Properties

Label 690.2.j.b.643.1
Level $690$
Weight $2$
Character 690.643
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 643.1
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.b.367.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.98078 + 1.03755i) q^{5} +1.00000 q^{6} +(0.124800 + 0.124800i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.98078 + 1.03755i) q^{5} +1.00000 q^{6} +(0.124800 + 0.124800i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(0.666968 - 2.13428i) q^{10} -0.552534i q^{11} +(-0.707107 + 0.707107i) q^{12} +(2.68793 + 2.68793i) q^{13} -0.176495 q^{14} +(2.13428 + 0.666968i) q^{15} -1.00000 q^{16} +(-3.61968 - 3.61968i) q^{17} +(-0.707107 - 0.707107i) q^{18} +1.08434 q^{19} +(1.03755 + 1.98078i) q^{20} -0.176495i q^{21} +(0.390701 + 0.390701i) q^{22} +(-4.79526 + 0.0741463i) q^{23} -1.00000i q^{24} +(2.84699 - 4.11031i) q^{25} -3.80130 q^{26} +(0.707107 - 0.707107i) q^{27} +(0.124800 - 0.124800i) q^{28} -8.68275i q^{29} +(-1.98078 + 1.03755i) q^{30} +2.45605 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.390701 + 0.390701i) q^{33} +5.11901 q^{34} +(-0.376689 - 0.117716i) q^{35} +1.00000 q^{36} +(-7.79545 - 7.79545i) q^{37} +(-0.766741 + 0.766741i) q^{38} -3.80130i q^{39} +(-2.13428 - 0.666968i) q^{40} -2.27486 q^{41} +(0.124800 + 0.124800i) q^{42} +(1.06804 - 1.06804i) q^{43} -0.552534 q^{44} +(-1.03755 - 1.98078i) q^{45} +(3.33833 - 3.44319i) q^{46} +(-0.597335 + 0.597335i) q^{47} +(0.707107 + 0.707107i) q^{48} -6.96885i q^{49} +(0.893297 + 4.91955i) q^{50} +5.11901i q^{51} +(2.68793 - 2.68793i) q^{52} +(-5.95295 + 5.95295i) q^{53} +1.00000i q^{54} +(0.573280 + 1.09445i) q^{55} +0.176495i q^{56} +(-0.766741 - 0.766741i) q^{57} +(6.13963 + 6.13963i) q^{58} -10.4090i q^{59} +(0.666968 - 2.13428i) q^{60} -9.12081i q^{61} +(-1.73669 + 1.73669i) q^{62} +(-0.124800 + 0.124800i) q^{63} +1.00000i q^{64} +(-8.11305 - 2.53535i) q^{65} -0.552534i q^{66} +(-5.38491 - 5.38491i) q^{67} +(-3.61968 + 3.61968i) q^{68} +(3.44319 + 3.33833i) q^{69} +(0.349597 - 0.183121i) q^{70} +8.16755 q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.12378 + 3.12378i) q^{73} +11.0244 q^{74} +(-4.91955 + 0.893297i) q^{75} -1.08434i q^{76} +(0.0689566 - 0.0689566i) q^{77} +(2.68793 + 2.68793i) q^{78} -6.76975 q^{79} +(1.98078 - 1.03755i) q^{80} -1.00000 q^{81} +(1.60857 - 1.60857i) q^{82} +(-0.190970 + 0.190970i) q^{83} -0.176495 q^{84} +(10.9254 + 3.41421i) q^{85} +1.51043i q^{86} +(-6.13963 + 6.13963i) q^{87} +(0.390701 - 0.390701i) q^{88} +8.76193 q^{89} +(2.13428 + 0.666968i) q^{90} +0.670909i q^{91} +(0.0741463 + 4.79526i) q^{92} +(-1.73669 - 1.73669i) q^{93} -0.844759i q^{94} +(-2.14783 + 1.12505i) q^{95} -1.00000 q^{96} +(-1.62982 - 1.62982i) q^{97} +(4.92772 + 4.92772i) q^{98} +0.552534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{6} + O(q^{10}) \) \( 24q + 24q^{6} + 16q^{13} - 24q^{16} + 16q^{23} - 16q^{25} + 16q^{31} + 24q^{36} + 8q^{46} + 40q^{47} - 8q^{50} + 16q^{52} - 56q^{55} - 16q^{58} - 8q^{62} + 32q^{70} + 64q^{71} - 16q^{73} + 32q^{75} + 16q^{77} + 16q^{78} - 24q^{81} + 24q^{82} - 48q^{85} + 16q^{87} + 16q^{92} - 8q^{93} + 24q^{95} - 24q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −1.98078 + 1.03755i −0.885833 + 0.464005i
\(6\) 1.00000 0.408248
\(7\) 0.124800 + 0.124800i 0.0471701 + 0.0471701i 0.730298 0.683128i \(-0.239381\pi\)
−0.683128 + 0.730298i \(0.739381\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 0.666968 2.13428i 0.210914 0.674919i
\(11\) 0.552534i 0.166595i −0.996525 0.0832977i \(-0.973455\pi\)
0.996525 0.0832977i \(-0.0265452\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 2.68793 + 2.68793i 0.745497 + 0.745497i 0.973630 0.228133i \(-0.0732621\pi\)
−0.228133 + 0.973630i \(0.573262\pi\)
\(14\) −0.176495 −0.0471701
\(15\) 2.13428 + 0.666968i 0.551069 + 0.172210i
\(16\) −1.00000 −0.250000
\(17\) −3.61968 3.61968i −0.877902 0.877902i 0.115415 0.993317i \(-0.463180\pi\)
−0.993317 + 0.115415i \(0.963180\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 1.08434 0.248764 0.124382 0.992234i \(-0.460305\pi\)
0.124382 + 0.992234i \(0.460305\pi\)
\(20\) 1.03755 + 1.98078i 0.232002 + 0.442916i
\(21\) 0.176495i 0.0385143i
\(22\) 0.390701 + 0.390701i 0.0832977 + 0.0832977i
\(23\) −4.79526 + 0.0741463i −0.999880 + 0.0154606i
\(24\) 1.00000i 0.204124i
\(25\) 2.84699 4.11031i 0.569399 0.822061i
\(26\) −3.80130 −0.745497
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0.124800 0.124800i 0.0235851 0.0235851i
\(29\) 8.68275i 1.61235i −0.591679 0.806173i \(-0.701535\pi\)
0.591679 0.806173i \(-0.298465\pi\)
\(30\) −1.98078 + 1.03755i −0.361640 + 0.189429i
\(31\) 2.45605 0.441119 0.220559 0.975374i \(-0.429212\pi\)
0.220559 + 0.975374i \(0.429212\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −0.390701 + 0.390701i −0.0680123 + 0.0680123i
\(34\) 5.11901 0.877902
\(35\) −0.376689 0.117716i −0.0636720 0.0198977i
\(36\) 1.00000 0.166667
\(37\) −7.79545 7.79545i −1.28156 1.28156i −0.939777 0.341787i \(-0.888968\pi\)
−0.341787 0.939777i \(-0.611032\pi\)
\(38\) −0.766741 + 0.766741i −0.124382 + 0.124382i
\(39\) 3.80130i 0.608696i
\(40\) −2.13428 0.666968i −0.337459 0.105457i
\(41\) −2.27486 −0.355274 −0.177637 0.984096i \(-0.556845\pi\)
−0.177637 + 0.984096i \(0.556845\pi\)
\(42\) 0.124800 + 0.124800i 0.0192571 + 0.0192571i
\(43\) 1.06804 1.06804i 0.162874 0.162874i −0.620965 0.783839i \(-0.713259\pi\)
0.783839 + 0.620965i \(0.213259\pi\)
\(44\) −0.552534 −0.0832977
\(45\) −1.03755 1.98078i −0.154668 0.295278i
\(46\) 3.33833 3.44319i 0.492210 0.507671i
\(47\) −0.597335 + 0.597335i −0.0871302 + 0.0871302i −0.749329 0.662198i \(-0.769624\pi\)
0.662198 + 0.749329i \(0.269624\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 6.96885i 0.995550i
\(50\) 0.893297 + 4.91955i 0.126331 + 0.695730i
\(51\) 5.11901i 0.716804i
\(52\) 2.68793 2.68793i 0.372748 0.372748i
\(53\) −5.95295 + 5.95295i −0.817701 + 0.817701i −0.985774 0.168073i \(-0.946245\pi\)
0.168073 + 0.985774i \(0.446245\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0.573280 + 1.09445i 0.0773011 + 0.147576i
\(56\) 0.176495i 0.0235851i
\(57\) −0.766741 0.766741i −0.101557 0.101557i
\(58\) 6.13963 + 6.13963i 0.806173 + 0.806173i
\(59\) 10.4090i 1.35514i −0.735460 0.677569i \(-0.763034\pi\)
0.735460 0.677569i \(-0.236966\pi\)
\(60\) 0.666968 2.13428i 0.0861052 0.275534i
\(61\) 9.12081i 1.16780i −0.811825 0.583900i \(-0.801526\pi\)
0.811825 0.583900i \(-0.198474\pi\)
\(62\) −1.73669 + 1.73669i −0.220559 + 0.220559i
\(63\) −0.124800 + 0.124800i −0.0157234 + 0.0157234i
\(64\) 1.00000i 0.125000i
\(65\) −8.11305 2.53535i −1.00630 0.314471i
\(66\) 0.552534i 0.0680123i
\(67\) −5.38491 5.38491i −0.657871 0.657871i 0.297005 0.954876i \(-0.404012\pi\)
−0.954876 + 0.297005i \(0.904012\pi\)
\(68\) −3.61968 + 3.61968i −0.438951 + 0.438951i
\(69\) 3.44319 + 3.33833i 0.414511 + 0.401888i
\(70\) 0.349597 0.183121i 0.0417849 0.0218872i
\(71\) 8.16755 0.969309 0.484655 0.874706i \(-0.338945\pi\)
0.484655 + 0.874706i \(0.338945\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) 3.12378 + 3.12378i 0.365610 + 0.365610i 0.865873 0.500263i \(-0.166763\pi\)
−0.500263 + 0.865873i \(0.666763\pi\)
\(74\) 11.0244 1.28156
\(75\) −4.91955 + 0.893297i −0.568061 + 0.103149i
\(76\) 1.08434i 0.124382i
\(77\) 0.0689566 0.0689566i 0.00785833 0.00785833i
\(78\) 2.68793 + 2.68793i 0.304348 + 0.304348i
\(79\) −6.76975 −0.761656 −0.380828 0.924646i \(-0.624361\pi\)
−0.380828 + 0.924646i \(0.624361\pi\)
\(80\) 1.98078 1.03755i 0.221458 0.116001i
\(81\) −1.00000 −0.111111
\(82\) 1.60857 1.60857i 0.177637 0.177637i
\(83\) −0.190970 + 0.190970i −0.0209616 + 0.0209616i −0.717510 0.696548i \(-0.754718\pi\)
0.696548 + 0.717510i \(0.254718\pi\)
\(84\) −0.176495 −0.0192571
\(85\) 10.9254 + 3.41421i 1.18503 + 0.370323i
\(86\) 1.51043i 0.162874i
\(87\) −6.13963 + 6.13963i −0.658238 + 0.658238i
\(88\) 0.390701 0.390701i 0.0416489 0.0416489i
\(89\) 8.76193 0.928762 0.464381 0.885635i \(-0.346277\pi\)
0.464381 + 0.885635i \(0.346277\pi\)
\(90\) 2.13428 + 0.666968i 0.224973 + 0.0703046i
\(91\) 0.670909i 0.0703304i
\(92\) 0.0741463 + 4.79526i 0.00773029 + 0.499940i
\(93\) −1.73669 1.73669i −0.180086 0.180086i
\(94\) 0.844759i 0.0871302i
\(95\) −2.14783 + 1.12505i −0.220363 + 0.115428i
\(96\) −1.00000 −0.102062
\(97\) −1.62982 1.62982i −0.165484 0.165484i 0.619507 0.784991i \(-0.287332\pi\)
−0.784991 + 0.619507i \(0.787332\pi\)
\(98\) 4.92772 + 4.92772i 0.497775 + 0.497775i
\(99\) 0.552534 0.0555318
\(100\) −4.11031 2.84699i −0.411031 0.284699i
\(101\) −5.93104 −0.590161 −0.295080 0.955472i \(-0.595346\pi\)
−0.295080 + 0.955472i \(0.595346\pi\)
\(102\) −3.61968 3.61968i −0.358402 0.358402i
\(103\) −3.77864 + 3.77864i −0.372321 + 0.372321i −0.868322 0.496001i \(-0.834801\pi\)
0.496001 + 0.868322i \(0.334801\pi\)
\(104\) 3.80130i 0.372748i
\(105\) 0.183121 + 0.349597i 0.0178708 + 0.0341172i
\(106\) 8.41875i 0.817701i
\(107\) 9.09321 + 9.09321i 0.879074 + 0.879074i 0.993439 0.114365i \(-0.0364834\pi\)
−0.114365 + 0.993439i \(0.536483\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 13.5947 1.30213 0.651067 0.759021i \(-0.274322\pi\)
0.651067 + 0.759021i \(0.274322\pi\)
\(110\) −1.17926 0.368523i −0.112438 0.0351373i
\(111\) 11.0244i 1.04639i
\(112\) −0.124800 0.124800i −0.0117925 0.0117925i
\(113\) 9.30335 9.30335i 0.875186 0.875186i −0.117846 0.993032i \(-0.537599\pi\)
0.993032 + 0.117846i \(0.0375990\pi\)
\(114\) 1.08434 0.101557
\(115\) 9.42143 5.12217i 0.878553 0.477645i
\(116\) −8.68275 −0.806173
\(117\) −2.68793 + 2.68793i −0.248499 + 0.248499i
\(118\) 7.36028 + 7.36028i 0.677569 + 0.677569i
\(119\) 0.903477i 0.0828216i
\(120\) 1.03755 + 1.98078i 0.0947146 + 0.180820i
\(121\) 10.6947 0.972246
\(122\) 6.44939 + 6.44939i 0.583900 + 0.583900i
\(123\) 1.60857 + 1.60857i 0.145040 + 0.145040i
\(124\) 2.45605i 0.220559i
\(125\) −1.37464 + 11.0955i −0.122952 + 0.992413i
\(126\) 0.176495i 0.0157234i
\(127\) −14.8431 + 14.8431i −1.31711 + 1.31711i −0.401054 + 0.916054i \(0.631356\pi\)
−0.916054 + 0.401054i \(0.868644\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −1.51043 −0.132986
\(130\) 7.52955 3.94403i 0.660386 0.345914i
\(131\) −8.69869 −0.760008 −0.380004 0.924985i \(-0.624077\pi\)
−0.380004 + 0.924985i \(0.624077\pi\)
\(132\) 0.390701 + 0.390701i 0.0340061 + 0.0340061i
\(133\) 0.135326 + 0.135326i 0.0117342 + 0.0117342i
\(134\) 7.61541 0.657871
\(135\) −0.666968 + 2.13428i −0.0574035 + 0.183690i
\(136\) 5.11901i 0.438951i
\(137\) −6.93107 6.93107i −0.592161 0.592161i 0.346053 0.938215i \(-0.387522\pi\)
−0.938215 + 0.346053i \(0.887522\pi\)
\(138\) −4.79526 + 0.0741463i −0.408199 + 0.00631175i
\(139\) 2.07505i 0.176003i −0.996120 0.0880017i \(-0.971952\pi\)
0.996120 0.0880017i \(-0.0280481\pi\)
\(140\) −0.117716 + 0.376689i −0.00994884 + 0.0318360i
\(141\) 0.844759 0.0711415
\(142\) −5.77533 + 5.77533i −0.484655 + 0.484655i
\(143\) 1.48517 1.48517i 0.124196 0.124196i
\(144\) 1.00000i 0.0833333i
\(145\) 9.00876 + 17.1986i 0.748137 + 1.42827i
\(146\) −4.41769 −0.365610
\(147\) −4.92772 + 4.92772i −0.406432 + 0.406432i
\(148\) −7.79545 + 7.79545i −0.640782 + 0.640782i
\(149\) −12.3141 −1.00881 −0.504406 0.863466i \(-0.668289\pi\)
−0.504406 + 0.863466i \(0.668289\pi\)
\(150\) 2.84699 4.11031i 0.232456 0.335605i
\(151\) −10.0500 −0.817860 −0.408930 0.912566i \(-0.634098\pi\)
−0.408930 + 0.912566i \(0.634098\pi\)
\(152\) 0.766741 + 0.766741i 0.0621909 + 0.0621909i
\(153\) 3.61968 3.61968i 0.292634 0.292634i
\(154\) 0.0975193i 0.00785833i
\(155\) −4.86489 + 2.54826i −0.390758 + 0.204681i
\(156\) −3.80130 −0.304348
\(157\) −3.40779 3.40779i −0.271972 0.271972i 0.557922 0.829893i \(-0.311599\pi\)
−0.829893 + 0.557922i \(0.811599\pi\)
\(158\) 4.78694 4.78694i 0.380828 0.380828i
\(159\) 8.41875 0.667650
\(160\) −0.666968 + 2.13428i −0.0527285 + 0.168730i
\(161\) −0.607704 0.589197i −0.0478938 0.0464352i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −10.9785 10.9785i −0.859900 0.859900i 0.131426 0.991326i \(-0.458044\pi\)
−0.991326 + 0.131426i \(0.958044\pi\)
\(164\) 2.27486i 0.177637i
\(165\) 0.368523 1.17926i 0.0286895 0.0918055i
\(166\) 0.270072i 0.0209616i
\(167\) 0.393053 0.393053i 0.0304153 0.0304153i −0.691736 0.722151i \(-0.743154\pi\)
0.722151 + 0.691736i \(0.243154\pi\)
\(168\) 0.124800 0.124800i 0.00962857 0.00962857i
\(169\) 1.44991i 0.111531i
\(170\) −10.1396 + 5.31121i −0.777674 + 0.407351i
\(171\) 1.08434i 0.0829212i
\(172\) −1.06804 1.06804i −0.0814370 0.0814370i
\(173\) −6.09087 6.09087i −0.463081 0.463081i 0.436583 0.899664i \(-0.356188\pi\)
−0.899664 + 0.436583i \(0.856188\pi\)
\(174\) 8.68275i 0.658238i
\(175\) 0.868275 0.157662i 0.0656354 0.0119181i
\(176\) 0.552534i 0.0416489i
\(177\) −7.36028 + 7.36028i −0.553233 + 0.553233i
\(178\) −6.19562 + 6.19562i −0.464381 + 0.464381i
\(179\) 23.2150i 1.73517i 0.497291 + 0.867584i \(0.334328\pi\)
−0.497291 + 0.867584i \(0.665672\pi\)
\(180\) −1.98078 + 1.03755i −0.147639 + 0.0773342i
\(181\) 6.45396i 0.479719i 0.970808 + 0.239860i \(0.0771014\pi\)
−0.970808 + 0.239860i \(0.922899\pi\)
\(182\) −0.474405 0.474405i −0.0351652 0.0351652i
\(183\) −6.44939 + 6.44939i −0.476753 + 0.476753i
\(184\) −3.44319 3.33833i −0.253835 0.246105i
\(185\) 23.5292 + 7.35295i 1.72990 + 0.540599i
\(186\) 2.45605 0.180086
\(187\) −2.00000 + 2.00000i −0.146254 + 0.146254i
\(188\) 0.597335 + 0.597335i 0.0435651 + 0.0435651i
\(189\) 0.176495 0.0128381
\(190\) 0.723217 2.31428i 0.0524677 0.167895i
\(191\) 22.6724i 1.64052i 0.571991 + 0.820260i \(0.306171\pi\)
−0.571991 + 0.820260i \(0.693829\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 7.13533 + 7.13533i 0.513612 + 0.513612i 0.915631 0.402019i \(-0.131692\pi\)
−0.402019 + 0.915631i \(0.631692\pi\)
\(194\) 2.30492 0.165484
\(195\) 3.94403 + 7.52955i 0.282438 + 0.539203i
\(196\) −6.96885 −0.497775
\(197\) 2.41931 2.41931i 0.172369 0.172369i −0.615651 0.788019i \(-0.711107\pi\)
0.788019 + 0.615651i \(0.211107\pi\)
\(198\) −0.390701 + 0.390701i −0.0277659 + 0.0277659i
\(199\) 22.7308 1.61134 0.805672 0.592362i \(-0.201805\pi\)
0.805672 + 0.592362i \(0.201805\pi\)
\(200\) 4.91955 0.893297i 0.347865 0.0631656i
\(201\) 7.61541i 0.537149i
\(202\) 4.19388 4.19388i 0.295080 0.295080i
\(203\) 1.08361 1.08361i 0.0760546 0.0760546i
\(204\) 5.11901 0.358402
\(205\) 4.50600 2.36027i 0.314713 0.164849i
\(206\) 5.34381i 0.372321i
\(207\) −0.0741463 4.79526i −0.00515352 0.333293i
\(208\) −2.68793 2.68793i −0.186374 0.186374i
\(209\) 0.599133i 0.0414429i
\(210\) −0.376689 0.117716i −0.0259940 0.00812319i
\(211\) −22.6042 −1.55613 −0.778067 0.628181i \(-0.783800\pi\)
−0.778067 + 0.628181i \(0.783800\pi\)
\(212\) 5.95295 + 5.95295i 0.408851 + 0.408851i
\(213\) −5.77533 5.77533i −0.395719 0.395719i
\(214\) −12.8597 −0.879074
\(215\) −1.00741 + 3.22368i −0.0687047 + 0.219853i
\(216\) 1.00000 0.0680414
\(217\) 0.306516 + 0.306516i 0.0208076 + 0.0208076i
\(218\) −9.61288 + 9.61288i −0.651067 + 0.651067i
\(219\) 4.41769i 0.298520i
\(220\) 1.09445 0.573280i 0.0737878 0.0386505i
\(221\) 19.4589i 1.30895i
\(222\) −7.79545 7.79545i −0.523197 0.523197i
\(223\) 10.6254 + 10.6254i 0.711531 + 0.711531i 0.966855 0.255325i \(-0.0821823\pi\)
−0.255325 + 0.966855i \(0.582182\pi\)
\(224\) 0.176495 0.0117925
\(225\) 4.11031 + 2.84699i 0.274020 + 0.189800i
\(226\) 13.1569i 0.875186i
\(227\) −4.66128 4.66128i −0.309380 0.309380i 0.535289 0.844669i \(-0.320203\pi\)
−0.844669 + 0.535289i \(0.820203\pi\)
\(228\) −0.766741 + 0.766741i −0.0507787 + 0.0507787i
\(229\) −6.63852 −0.438686 −0.219343 0.975648i \(-0.570391\pi\)
−0.219343 + 0.975648i \(0.570391\pi\)
\(230\) −3.04004 + 10.2839i −0.200454 + 0.678099i
\(231\) −0.0975193 −0.00641630
\(232\) 6.13963 6.13963i 0.403087 0.403087i
\(233\) −3.52576 3.52576i −0.230980 0.230980i 0.582122 0.813102i \(-0.302223\pi\)
−0.813102 + 0.582122i \(0.802223\pi\)
\(234\) 3.80130i 0.248499i
\(235\) 0.563427 1.80295i 0.0367539 0.117612i
\(236\) −10.4090 −0.677569
\(237\) 4.78694 + 4.78694i 0.310945 + 0.310945i
\(238\) 0.638854 + 0.638854i 0.0414108 + 0.0414108i
\(239\) 19.3650i 1.25262i 0.779574 + 0.626310i \(0.215436\pi\)
−0.779574 + 0.626310i \(0.784564\pi\)
\(240\) −2.13428 0.666968i −0.137767 0.0430526i
\(241\) 20.0648i 1.29248i −0.763132 0.646242i \(-0.776339\pi\)
0.763132 0.646242i \(-0.223661\pi\)
\(242\) −7.56230 + 7.56230i −0.486123 + 0.486123i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) −9.12081 −0.583900
\(245\) 7.23051 + 13.8038i 0.461940 + 0.881891i
\(246\) −2.27486 −0.145040
\(247\) 2.91461 + 2.91461i 0.185452 + 0.185452i
\(248\) 1.73669 + 1.73669i 0.110280 + 0.110280i
\(249\) 0.270072 0.0171151
\(250\) −6.87369 8.81773i −0.434731 0.557682i
\(251\) 29.2252i 1.84468i −0.386381 0.922339i \(-0.626275\pi\)
0.386381 0.922339i \(-0.373725\pi\)
\(252\) 0.124800 + 0.124800i 0.00786169 + 0.00786169i
\(253\) 0.0409684 + 2.64955i 0.00257566 + 0.166576i
\(254\) 20.9913i 1.31711i
\(255\) −5.31121 10.1396i −0.332601 0.634969i
\(256\) 1.00000 0.0625000
\(257\) 2.47796 2.47796i 0.154571 0.154571i −0.625585 0.780156i \(-0.715140\pi\)
0.780156 + 0.625585i \(0.215140\pi\)
\(258\) 1.06804 1.06804i 0.0664930 0.0664930i
\(259\) 1.94575i 0.120903i
\(260\) −2.53535 + 8.11305i −0.157236 + 0.503150i
\(261\) 8.68275 0.537449
\(262\) 6.15090 6.15090i 0.380004 0.380004i
\(263\) 6.69369 6.69369i 0.412751 0.412751i −0.469945 0.882696i \(-0.655726\pi\)
0.882696 + 0.469945i \(0.155726\pi\)
\(264\) −0.552534 −0.0340061
\(265\) 5.61504 17.9680i 0.344929 1.10376i
\(266\) −0.191379 −0.0117342
\(267\) −6.19562 6.19562i −0.379166 0.379166i
\(268\) −5.38491 + 5.38491i −0.328935 + 0.328935i
\(269\) 8.21211i 0.500701i −0.968155 0.250350i \(-0.919454\pi\)
0.968155 0.250350i \(-0.0805459\pi\)
\(270\) −1.03755 1.98078i −0.0631431 0.120547i
\(271\) 8.60224 0.522549 0.261274 0.965265i \(-0.415857\pi\)
0.261274 + 0.965265i \(0.415857\pi\)
\(272\) 3.61968 + 3.61968i 0.219476 + 0.219476i
\(273\) 0.474405 0.474405i 0.0287123 0.0287123i
\(274\) 9.80202 0.592161
\(275\) −2.27109 1.57306i −0.136952 0.0948592i
\(276\) 3.33833 3.44319i 0.200944 0.207256i
\(277\) −9.28544 + 9.28544i −0.557908 + 0.557908i −0.928711 0.370803i \(-0.879082\pi\)
0.370803 + 0.928711i \(0.379082\pi\)
\(278\) 1.46728 + 1.46728i 0.0880017 + 0.0880017i
\(279\) 2.45605i 0.147040i
\(280\) −0.183121 0.349597i −0.0109436 0.0208924i
\(281\) 15.2296i 0.908521i −0.890869 0.454261i \(-0.849903\pi\)
0.890869 0.454261i \(-0.150097\pi\)
\(282\) −0.597335 + 0.597335i −0.0355708 + 0.0355708i
\(283\) −11.6676 + 11.6676i −0.693566 + 0.693566i −0.963015 0.269449i \(-0.913158\pi\)
0.269449 + 0.963015i \(0.413158\pi\)
\(284\) 8.16755i 0.484655i
\(285\) 2.31428 + 0.723217i 0.137086 + 0.0428397i
\(286\) 2.10035i 0.124196i
\(287\) −0.283904 0.283904i −0.0167583 0.0167583i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 9.20422i 0.541425i
\(290\) −18.5314 5.79112i −1.08820 0.340066i
\(291\) 2.30492i 0.135117i
\(292\) 3.12378 3.12378i 0.182805 0.182805i
\(293\) 21.8568 21.8568i 1.27689 1.27689i 0.334484 0.942401i \(-0.391438\pi\)
0.942401 0.334484i \(-0.108562\pi\)
\(294\) 6.96885i 0.406432i
\(295\) 10.7998 + 20.6180i 0.628790 + 1.20042i
\(296\) 11.0244i 0.640782i
\(297\) −0.390701 0.390701i −0.0226708 0.0226708i
\(298\) 8.70740 8.70740i 0.504406 0.504406i
\(299\) −13.0886 12.6900i −0.756934 0.733882i
\(300\) 0.893297 + 4.91955i 0.0515745 + 0.284031i
\(301\) 0.266583 0.0153656
\(302\) 7.10645 7.10645i 0.408930 0.408930i
\(303\) 4.19388 + 4.19388i 0.240932 + 0.240932i
\(304\) −1.08434 −0.0621909
\(305\) 9.46327 + 18.0663i 0.541865 + 1.03448i
\(306\) 5.11901i 0.292634i
\(307\) −6.33351 + 6.33351i −0.361473 + 0.361473i −0.864355 0.502882i \(-0.832273\pi\)
0.502882 + 0.864355i \(0.332273\pi\)
\(308\) −0.0689566 0.0689566i −0.00392917 0.00392917i
\(309\) 5.34381 0.303999
\(310\) 1.63810 5.24189i 0.0930381 0.297719i
\(311\) 21.7763 1.23482 0.617410 0.786641i \(-0.288182\pi\)
0.617410 + 0.786641i \(0.288182\pi\)
\(312\) 2.68793 2.68793i 0.152174 0.152174i
\(313\) 21.2955 21.2955i 1.20369 1.20369i 0.230658 0.973035i \(-0.425912\pi\)
0.973035 0.230658i \(-0.0740877\pi\)
\(314\) 4.81935 0.271972
\(315\) 0.117716 0.376689i 0.00663256 0.0212240i
\(316\) 6.76975i 0.380828i
\(317\) 13.1005 13.1005i 0.735797 0.735797i −0.235965 0.971762i \(-0.575825\pi\)
0.971762 + 0.235965i \(0.0758251\pi\)
\(318\) −5.95295 + 5.95295i −0.333825 + 0.333825i
\(319\) −4.79752 −0.268610
\(320\) −1.03755 1.98078i −0.0580006 0.110729i
\(321\) 12.8597i 0.717761i
\(322\) 0.846337 0.0130864i 0.0471645 0.000729278i
\(323\) −3.92495 3.92495i −0.218390 0.218390i
\(324\) 1.00000i 0.0555556i
\(325\) 18.7007 3.39569i 1.03733 0.188359i
\(326\) 15.5259 0.859900
\(327\) −9.61288 9.61288i −0.531594 0.531594i
\(328\) −1.60857 1.60857i −0.0888184 0.0888184i
\(329\) −0.149095 −0.00821989
\(330\) 0.573280 + 1.09445i 0.0315580 + 0.0602475i
\(331\) −18.0446 −0.991822 −0.495911 0.868373i \(-0.665166\pi\)
−0.495911 + 0.868373i \(0.665166\pi\)
\(332\) 0.190970 + 0.190970i 0.0104808 + 0.0104808i
\(333\) 7.79545 7.79545i 0.427188 0.427188i
\(334\) 0.555860i 0.0304153i
\(335\) 16.2534 + 5.07923i 0.888019 + 0.277508i
\(336\) 0.176495i 0.00962857i
\(337\) 11.3825 + 11.3825i 0.620045 + 0.620045i 0.945543 0.325498i \(-0.105532\pi\)
−0.325498 + 0.945543i \(0.605532\pi\)
\(338\) −1.02524 1.02524i −0.0557657 0.0557657i
\(339\) −13.1569 −0.714586
\(340\) 3.41421 10.9254i 0.185162 0.592513i
\(341\) 1.35705i 0.0734884i
\(342\) −0.766741 0.766741i −0.0414606 0.0414606i
\(343\) 1.74332 1.74332i 0.0941304 0.0941304i
\(344\) 1.51043 0.0814370
\(345\) −10.2839 3.04004i −0.553665 0.163670i
\(346\) 8.61380 0.463081
\(347\) 0.783931 0.783931i 0.0420836 0.0420836i −0.685752 0.727835i \(-0.740526\pi\)
0.727835 + 0.685752i \(0.240526\pi\)
\(348\) 6.13963 + 6.13963i 0.329119 + 0.329119i
\(349\) 2.79894i 0.149824i −0.997190 0.0749120i \(-0.976132\pi\)
0.997190 0.0749120i \(-0.0238676\pi\)
\(350\) −0.502479 + 0.725447i −0.0268586 + 0.0387768i
\(351\) 3.80130 0.202899
\(352\) −0.390701 0.390701i −0.0208244 0.0208244i
\(353\) −8.28523 8.28523i −0.440978 0.440978i 0.451362 0.892341i \(-0.350938\pi\)
−0.892341 + 0.451362i \(0.850938\pi\)
\(354\) 10.4090i 0.553233i
\(355\) −16.1781 + 8.47421i −0.858646 + 0.449764i
\(356\) 8.76193i 0.464381i
\(357\) −0.638854 + 0.638854i −0.0338118 + 0.0338118i
\(358\) −16.4155 16.4155i −0.867584 0.867584i
\(359\) 18.5465 0.978847 0.489424 0.872046i \(-0.337207\pi\)
0.489424 + 0.872046i \(0.337207\pi\)
\(360\) 0.666968 2.13428i 0.0351523 0.112486i
\(361\) −17.8242 −0.938117
\(362\) −4.56364 4.56364i −0.239860 0.239860i
\(363\) −7.56230 7.56230i −0.396918 0.396918i
\(364\) 0.670909 0.0351652
\(365\) −9.42859 2.94646i −0.493515 0.154225i
\(366\) 9.12081i 0.476753i
\(367\) −14.6933 14.6933i −0.766985 0.766985i 0.210590 0.977574i \(-0.432462\pi\)
−0.977574 + 0.210590i \(0.932462\pi\)
\(368\) 4.79526 0.0741463i 0.249970 0.00386514i
\(369\) 2.27486i 0.118425i
\(370\) −21.8370 + 11.4384i −1.13525 + 0.594652i
\(371\) −1.48586 −0.0771422
\(372\) −1.73669 + 1.73669i −0.0900430 + 0.0900430i
\(373\) −3.14679 + 3.14679i −0.162935 + 0.162935i −0.783865 0.620931i \(-0.786755\pi\)
0.620931 + 0.783865i \(0.286755\pi\)
\(374\) 2.82843i 0.146254i
\(375\) 8.81773 6.87369i 0.455346 0.354956i
\(376\) −0.844759 −0.0435651
\(377\) 23.3386 23.3386i 1.20200 1.20200i
\(378\) −0.124800 + 0.124800i −0.00641904 + 0.00641904i
\(379\) −16.5615 −0.850706 −0.425353 0.905028i \(-0.639850\pi\)
−0.425353 + 0.905028i \(0.639850\pi\)
\(380\) 1.12505 + 2.14783i 0.0577138 + 0.110181i
\(381\) 20.9913 1.07541
\(382\) −16.0318 16.0318i −0.820260 0.820260i
\(383\) 11.2204 11.2204i 0.573338 0.573338i −0.359722 0.933060i \(-0.617128\pi\)
0.933060 + 0.359722i \(0.117128\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −0.0650423 + 0.208134i −0.00331486 + 0.0106075i
\(386\) −10.0909 −0.513612
\(387\) 1.06804 + 1.06804i 0.0542913 + 0.0542913i
\(388\) −1.62982 + 1.62982i −0.0827418 + 0.0827418i
\(389\) −26.6584 −1.35164 −0.675818 0.737068i \(-0.736210\pi\)
−0.675818 + 0.737068i \(0.736210\pi\)
\(390\) −8.11305 2.53535i −0.410820 0.128382i
\(391\) 17.6257 + 17.0889i 0.891370 + 0.864224i
\(392\) 4.92772 4.92772i 0.248887 0.248887i
\(393\) 6.15090 + 6.15090i 0.310272 + 0.310272i
\(394\) 3.42142i 0.172369i
\(395\) 13.4094 7.02393i 0.674700 0.353412i
\(396\) 0.552534i 0.0277659i
\(397\) 1.03788 1.03788i 0.0520899 0.0520899i −0.680582 0.732672i \(-0.738273\pi\)
0.732672 + 0.680582i \(0.238273\pi\)
\(398\) −16.0731 + 16.0731i −0.805672 + 0.805672i
\(399\) 0.191379i 0.00958095i
\(400\) −2.84699 + 4.11031i −0.142350 + 0.205515i
\(401\) 24.1332i 1.20516i 0.798060 + 0.602578i \(0.205860\pi\)
−0.798060 + 0.602578i \(0.794140\pi\)
\(402\) −5.38491 5.38491i −0.268575 0.268575i
\(403\) 6.60168 + 6.60168i 0.328853 + 0.328853i
\(404\) 5.93104i 0.295080i
\(405\) 1.98078 1.03755i 0.0984258 0.0515561i
\(406\) 1.53246i 0.0760546i
\(407\) −4.30726 + 4.30726i −0.213503 + 0.213503i
\(408\) −3.61968 + 3.61968i −0.179201 + 0.179201i
\(409\) 17.2612i 0.853511i 0.904367 + 0.426756i \(0.140344\pi\)
−0.904367 + 0.426756i \(0.859656\pi\)
\(410\) −1.51726 + 4.85519i −0.0749321 + 0.239781i
\(411\) 9.80202i 0.483498i
\(412\) 3.77864 + 3.77864i 0.186160 + 0.186160i
\(413\) 1.29905 1.29905i 0.0639220 0.0639220i
\(414\) 3.44319 + 3.33833i 0.169224 + 0.164070i
\(415\) 0.180129 0.576409i 0.00884220 0.0282948i
\(416\) 3.80130 0.186374
\(417\) −1.46728 + 1.46728i −0.0718531 + 0.0718531i
\(418\) 0.423651 + 0.423651i 0.0207214 + 0.0207214i
\(419\) −8.83329 −0.431534 −0.215767 0.976445i \(-0.569225\pi\)
−0.215767 + 0.976445i \(0.569225\pi\)
\(420\) 0.349597 0.183121i 0.0170586 0.00893540i
\(421\) 22.9157i 1.11684i 0.829558 + 0.558421i \(0.188592\pi\)
−0.829558 + 0.558421i \(0.811408\pi\)
\(422\) 15.9836 15.9836i 0.778067 0.778067i
\(423\) −0.597335 0.597335i −0.0290434 0.0290434i
\(424\) −8.41875 −0.408851
\(425\) −25.1832 + 4.57279i −1.22157 + 0.221813i
\(426\) 8.16755 0.395719
\(427\) 1.13828 1.13828i 0.0550853 0.0550853i
\(428\) 9.09321 9.09321i 0.439537 0.439537i
\(429\) −2.10035 −0.101406
\(430\) −1.56714 2.99183i −0.0755743 0.144279i
\(431\) 4.11877i 0.198394i −0.995068 0.0991970i \(-0.968373\pi\)
0.995068 0.0991970i \(-0.0316274\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −13.2007 + 13.2007i −0.634383 + 0.634383i −0.949164 0.314781i \(-0.898069\pi\)
0.314781 + 0.949164i \(0.398069\pi\)
\(434\) −0.433479 −0.0208076
\(435\) 5.79112 18.5314i 0.277663 0.888514i
\(436\) 13.5947i 0.651067i
\(437\) −5.19967 + 0.0803995i −0.248734 + 0.00384603i
\(438\) 3.12378 + 3.12378i 0.149260 + 0.149260i
\(439\) 13.3446i 0.636905i 0.947939 + 0.318452i \(0.103163\pi\)
−0.947939 + 0.318452i \(0.896837\pi\)
\(440\) −0.368523 + 1.17926i −0.0175686 + 0.0562192i
\(441\) 6.96885 0.331850
\(442\) 13.7595 + 13.7595i 0.654473 + 0.654473i
\(443\) −17.1528 17.1528i −0.814955 0.814955i 0.170417 0.985372i \(-0.445489\pi\)
−0.985372 + 0.170417i \(0.945489\pi\)
\(444\) 11.0244 0.523197
\(445\) −17.3555 + 9.09091i −0.822728 + 0.430950i
\(446\) −15.0266 −0.711531
\(447\) 8.70740 + 8.70740i 0.411846 + 0.411846i
\(448\) −0.124800 + 0.124800i −0.00589627 + 0.00589627i
\(449\) 7.35156i 0.346942i 0.984839 + 0.173471i \(0.0554982\pi\)
−0.984839 + 0.173471i \(0.944502\pi\)
\(450\) −4.91955 + 0.893297i −0.231910 + 0.0421104i
\(451\) 1.25694i 0.0591870i
\(452\) −9.30335 9.30335i −0.437593 0.437593i
\(453\) 7.10645 + 7.10645i 0.333890 + 0.333890i
\(454\) 6.59205 0.309380
\(455\) −0.696100 1.32893i −0.0326337 0.0623010i
\(456\) 1.08434i 0.0507787i
\(457\) 1.61697 + 1.61697i 0.0756388 + 0.0756388i 0.743914 0.668275i \(-0.232967\pi\)
−0.668275 + 0.743914i \(0.732967\pi\)
\(458\) 4.69415 4.69415i 0.219343 0.219343i
\(459\) −5.11901 −0.238935
\(460\) −5.12217 9.42143i −0.238822 0.439276i
\(461\) −19.4223 −0.904586 −0.452293 0.891869i \(-0.649394\pi\)
−0.452293 + 0.891869i \(0.649394\pi\)
\(462\) 0.0689566 0.0689566i 0.00320815 0.00320815i
\(463\) −16.6725 16.6725i −0.774836 0.774836i 0.204112 0.978948i \(-0.434569\pi\)
−0.978948 + 0.204112i \(0.934569\pi\)
\(464\) 8.68275i 0.403087i
\(465\) 5.24189 + 1.63810i 0.243087 + 0.0759653i
\(466\) 4.98618 0.230980
\(467\) 18.7427 + 18.7427i 0.867310 + 0.867310i 0.992174 0.124864i \(-0.0398495\pi\)
−0.124864 + 0.992174i \(0.539850\pi\)
\(468\) 2.68793 + 2.68793i 0.124249 + 0.124249i
\(469\) 1.34408i 0.0620637i
\(470\) 0.876477 + 1.67328i 0.0404289 + 0.0771828i
\(471\) 4.81935i 0.222064i
\(472\) 7.36028 7.36028i 0.338784 0.338784i
\(473\) −0.590127 0.590127i −0.0271341 0.0271341i
\(474\) −6.76975 −0.310945
\(475\) 3.08710 4.45695i 0.141646 0.204499i
\(476\) −0.903477 −0.0414108
\(477\) −5.95295 5.95295i −0.272567 0.272567i
\(478\) −13.6932 13.6932i −0.626310 0.626310i
\(479\) 4.02931 0.184104 0.0920520 0.995754i \(-0.470657\pi\)
0.0920520 + 0.995754i \(0.470657\pi\)
\(480\) 1.98078 1.03755i 0.0904099 0.0473573i
\(481\) 41.9072i 1.91081i
\(482\) 14.1879 + 14.1879i 0.646242 + 0.646242i
\(483\) 0.0130864 + 0.846337i 0.000595453 + 0.0385097i
\(484\) 10.6947i 0.486123i
\(485\) 4.91935 + 1.53731i 0.223376 + 0.0698056i
\(486\) −1.00000 −0.0453609
\(487\) −15.4120 + 15.4120i −0.698385 + 0.698385i −0.964062 0.265677i \(-0.914404\pi\)
0.265677 + 0.964062i \(0.414404\pi\)
\(488\) 6.44939 6.44939i 0.291950 0.291950i
\(489\) 15.5259i 0.702105i
\(490\) −14.8735 4.64800i −0.671915 0.209975i
\(491\) 2.44078 0.110151 0.0550755 0.998482i \(-0.482460\pi\)
0.0550755 + 0.998482i \(0.482460\pi\)
\(492\) 1.60857 1.60857i 0.0725199 0.0725199i
\(493\) −31.4288 + 31.4288i −1.41548 + 1.41548i
\(494\) −4.12189 −0.185452
\(495\) −1.09445 + 0.573280i −0.0491919 + 0.0257670i
\(496\) −2.45605 −0.110280
\(497\) 1.01931 + 1.01931i 0.0457225 + 0.0457225i
\(498\) −0.190970 + 0.190970i −0.00855756 + 0.00855756i
\(499\) 42.3741i 1.89693i −0.316889 0.948463i \(-0.602638\pi\)
0.316889 0.948463i \(-0.397362\pi\)
\(500\) 11.0955 + 1.37464i 0.496206 + 0.0614758i
\(501\) −0.555860 −0.0248340
\(502\) 20.6653 + 20.6653i 0.922339 + 0.922339i
\(503\) 28.9820 28.9820i 1.29224 1.29224i 0.358846 0.933397i \(-0.383170\pi\)
0.933397 0.358846i \(-0.116830\pi\)
\(504\) −0.176495 −0.00786169
\(505\) 11.7481 6.15373i 0.522784 0.273838i
\(506\) −1.90248 1.84454i −0.0845756 0.0819999i
\(507\) 1.02524 1.02524i 0.0455325 0.0455325i
\(508\) 14.8431 + 14.8431i 0.658554 + 0.658554i
\(509\) 3.86372i 0.171257i −0.996327 0.0856283i \(-0.972710\pi\)
0.996327 0.0856283i \(-0.0272897\pi\)
\(510\) 10.9254 + 3.41421i 0.483785 + 0.151184i
\(511\) 0.779698i 0.0344918i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0.766741 0.766741i 0.0338524 0.0338524i
\(514\) 3.50437i 0.154571i
\(515\) 3.56415 11.4052i 0.157055 0.502573i
\(516\) 1.51043i 0.0664930i
\(517\) 0.330048 + 0.330048i 0.0145155 + 0.0145155i
\(518\) 1.37586 + 1.37586i 0.0604516 + 0.0604516i
\(519\) 8.61380i 0.378104i
\(520\) −3.94403 7.52955i −0.172957 0.330193i
\(521\) 19.8403i 0.869221i 0.900619 + 0.434610i \(0.143114\pi\)
−0.900619 + 0.434610i \(0.856886\pi\)
\(522\) −6.13963 + 6.13963i −0.268724 + 0.268724i
\(523\) −13.6045 + 13.6045i −0.594883 + 0.594883i −0.938946 0.344063i \(-0.888197\pi\)
0.344063 + 0.938946i \(0.388197\pi\)
\(524\) 8.69869i 0.380004i
\(525\) −0.725447 0.502479i −0.0316611 0.0219300i
\(526\) 9.46631i 0.412751i
\(527\) −8.89011 8.89011i −0.387259 0.387259i
\(528\) 0.390701 0.390701i 0.0170031 0.0170031i
\(529\) 22.9890 0.711101i 0.999522 0.0309175i
\(530\) 8.73484 + 16.6757i 0.379417 + 0.724346i
\(531\) 10.4090 0.451712
\(532\) 0.135326 0.135326i 0.00586711 0.00586711i
\(533\) −6.11466 6.11466i −0.264855 0.264855i
\(534\) 8.76193 0.379166
\(535\) −27.4463 8.57704i −1.18661 0.370818i
\(536\) 7.61541i 0.328935i
\(537\) 16.4155 16.4155i 0.708379 0.708379i
\(538\) 5.80684 + 5.80684i 0.250350 + 0.250350i
\(539\) −3.85053 −0.165854
\(540\) 2.13428 + 0.666968i 0.0918448 + 0.0287017i
\(541\) −21.3249 −0.916828 −0.458414 0.888739i \(-0.651582\pi\)
−0.458414 + 0.888739i \(0.651582\pi\)
\(542\) −6.08270 + 6.08270i −0.261274 + 0.261274i
\(543\) 4.56364 4.56364i 0.195845 0.195845i
\(544\) −5.11901 −0.219476
\(545\) −26.9281 + 14.1051i −1.15347 + 0.604196i
\(546\) 0.670909i 0.0287123i
\(547\) 21.0991 21.0991i 0.902131 0.902131i −0.0934889 0.995620i \(-0.529802\pi\)
0.995620 + 0.0934889i \(0.0298020\pi\)
\(548\) −6.93107 + 6.93107i −0.296081 + 0.296081i
\(549\) 9.12081 0.389267
\(550\) 2.71822 0.493577i 0.115905 0.0210462i
\(551\) 9.41502i 0.401093i
\(552\) 0.0741463 + 4.79526i 0.00315588 + 0.204100i
\(553\) −0.844868 0.844868i −0.0359274 0.0359274i
\(554\) 13.1316i 0.557908i
\(555\) −11.4384 21.8370i −0.485532 0.926929i
\(556\) −2.07505 −0.0880017
\(557\) 27.8064 + 27.8064i 1.17820 + 1.17820i 0.980203 + 0.197993i \(0.0634423\pi\)
0.197993 + 0.980203i \(0.436558\pi\)
\(558\) −1.73669 1.73669i −0.0735198 0.0735198i
\(559\) 5.74161 0.242844
\(560\) 0.376689 + 0.117716i 0.0159180 + 0.00497442i
\(561\) 2.82843 0.119416
\(562\) 10.7689 + 10.7689i 0.454261 + 0.454261i
\(563\) −22.4843 + 22.4843i −0.947602 + 0.947602i −0.998694 0.0510924i \(-0.983730\pi\)
0.0510924 + 0.998694i \(0.483730\pi\)
\(564\) 0.844759i 0.0355708i
\(565\) −8.77525 + 28.0806i −0.369178 + 1.18136i
\(566\) 16.5005i 0.693566i
\(567\) −0.124800 0.124800i −0.00524113 0.00524113i
\(568\) 5.77533 + 5.77533i 0.242327 + 0.242327i
\(569\) −33.7165 −1.41347 −0.706735 0.707479i \(-0.749832\pi\)
−0.706735 + 0.707479i \(0.749832\pi\)
\(570\) −2.14783 + 1.12505i −0.0899628 + 0.0471231i
\(571\) 36.2733i 1.51799i 0.651097 + 0.758995i \(0.274309\pi\)
−0.651097 + 0.758995i \(0.725691\pi\)
\(572\) −1.48517 1.48517i −0.0620982 0.0620982i
\(573\) 16.0318 16.0318i 0.669740 0.669740i
\(574\) 0.401501 0.0167583
\(575\) −13.3473 + 19.9211i −0.556621 + 0.830766i
\(576\) −1.00000 −0.0416667
\(577\) −21.9088 + 21.9088i −0.912076 + 0.912076i −0.996435 0.0843592i \(-0.973116\pi\)
0.0843592 + 0.996435i \(0.473116\pi\)
\(578\) −6.50837 6.50837i −0.270712 0.270712i
\(579\) 10.0909i 0.419362i
\(580\) 17.1986 9.00876i 0.714135 0.374068i
\(581\) −0.0476662 −0.00197753
\(582\) −1.62982 1.62982i −0.0675584 0.0675584i
\(583\) 3.28921 + 3.28921i 0.136225 + 0.136225i
\(584\) 4.41769i 0.182805i
\(585\) 2.53535 8.11305i 0.104824 0.335433i
\(586\) 30.9101i 1.27689i
\(587\) 28.8834 28.8834i 1.19215 1.19215i 0.215684 0.976463i \(-0.430802\pi\)
0.976463 0.215684i \(-0.0691980\pi\)
\(588\) 4.92772 + 4.92772i 0.203216 + 0.203216i
\(589\) 2.66318 0.109734
\(590\) −22.2157 6.94248i −0.914608 0.285817i
\(591\) −3.42142 −0.140738
\(592\) 7.79545 + 7.79545i 0.320391 + 0.320391i
\(593\) −21.3435 21.3435i −0.876474 0.876474i 0.116694 0.993168i \(-0.462770\pi\)
−0.993168 + 0.116694i \(0.962770\pi\)
\(594\) 0.552534 0.0226708
\(595\) 0.937399 + 1.78959i 0.0384296 + 0.0733660i
\(596\) 12.3141i 0.504406i
\(597\) −16.0731 16.0731i −0.657828 0.657828i
\(598\) 18.2282 0.281853i 0.745408 0.0115258i
\(599\) 38.3444i 1.56671i 0.621576 + 0.783354i \(0.286493\pi\)
−0.621576 + 0.783354i \(0.713507\pi\)
\(600\) −4.11031 2.84699i −0.167803 0.116228i
\(601\) 16.2980 0.664808 0.332404 0.943137i \(-0.392140\pi\)
0.332404 + 0.943137i \(0.392140\pi\)
\(602\) −0.188502 + 0.188502i −0.00768279 + 0.00768279i
\(603\) 5.38491 5.38491i 0.219290 0.219290i
\(604\) 10.0500i 0.408930i
\(605\) −21.1839 + 11.0963i −0.861247 + 0.451127i
\(606\) −5.93104 −0.240932
\(607\) 1.17706 1.17706i 0.0477754 0.0477754i −0.682815 0.730591i \(-0.739245\pi\)
0.730591 + 0.682815i \(0.239245\pi\)
\(608\) 0.766741 0.766741i 0.0310954 0.0310954i
\(609\) −1.53246 −0.0620984
\(610\) −19.4664 6.08329i −0.788171 0.246305i
\(611\) −3.21119 −0.129911
\(612\) −3.61968 3.61968i −0.146317 0.146317i
\(613\) 20.0004 20.0004i 0.807808 0.807808i −0.176494 0.984302i \(-0.556476\pi\)
0.984302 + 0.176494i \(0.0564756\pi\)
\(614\) 8.95694i 0.361473i
\(615\) −4.85519 1.51726i −0.195780 0.0611818i
\(616\) 0.0975193 0.00392917
\(617\) 18.9554 + 18.9554i 0.763117 + 0.763117i 0.976885 0.213767i \(-0.0685734\pi\)
−0.213767 + 0.976885i \(0.568573\pi\)
\(618\) −3.77864 + 3.77864i −0.151999 + 0.151999i
\(619\) −3.91634 −0.157411 −0.0787055 0.996898i \(-0.525079\pi\)
−0.0787055 + 0.996898i \(0.525079\pi\)
\(620\) 2.54826 + 4.86489i 0.102341 + 0.195379i
\(621\) −3.33833 + 3.44319i −0.133963 + 0.138170i
\(622\) −15.3982 + 15.3982i −0.617410 + 0.617410i
\(623\) 1.09349 + 1.09349i 0.0438099 + 0.0438099i
\(624\) 3.80130i 0.152174i
\(625\) −8.78925 23.4040i −0.351570 0.936162i
\(626\) 30.1164i 1.20369i
\(627\) −0.423651 + 0.423651i −0.0169190 + 0.0169190i
\(628\) −3.40779 + 3.40779i −0.135986 + 0.135986i
\(629\) 56.4342i 2.25018i
\(630\) 0.183121 + 0.349597i 0.00729573 + 0.0139283i
\(631\) 34.6601i 1.37980i 0.723906 + 0.689899i \(0.242345\pi\)
−0.723906 + 0.689899i \(0.757655\pi\)
\(632\) −4.78694 4.78694i −0.190414 0.190414i
\(633\) 15.9836 + 15.9836i 0.635289 + 0.635289i
\(634\) 18.5269i 0.735797i
\(635\) 14.0005 44.8012i 0.555593 1.77788i
\(636\) 8.41875i 0.333825i
\(637\) 18.7318 18.7318i 0.742179 0.742179i
\(638\) 3.39236 3.39236i 0.134305 0.134305i
\(639\) 8.16755i 0.323103i
\(640\) 2.13428 + 0.666968i 0.0843648 + 0.0263642i
\(641\) 39.3379i 1.55375i −0.629653 0.776876i \(-0.716803\pi\)
0.629653 0.776876i \(-0.283197\pi\)
\(642\) 9.09321 + 9.09321i 0.358880 + 0.358880i
\(643\) 16.8975 16.8975i 0.666371 0.666371i −0.290503 0.956874i \(-0.593823\pi\)
0.956874 + 0.290503i \(0.0938226\pi\)
\(644\) −0.589197 + 0.607704i −0.0232176 + 0.0239469i
\(645\) 2.99183 1.56714i 0.117803 0.0617062i
\(646\) 5.55072 0.218390
\(647\) −29.2297 + 29.2297i −1.14914 + 1.14914i −0.162414 + 0.986723i \(0.551928\pi\)
−0.986723 + 0.162414i \(0.948072\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) −5.75134 −0.225760
\(650\) −10.8223 + 15.6245i −0.424485 + 0.612844i
\(651\) 0.433479i 0.0169894i
\(652\) −10.9785 + 10.9785i −0.429950 + 0.429950i
\(653\) −17.2954 17.2954i −0.676820 0.676820i 0.282459 0.959279i \(-0.408850\pi\)
−0.959279 + 0.282459i \(0.908850\pi\)
\(654\) 13.5947 0.531594
\(655\) 17.2302 9.02529i 0.673240 0.352647i
\(656\) 2.27486 0.0888184
\(657\) −3.12378 + 3.12378i −0.121870 + 0.121870i
\(658\) 0.105426 0.105426i 0.00410995 0.00410995i
\(659\) −12.9859 −0.505860 −0.252930 0.967485i \(-0.581394\pi\)
−0.252930 + 0.967485i \(0.581394\pi\)
\(660\) −1.17926 0.368523i −0.0459028 0.0143447i
\(661\) 30.6022i 1.19029i −0.803620 0.595143i \(-0.797095\pi\)
0.803620 0.595143i \(-0.202905\pi\)
\(662\) 12.7595 12.7595i 0.495911 0.495911i
\(663\) −13.7595 + 13.7595i −0.534375 + 0.534375i
\(664\) −0.270072 −0.0104808
\(665\) −0.408457 0.127644i −0.0158393 0.00494982i
\(666\) 11.0244i 0.427188i
\(667\) 0.643794 + 41.6360i 0.0249278 + 1.61215i
\(668\) −0.393053 0.393053i −0.0152077 0.0152077i
\(669\) 15.0266i 0.580963i
\(670\) −15.0845 + 7.90134i −0.582764 + 0.305255i
\(671\) −5.03956 −0.194550
\(672\) −0.124800 0.124800i −0.00481428 0.00481428i
\(673\) 6.26582 + 6.26582i 0.241530 + 0.241530i 0.817483 0.575953i \(-0.195369\pi\)
−0.575953 + 0.817483i \(0.695369\pi\)
\(674\) −16.0973 −0.620045
\(675\) −0.893297 4.91955i −0.0343830 0.189354i
\(676\) 1.44991 0.0557657
\(677\) 31.0473 + 31.0473i 1.19325 + 1.19325i 0.976150 + 0.217096i \(0.0696583\pi\)
0.217096 + 0.976150i \(0.430342\pi\)
\(678\) 9.30335 9.30335i 0.357293 0.357293i
\(679\) 0.406806i 0.0156118i
\(680\) 5.31121 + 10.1396i 0.203675 + 0.388837i
\(681\) 6.59205i 0.252608i
\(682\) 0.959580 + 0.959580i 0.0367442 + 0.0367442i
\(683\) 36.0336 + 36.0336i 1.37879 + 1.37879i 0.846669 + 0.532120i \(0.178605\pi\)
0.532120 + 0.846669i \(0.321395\pi\)
\(684\) 1.08434 0.0414606
\(685\) 20.9203 + 6.53763i 0.799322 + 0.249790i
\(686\) 2.46543i 0.0941304i
\(687\) 4.69415 + 4.69415i 0.179093 + 0.179093i
\(688\) −1.06804 + 1.06804i −0.0407185 + 0.0407185i
\(689\) −32.0022 −1.21919
\(690\) 9.42143 5.12217i 0.358668 0.194998i
\(691\) 13.8803 0.528031 0.264016 0.964518i \(-0.414953\pi\)
0.264016 + 0.964518i \(0.414953\pi\)
\(692\) −6.09087 + 6.09087i −0.231540 + 0.231540i
\(693\) 0.0689566 + 0.0689566i 0.00261944 + 0.00261944i
\(694\) 1.10865i 0.0420836i
\(695\) 2.15296 + 4.11022i 0.0816664 + 0.155910i
\(696\) −8.68275 −0.329119
\(697\) 8.23428 + 8.23428i 0.311896 + 0.311896i
\(698\) 1.97915 + 1.97915i 0.0749120 + 0.0749120i
\(699\) 4.98618i 0.188595i
\(700\) −0.157662 0.868275i −0.00595907 0.0328177i
\(701\) 18.1607i 0.685920i 0.939350 + 0.342960i \(0.111430\pi\)
−0.939350 + 0.342960i \(0.888570\pi\)
\(702\) −2.68793 + 2.68793i −0.101449 + 0.101449i
\(703\) −8.45289 8.45289i −0.318807 0.318807i
\(704\) 0.552534 0.0208244
\(705\) −1.67328 + 0.876477i −0.0630195 + 0.0330100i
\(706\) 11.7171 0.440978
\(707\) −0.740197 0.740197i −0.0278380 0.0278380i
\(708\) 7.36028 + 7.36028i 0.276616 + 0.276616i
\(709\) −7.89324 −0.296437 −0.148218 0.988955i \(-0.547354\pi\)
−0.148218 + 0.988955i \(0.547354\pi\)
\(710\) 5.44749 17.4318i 0.204441 0.654205i
\(711\) 6.76975i 0.253885i
\(712\) 6.19562 + 6.19562i 0.232191 + 0.232191i
\(713\) −11.7774 + 0.182107i −0.441066 + 0.00681995i
\(714\) 0.903477i 0.0338118i
\(715\) −1.40087 + 4.48274i −0.0523895 + 0.167645i
\(716\) 23.2150 0.867584
\(717\) 13.6932 13.6932i 0.511380 0.511380i
\(718\) −13.1144 + 13.1144i −0.489424 + 0.489424i
\(719\) 21.8935i 0.816490i 0.912872 + 0.408245i \(0.133859\pi\)
−0.912872 + 0.408245i \(0.866141\pi\)
\(720\) 1.03755 + 1.98078i 0.0386671 + 0.0738194i
\(721\) −0.943153 −0.0351249
\(722\) 12.6036 12.6036i 0.469058 0.469058i
\(723\) −14.1879 + 14.1879i −0.527655 + 0.527655i
\(724\) 6.45396 0.239860
\(725\) −35.6888 24.7197i −1.32545 0.918068i
\(726\) 10.6947 0.396918
\(727\) 2.54984 + 2.54984i 0.0945684 + 0.0945684i 0.752808 0.658240i \(-0.228699\pi\)
−0.658240 + 0.752808i \(0.728699\pi\)
\(728\) −0.474405 + 0.474405i −0.0175826 + 0.0175826i
\(729\) 1.00000i 0.0370370i
\(730\) 8.75048 4.58356i 0.323870 0.169645i
\(731\) −7.73190 −0.285975
\(732\) 6.44939 + 6.44939i 0.238376 + 0.238376i
\(733\) −22.3443 + 22.3443i −0.825304 + 0.825304i −0.986863 0.161559i \(-0.948348\pi\)
0.161559 + 0.986863i \(0.448348\pi\)
\(734\) 20.7795 0.766985
\(735\) 4.64800 14.8735i 0.171444 0.548617i
\(736\) −3.33833 + 3.44319i −0.123052 + 0.126918i
\(737\) −2.97535 + 2.97535i −0.109598 + 0.109598i
\(738\) 1.60857 + 1.60857i 0.0592123 + 0.0592123i
\(739\) 11.6646i 0.429089i 0.976714 + 0.214545i \(0.0688267\pi\)
−0.976714 + 0.214545i \(0.931173\pi\)
\(740\) 7.35295 23.5292i 0.270300 0.864952i
\(741\) 4.12189i 0.151421i
\(742\) 1.05066 1.05066i 0.0385711 0.0385711i
\(743\) 1.05995 1.05995i 0.0388859 0.0388859i −0.687396 0.726282i \(-0.741246\pi\)
0.726282 + 0.687396i \(0.241246\pi\)
\(744\) 2.45605i 0.0900430i
\(745\) 24.3916 12.7765i 0.893639 0.468094i
\(746\) 4.45023i 0.162935i
\(747\) −0.190970 0.190970i −0.00698722 0.00698722i
\(748\) 2.00000 + 2.00000i 0.0731272 + 0.0731272i
\(749\) 2.26967i 0.0829321i
\(750\) −1.37464 + 11.0955i −0.0501947 + 0.405151i
\(751\) 20.0466i 0.731510i 0.930711 + 0.365755i \(0.119189\pi\)
−0.930711 + 0.365755i \(0.880811\pi\)
\(752\) 0.597335 0.597335i 0.0217826 0.0217826i
\(753\) −20.6653 + 20.6653i −0.753087 + 0.753087i
\(754\) 33.0058i 1.20200i
\(755\) 19.9069 10.4274i 0.724487 0.379491i
\(756\) 0.176495i 0.00641904i
\(757\) −35.9979 35.9979i −1.30837 1.30837i −0.922595 0.385770i \(-0.873936\pi\)
−0.385770 0.922595i \(-0.626064\pi\)
\(758\) 11.7107 11.7107i 0.425353 0.425353i
\(759\) 1.84454 1.90248i 0.0669527 0.0690557i
\(760\) −2.31428 0.723217i −0.0839476 0.0262338i
\(761\) −13.7196 −0.497334 −0.248667 0.968589i \(-0.579992\pi\)
−0.248667 + 0.968589i \(0.579992\pi\)
\(762\) −14.8431 + 14.8431i −0.537707 + 0.537707i
\(763\) 1.69662 + 1.69662i 0.0614218 + 0.0614218i
\(764\) 22.6724 0.820260
\(765\) −3.41421 + 10.9254i −0.123441 + 0.395008i
\(766\) 15.8681i 0.573338i
\(767\) 27.9787 27.9787i 1.01025 1.01025i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 2.88500 0.104036 0.0520179 0.998646i \(-0.483435\pi\)
0.0520179 + 0.998646i \(0.483435\pi\)
\(770\) −0.101181 0.193165i −0.00364630 0.00696117i
\(771\) −3.50437 −0.126207
\(772\) 7.13533 7.13533i 0.256806 0.256806i
\(773\) 26.4041 26.4041i 0.949689 0.949689i −0.0491046 0.998794i \(-0.515637\pi\)
0.998794 + 0.0491046i \(0.0156368\pi\)
\(774\) −1.51043 −0.0542913
\(775\) 6.99235 10.0951i 0.251173 0.362627i
\(776\) 2.30492i 0.0827418i
\(777\) −1.37586 + 1.37586i −0.0493585 + 0.0493585i
\(778\) 18.8504 18.8504i 0.675818 0.675818i
\(779\) −2.46671 −0.0883791