0000i 1.17456 + 0.587280i
\(491\) 22.3607i 1.00912i −0.863376 0.504562i \(-0.831654\pi\)
0.863376 0.504562i \(-0.168346\pi\)
\(492\) 9.15298 3.49613i 0.412648 0.157618i
\(493\) −10.0000 + 10.0000i −0.450377 + 0.450377i
\(494\) 17.8885 + 14.1421i 0.804844 + 0.636285i
\(495\) 32.9443 + 18.8328i 1.48073 + 0.846472i
\(496\) 3.16228i 0.141990i
\(497\) 4.47214 4.47214i 0.200603 0.200603i
\(498\) 2.47214 + 6.47214i 0.110779 + 0.290023i
\(499\) −12.6491 −0.566252 −0.283126 0.959083i \(-0.591371\pi\)
−0.283126 + 0.959083i \(0.591371\pi\)
\(500\) 6.36396 9.19239i 0.284605 0.411096i
\(501\) 12.7279 28.4605i 0.568642 1.27152i
\(502\) −12.6491 + 12.6491i −0.564557 + 0.564557i
\(503\) 4.47214 + 4.47214i 0.199403 + 0.199403i 0.799744 0.600341i \(-0.204969\pi\)
−0.600341 + 0.799744i \(0.704969\pi\)
\(504\) 8.94427 + 10.0000i 0.398410 + 0.445435i
\(505\) 9.48683 3.16228i 0.422159 0.140720i
\(506\) 0 0
\(507\) −12.6717 18.6126i −0.562769 0.826614i
\(508\) 2.00000 2.00000i 0.0887357 0.0887357i
\(509\) 24.0416i 1.06563i 0.846233 + 0.532813i \(0.178865\pi\)
−0.846233 + 0.532813i \(0.821135\pi\)
\(510\) −9.47214 + 7.76393i −0.419433 + 0.343793i
\(511\) 20.0000 0.884748
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 29.2070 + 15.0649i 1.28952 + 0.665131i
\(514\) 28.4605 1.25534
\(515\) 0 0
\(516\) −5.00000 + 11.1803i −0.220113 + 0.492187i
\(517\) −8.00000 8.00000i −0.351840 0.351840i
\(518\) 14.1421 14.1421i 0.621370 0.621370i
\(519\) −13.4164 + 30.0000i −0.588915 + 1.31685i
\(520\) −7.58114 2.74342i −0.332455 0.120307i
\(521\) 26.8328i 1.17557i −0.809018 0.587784i \(-0.800001\pi\)
0.809018 0.587784i \(-0.199999\pi\)
\(522\) −13.3956 0.746512i −0.586310 0.0326740i
\(523\) −15.0000 + 15.0000i −0.655904 + 0.655904i −0.954408 0.298504i \(-0.903512\pi\)
0.298504 + 0.954408i \(0.403512\pi\)
\(524\) −17.8885 −0.781465
\(525\) −37.7711 + 8.56409i −1.64847 + 0.373768i
\(526\) 12.6491i 0.551527i
\(527\) 7.07107 + 7.07107i 0.308021 + 0.308021i
\(528\) −3.49613 9.15298i −0.152149 0.398332i
\(529\) 23.0000i 1.00000i
\(530\) −13.4164 + 4.47214i −0.582772 + 0.194257i
\(531\) 5.65685 + 6.32456i 0.245487 + 0.274462i
\(532\) −20.0000 20.0000i −0.867110 0.867110i
\(533\) 20.2580 2.36944i 0.877471 0.102632i
\(534\) 4.47214 + 2.00000i 0.193528 + 0.0865485i
\(535\) 6.32456 + 3.16228i 0.273434 + 0.136717i
\(536\) 0 0
\(537\) −11.0557 28.9443i −0.477090 1.24904i
\(538\) 15.8114 + 15.8114i 0.681677 + 0.681677i
\(539\) 73.5391i 3.16755i
\(540\) −11.4806 1.78747i −0.494048 0.0769205i
\(541\) 41.1096i 1.76744i 0.468016 + 0.883720i \(0.344969\pi\)
−0.468016 + 0.883720i \(0.655031\pi\)
\(542\) 6.70820 6.70820i 0.288142 0.288142i
\(543\) 13.5967 + 35.5967i 0.583492 + 1.52760i
\(544\) 3.16228 0.135582
\(545\) −2.23607 6.70820i −0.0957826 0.287348i
\(546\) 12.9289 + 24.7557i 0.553307 + 1.05944i
\(547\) 5.00000 + 5.00000i 0.213785 + 0.213785i 0.805873 0.592088i \(-0.201696\pi\)
−0.592088 + 0.805873i \(0.701696\pi\)
\(548\) −12.7279 + 12.7279i −0.543710 + 0.543710i
\(549\) −22.3607 + 20.0000i −0.954331 + 0.853579i
\(550\) 28.0000 + 4.00000i 1.19392 + 0.170561i
\(551\) 28.2843 1.20495
\(552\) 0 0
\(553\) 0 0
\(554\) 14.1421i 0.600842i
\(555\) −1.70820 + 17.2361i −0.0725092 + 0.731630i
\(556\) 4.00000 0.169638
\(557\) 12.7279 + 12.7279i 0.539299 + 0.539299i 0.923323 0.384024i \(-0.125462\pi\)
−0.384024 + 0.923323i \(0.625462\pi\)
\(558\) −0.527864 + 9.47214i −0.0223463 + 0.400987i
\(559\) −15.8114 + 20.0000i −0.668750 + 0.845910i
\(560\) 8.94427 + 4.47214i 0.377964 + 0.188982i
\(561\) −28.2843 12.6491i −1.19416 0.534046i
\(562\) 6.00000 + 6.00000i 0.253095 + 0.253095i
\(563\) −20.1246 20.1246i −0.848151 0.848151i 0.141751 0.989902i \(-0.454727\pi\)
−0.989902 + 0.141751i \(0.954727\pi\)
\(564\) 3.16228 + 1.41421i 0.133156 + 0.0595491i
\(565\) −9.48683 + 18.9737i −0.399114 + 0.798228i
\(566\) 12.7279 0.534994
\(567\) 25.1220 + 31.4465i 1.05502 + 1.32063i
\(568\) 1.00000 1.00000i 0.0419591 0.0419591i
\(569\) −8.94427 −0.374963 −0.187482 0.982268i \(-0.560033\pi\)
−0.187482 + 0.982268i \(0.560033\pi\)
\(570\) 24.3755 + 2.41577i 1.02098 + 0.101185i
\(571\) −10.0000 −0.418487 −0.209243 0.977864i \(-0.567100\pi\)
−0.209243 + 0.977864i \(0.567100\pi\)
\(572\) −2.36944 20.2580i −0.0990711 0.847029i
\(573\) −14.4721 + 5.52786i −0.604582 + 0.230930i
\(574\) −25.2982 −1.05593
\(575\) 0 0
\(576\) 2.00000 + 2.23607i 0.0833333 + 0.0931695i
\(577\) 9.48683 9.48683i 0.394942 0.394942i −0.481503 0.876445i \(-0.659909\pi\)
0.876445 + 0.481503i \(0.159909\pi\)
\(578\) −4.94975 + 4.94975i −0.205882 + 0.205882i
\(579\) −9.48683 + 21.2132i −0.394259 + 0.881591i
\(580\) −9.48683 + 3.16228i −0.393919 + 0.131306i
\(581\) 17.8885i 0.742142i
\(582\) 8.29180 + 21.7082i 0.343706 + 0.899834i
\(583\) −25.2982 25.2982i −1.04775 1.04775i
\(584\) 4.47214 0.185058
\(585\) −22.2502 9.48298i −0.919934 0.392073i
\(586\) −16.0000 −0.660954
\(587\) −8.48528 8.48528i −0.350225 0.350225i 0.509968 0.860193i \(-0.329657\pi\)
−0.860193 + 0.509968i \(0.829657\pi\)
\(588\) −8.03444 21.0344i −0.331335 0.867446i
\(589\) 20.0000i 0.824086i
\(590\) 5.65685 + 2.82843i 0.232889 + 0.116445i
\(591\) 1.41421 3.16228i 0.0581730 0.130079i
\(592\) 3.16228 3.16228i 0.129969 0.129969i
\(593\) 4.24264 4.24264i 0.174224 0.174224i −0.614608 0.788833i \(-0.710686\pi\)
0.788833 + 0.614608i \(0.210686\pi\)
\(594\) −8.94427 28.0000i −0.366988 1.14885i
\(595\) 30.0000 10.0000i 1.22988 0.409960i
\(596\) −4.24264 −0.173785
\(597\) 32.3607 12.3607i 1.32443 0.505889i
\(598\) 0 0
\(599\) −8.94427 −0.365453 −0.182727 0.983164i \(-0.558492\pi\)
−0.182727 + 0.983164i \(0.558492\pi\)
\(600\) −8.44588 + 1.91499i −0.344801 + 0.0781791i
\(601\) −40.0000 −1.63163 −0.815817 0.578310i \(-0.803712\pi\)
−0.815817 + 0.578310i \(0.803712\pi\)
\(602\) 22.3607 22.3607i 0.911353 0.911353i
\(603\) 0 0
\(604\) 22.1359 0.900699
\(605\) 14.8492 + 44.5477i 0.603708 + 1.81112i
\(606\) −7.07107 3.16228i −0.287242 0.128459i
\(607\) 30.0000 + 30.0000i 1.21766 + 1.21766i 0.968448 + 0.249214i \(0.0801723\pi\)
0.249214 + 0.968448i \(0.419828\pi\)
\(608\) −4.47214 4.47214i −0.181369 0.181369i
\(609\) 31.6228 + 14.1421i 1.28142 + 0.573068i
\(610\) −10.0000 + 20.0000i −0.404888 + 0.809776i
\(611\) 5.65685 + 4.47214i 0.228852 + 0.180923i
\(612\) 9.47214 + 0.527864i 0.382888 + 0.0213376i
\(613\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) 0 0
\(615\) 16.9443 13.8885i 0.683259 0.560040i
\(616\) 25.2982i 1.01929i
\(617\) −12.7279 12.7279i −0.512407 0.512407i 0.402856 0.915263i \(-0.368017\pi\)
−0.915263 + 0.402856i \(0.868017\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 2.23607 + 6.70820i 0.0898027 + 0.269408i
\(621\) 0 0
\(622\) 6.32456 6.32456i 0.253592 0.253592i
\(623\) −8.94427 8.94427i −0.358345 0.358345i
\(624\) 2.89100 + 5.53553i 0.115733 + 0.221599i
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) −1.41421 −0.0565233
\(627\) 22.1115 + 57.8885i 0.883047 + 2.31185i
\(628\) 0 0
\(629\) 14.1421i 0.563884i
\(630\) 26.0447 + 14.8886i 1.03765 + 0.593178i
\(631\) 15.8114i 0.629441i −0.949184 0.314721i \(-0.898089\pi\)
0.949184 0.314721i \(-0.101911\pi\)
\(632\) 0 0
\(633\) −12.3607 32.3607i −0.491293 1.28622i
\(634\) 28.0000i 1.11202i
\(635\) 2.82843 5.65685i 0.112243 0.224485i
\(636\) 10.0000 + 4.47214i 0.396526 + 0.177332i
\(637\) −5.44520 46.5548i −0.215746 1.84457i
\(638\) −17.8885 17.8885i −0.708214 0.708214i
\(639\) 3.16228 2.82843i 0.125098 0.111891i
\(640\) 2.00000 + 1.00000i 0.0790569 + 0.0395285i
\(641\) 49.1935i 1.94303i 0.236986 + 0.971513i \(0.423841\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) −1.95440 5.11667i −0.0771338 0.201939i
\(643\) −18.9737 18.9737i −0.748248 0.748248i 0.225902 0.974150i \(-0.427467\pi\)
−0.974150 + 0.225902i \(0.927467\pi\)
\(644\) 0 0
\(645\) −2.70091 + 27.2526i −0.106348 + 1.07307i
\(646\) −20.0000 −0.786889
\(647\) −22.3607 + 22.3607i −0.879089 + 0.879089i −0.993440 0.114351i \(-0.963521\pi\)
0.114351 + 0.993440i \(0.463521\pi\)
\(648\) 5.61745 + 7.03166i 0.220674 + 0.276230i
\(649\) 16.0000i 0.628055i
\(650\) −18.0219 0.458991i −0.706878 0.0180031i
\(651\) 10.0000 22.3607i 0.391931 0.876384i
\(652\) 0 0
\(653\) −17.8885 17.8885i −0.700033 0.700033i 0.264385 0.964417i \(-0.414831\pi\)
−0.964417 + 0.264385i \(0.914831\pi\)
\(654\) −2.23607 + 5.00000i −0.0874372 + 0.195515i
\(655\) −37.9473 + 12.6491i −1.48272 + 0.494242i
\(656\) −5.65685 −0.220863
\(657\) 13.3956 + 0.746512i 0.522613 + 0.0291242i
\(658\) −6.32456 6.32456i −0.246557 0.246557i
\(659\) −31.3050 −1.21947 −0.609734 0.792606i \(-0.708724\pi\)
−0.609734 + 0.792606i \(0.708724\pi\)
\(660\) −13.8885 16.9443i −0.540611 0.659555i
\(661\) 41.1096i 1.59898i −0.600680 0.799489i \(-0.705104\pi\)
0.600680 0.799489i \(-0.294896\pi\)
\(662\) −8.94427 + 8.94427i −0.347629 + 0.347629i
\(663\) 18.8423 + 5.91336i 0.731774 + 0.229656i
\(664\) 4.00000i 0.155230i
\(665\) −56.5685 28.2843i −2.19363 1.09682i
\(666\) 10.0000 8.94427i 0.387492 0.346583i
\(667\) 0 0
\(668\) −12.7279 + 12.7279i −0.492458 + 0.492458i
\(669\) 18.9737 42.4264i 0.733564 1.64030i
\(670\) 0 0
\(671\) −56.5685 −2.18380
\(672\) −2.76393 7.23607i −0.106621 0.279137i
\(673\) −15.0000 + 15.0000i −0.578208 + 0.578208i −0.934409 0.356202i \(-0.884072\pi\)
0.356202 + 0.934409i \(0.384072\pi\)
\(674\) 18.3848i 0.708155i
\(675\) −25.6180 + 4.32624i −0.986039 + 0.166517i
\(676\) 3.00000 + 12.6491i 0.115385 + 0.486504i
\(677\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(678\) 15.3500 5.86319i 0.589514 0.225174i
\(679\) 60.0000i 2.30259i
\(680\) 6.70820 2.23607i 0.257248 0.0857493i
\(681\) −8.48528 + 18.9737i −0.325157 + 0.727072i
\(682\) −12.6491 + 12.6491i −0.484359 + 0.484359i
\(683\) 16.9706 16.9706i 0.649361 0.649361i −0.303478 0.952838i \(-0.598148\pi\)
0.952838 + 0.303478i \(0.0981479\pi\)
\(684\) −12.6491 14.1421i −0.483651 0.540738i
\(685\) −18.0000 + 36.0000i −0.687745 + 1.37549i
\(686\) 26.8328i 1.02448i
\(687\) 5.86319 + 15.3500i 0.223694 + 0.585640i
\(688\) 5.00000 5.00000i 0.190623 0.190623i
\(689\) 17.8885 + 14.1421i 0.681499 + 0.538772i
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 13.4164 13.4164i 0.510015 0.510015i
\(693\) −4.22291 + 75.7771i −0.160415 + 2.87853i
\(694\) −28.4605 −1.08035
\(695\) 8.48528 2.82843i 0.321865 0.107288i
\(696\) 7.07107 + 3.16228i 0.268028 + 0.119866i
\(697\) −12.6491 + 12.6491i −0.479119 + 0.479119i
\(698\) −2.23607 2.23607i −0.0846364 0.0846364i
\(699\) −2.23607 + 5.00000i −0.0845759 + 0.189117i
\(700\) 22.1359 + 3.16228i 0.836660 + 0.119523i
\(701\) 49.1935i 1.85801i 0.370064 + 0.929006i \(0.379336\pi\)
−0.370064 + 0.929006i \(0.620664\pi\)
\(702\) 7.73553 + 17.0635i 0.291959 + 0.644019i
\(703\) −20.0000 + 20.0000i −0.754314 + 0.754314i
\(704\) 5.65685i 0.213201i
\(705\) 7.70820 + 0.763932i 0.290308 + 0.0287713i
\(706\) 14.0000 0.526897
\(707\) 14.1421 + 14.1421i 0.531870 + 0.531870i
\(708\) −1.74806 4.57649i −0.0656963 0.171995i
\(709\) −47.4342 −1.78143 −0.890714 0.454565i \(-0.849795\pi\)
−0.890714 + 0.454565i \(0.849795\pi\)
\(710\) 1.41421 2.82843i 0.0530745 0.106149i
\(711\) 0 0
\(712\) −2.00000 2.00000i −0.0749532 0.0749532i
\(713\) 0 0
\(714\) −22.3607 10.0000i −0.836827 0.374241i
\(715\) −19.3509 41.2982i −0.723682 1.54447i
\(716\) 17.8885i 0.668526i
\(717\) 6.86474 2.62210i 0.256368 0.0979240i
\(718\) 23.0000 23.0000i 0.858352 0.858352i
\(719\) 17.8885 0.667130 0.333565 0.942727i \(-0.391748\pi\)
0.333565 + 0.942727i \(0.391748\pi\)
\(720\) 5.82378 + 3.32920i 0.217039 + 0.124072i
\(721\) 0 0
\(722\) 14.8492 + 14.8492i 0.552632 + 0.552632i
\(723\) 20.4667 7.81758i 0.761164 0.290739i
\(724\) 22.0000i 0.817624i
\(725\) −17.8885 + 13.4164i −0.664364 + 0.498273i
\(726\) 14.8492 33.2039i 0.551107 1.23231i
\(727\) 18.0000 + 18.0000i 0.667583 + 0.667583i 0.957156 0.289573i \(-0.0935133\pi\)
−0.289573 + 0.957156i \(0.593513\pi\)
\(728\) −1.87320 16.0153i −0.0694256 0.593568i
\(729\) 15.6525 + 22.0000i 0.579721 + 0.814815i
\(730\) 9.48683 3.16228i 0.351123 0.117041i
\(731\) 22.3607i 0.827040i
\(732\) 16.1803 6.18034i 0.598043 0.228432i
\(733\) −9.48683 9.48683i −0.350404 0.350404i 0.509856 0.860260i \(-0.329699\pi\)
−0.860260 + 0.509856i \(0.829699\pi\)
\(734\) 28.2843i 1.04399i
\(735\) −31.9172 38.9396i −1.17728 1.43631i
\(736\) 0 0
\(737\) 0 0
\(738\) −16.9443 0.944272i −0.623727 0.0347591i
\(739\) 44.2719 1.62857 0.814284 0.580467i \(-0.197130\pi\)
0.814284 + 0.580467i \(0.197130\pi\)
\(740\) 4.47214 8.94427i 0.164399 0.328798i
\(741\) −18.2843 35.0098i −0.671689 1.28612i
\(742\) −20.0000 20.0000i −0.734223 0.734223i
\(743\) −16.9706 + 16.9706i −0.622590 + 0.622590i −0.946193 0.323603i \(-0.895106\pi\)
0.323603 + 0.946193i \(0.395106\pi\)
\(744\) 2.23607 5.00000i 0.0819782 0.183309i
\(745\) −9.00000 + 3.00000i −0.329734 + 0.109911i
\(746\) 22.6274 0.828449
\(747\) 0.667701 11.9814i 0.0244299 0.438377i
\(748\) 12.6491 + 12.6491i 0.462497 + 0.462497i
\(749\) 14.1421i 0.516742i
\(750\) −16.5623 + 10.0344i −0.604770 + 0.366406i
\(751\) 48.0000 1.75154 0.875772 0.482724i \(-0.160353\pi\)
0.875772 + 0.482724i \(0.160353\pi\)
\(752\) −1.41421 1.41421i −0.0515711 0.0515711i
\(753\) 28.9443 11.0557i 1.05479 0.402893i
\(754\) 12.6491 + 10.0000i 0.460653 + 0.364179i
\(755\) 46.9574 15.6525i 1.70896 0.569652i
\(756\) −7.07107 22.1359i −0.257172 0.805076i
\(757\) −18.0000 18.0000i −0.654221 0.654221i 0.299786 0.954007i \(-0.403085\pi\)
−0.954007 + 0.299786i \(0.903085\pi\)
\(758\) −4.47214 4.47214i −0.162435 0.162435i
\(759\) 0 0
\(760\) −12.6491 6.32456i −0.458831 0.229416i
\(761\) 36.7696 1.33290 0.666448 0.745552i \(-0.267814\pi\)
0.666448 + 0.745552i \(0.267814\pi\)
\(762\) −4.57649 + 1.74806i −0.165789 + 0.0633257i
\(763\) 10.0000 10.0000i 0.362024 0.362024i
\(764\) 8.94427 0.323592
\(765\) 20.4667 5.57804i 0.739975 0.201675i
\(766\) 16.0000 0.578103
\(767\) −1.18472 10.1290i −0.0427777 0.365737i
\(768\) −0.618034 1.61803i −0.0223014 0.0583858i
\(769\) 50.5964 1.82455 0.912277 0.409573i \(-0.134322\pi\)
0.912277 + 0.409573i \(0.134322\pi\)
\(770\) 17.8885 + 53.6656i 0.644658 + 1.93398i
\(771\) −45.0000 20.1246i −1.62064 0.724770i
\(772\) 9.48683 9.48683i 0.341439 0.341439i
\(773\) 4.24264 4.24264i 0.152597 0.152597i −0.626680 0.779277i \(-0.715587\pi\)
0.779277 + 0.626680i \(0.215587\pi\)
\(774\) 15.8114 14.1421i 0.568329 0.508329i
\(775\) 9.48683 + 12.6491i 0.340777 + 0.454369i
\(776\) 13.4164i 0.481621i
\(777\) −32.3607 + 12.3607i −1.16093 + 0.443437i
\(778\) −9.48683 9.48683i