Properties

Label 210.2.b.a.41.3
Level $210$
Weight $2$
Character 210.41
Analytic conductor $1.677$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 41.3
Root \(0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 210.41
Dual form 210.2.b.a.41.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-1.61803 - 0.618034i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.618034 - 1.61803i) q^{6} +(2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(2.23607 + 2.00000i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-1.61803 - 0.618034i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(0.618034 - 1.61803i) q^{6} +(2.61803 + 0.381966i) q^{7} -1.00000i q^{8} +(2.23607 + 2.00000i) q^{9} +1.00000i q^{10} +4.47214i q^{11} +(1.61803 + 0.618034i) q^{12} -1.23607i q^{13} +(-0.381966 + 2.61803i) q^{14} +(-1.61803 - 0.618034i) q^{15} +1.00000 q^{16} +5.23607 q^{17} +(-2.00000 + 2.23607i) q^{18} +8.47214i q^{19} -1.00000 q^{20} +(-4.00000 - 2.23607i) q^{21} -4.47214 q^{22} -4.00000i q^{23} +(-0.618034 + 1.61803i) q^{24} +1.00000 q^{25} +1.23607 q^{26} +(-2.38197 - 4.61803i) q^{27} +(-2.61803 - 0.381966i) q^{28} -7.70820i q^{29} +(0.618034 - 1.61803i) q^{30} -2.76393i q^{31} +1.00000i q^{32} +(2.76393 - 7.23607i) q^{33} +5.23607i q^{34} +(2.61803 + 0.381966i) q^{35} +(-2.23607 - 2.00000i) q^{36} +0.763932 q^{37} -8.47214 q^{38} +(-0.763932 + 2.00000i) q^{39} -1.00000i q^{40} -2.47214 q^{41} +(2.23607 - 4.00000i) q^{42} -4.94427 q^{43} -4.47214i q^{44} +(2.23607 + 2.00000i) q^{45} +4.00000 q^{46} -6.47214 q^{47} +(-1.61803 - 0.618034i) q^{48} +(6.70820 + 2.00000i) q^{49} +1.00000i q^{50} +(-8.47214 - 3.23607i) q^{51} +1.23607i q^{52} +0.472136i q^{53} +(4.61803 - 2.38197i) q^{54} +4.47214i q^{55} +(0.381966 - 2.61803i) q^{56} +(5.23607 - 13.7082i) q^{57} +7.70820 q^{58} +4.47214 q^{59} +(1.61803 + 0.618034i) q^{60} +7.23607i q^{61} +2.76393 q^{62} +(5.09017 + 6.09017i) q^{63} -1.00000 q^{64} -1.23607i q^{65} +(7.23607 + 2.76393i) q^{66} -12.0000 q^{67} -5.23607 q^{68} +(-2.47214 + 6.47214i) q^{69} +(-0.381966 + 2.61803i) q^{70} -7.23607i q^{71} +(2.00000 - 2.23607i) q^{72} -11.2361i q^{73} +0.763932i q^{74} +(-1.61803 - 0.618034i) q^{75} -8.47214i q^{76} +(-1.70820 + 11.7082i) q^{77} +(-2.00000 - 0.763932i) q^{78} -8.94427 q^{79} +1.00000 q^{80} +(1.00000 + 8.94427i) q^{81} -2.47214i q^{82} +14.6525 q^{83} +(4.00000 + 2.23607i) q^{84} +5.23607 q^{85} -4.94427i q^{86} +(-4.76393 + 12.4721i) q^{87} +4.47214 q^{88} -5.52786 q^{89} +(-2.00000 + 2.23607i) q^{90} +(0.472136 - 3.23607i) q^{91} +4.00000i q^{92} +(-1.70820 + 4.47214i) q^{93} -6.47214i q^{94} +8.47214i q^{95} +(0.618034 - 1.61803i) q^{96} +0.763932i q^{97} +(-2.00000 + 6.70820i) q^{98} +(-8.94427 + 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 4q^{4} + 4q^{5} - 2q^{6} + 6q^{7} + O(q^{10}) \) \( 4q - 2q^{3} - 4q^{4} + 4q^{5} - 2q^{6} + 6q^{7} + 2q^{12} - 6q^{14} - 2q^{15} + 4q^{16} + 12q^{17} - 8q^{18} - 4q^{20} - 16q^{21} + 2q^{24} + 4q^{25} - 4q^{26} - 14q^{27} - 6q^{28} - 2q^{30} + 20q^{33} + 6q^{35} + 12q^{37} - 16q^{38} - 12q^{39} + 8q^{41} + 16q^{43} + 16q^{46} - 8q^{47} - 2q^{48} - 16q^{51} + 14q^{54} + 6q^{56} + 12q^{57} + 4q^{58} + 2q^{60} + 20q^{62} - 2q^{63} - 4q^{64} + 20q^{66} - 48q^{67} - 12q^{68} + 8q^{69} - 6q^{70} + 8q^{72} - 2q^{75} + 20q^{77} - 8q^{78} + 4q^{80} + 4q^{81} - 4q^{83} + 16q^{84} + 12q^{85} - 28q^{87} - 40q^{89} - 8q^{90} - 16q^{91} + 20q^{93} - 2q^{96} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.61803 0.618034i −0.934172 0.356822i
\(4\) −1.00000 −0.500000
\(5\) 1.00000 0.447214
\(6\) 0.618034 1.61803i 0.252311 0.660560i
\(7\) 2.61803 + 0.381966i 0.989524 + 0.144370i
\(8\) 1.00000i 0.353553i
\(9\) 2.23607 + 2.00000i 0.745356 + 0.666667i
\(10\) 1.00000i 0.316228i
\(11\) 4.47214i 1.34840i 0.738549 + 0.674200i \(0.235511\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 1.61803 + 0.618034i 0.467086 + 0.178411i
\(13\) 1.23607i 0.342824i −0.985199 0.171412i \(-0.945167\pi\)
0.985199 0.171412i \(-0.0548329\pi\)
\(14\) −0.381966 + 2.61803i −0.102085 + 0.699699i
\(15\) −1.61803 0.618034i −0.417775 0.159576i
\(16\) 1.00000 0.250000
\(17\) 5.23607 1.26993 0.634967 0.772540i \(-0.281014\pi\)
0.634967 + 0.772540i \(0.281014\pi\)
\(18\) −2.00000 + 2.23607i −0.471405 + 0.527046i
\(19\) 8.47214i 1.94364i 0.235722 + 0.971821i \(0.424255\pi\)
−0.235722 + 0.971821i \(0.575745\pi\)
\(20\) −1.00000 −0.223607
\(21\) −4.00000 2.23607i −0.872872 0.487950i
\(22\) −4.47214 −0.953463
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) −0.618034 + 1.61803i −0.126156 + 0.330280i
\(25\) 1.00000 0.200000
\(26\) 1.23607 0.242413
\(27\) −2.38197 4.61803i −0.458410 0.888741i
\(28\) −2.61803 0.381966i −0.494762 0.0721848i
\(29\) 7.70820i 1.43138i −0.698419 0.715689i \(-0.746113\pi\)
0.698419 0.715689i \(-0.253887\pi\)
\(30\) 0.618034 1.61803i 0.112837 0.295411i
\(31\) 2.76393i 0.496417i −0.968707 0.248208i \(-0.920158\pi\)
0.968707 0.248208i \(-0.0798418\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.76393 7.23607i 0.481139 1.25964i
\(34\) 5.23607i 0.897978i
\(35\) 2.61803 + 0.381966i 0.442529 + 0.0645640i
\(36\) −2.23607 2.00000i −0.372678 0.333333i
\(37\) 0.763932 0.125590 0.0627948 0.998026i \(-0.479999\pi\)
0.0627948 + 0.998026i \(0.479999\pi\)
\(38\) −8.47214 −1.37436
\(39\) −0.763932 + 2.00000i −0.122327 + 0.320256i
\(40\) 1.00000i 0.158114i
\(41\) −2.47214 −0.386083 −0.193041 0.981191i \(-0.561835\pi\)
−0.193041 + 0.981191i \(0.561835\pi\)
\(42\) 2.23607 4.00000i 0.345033 0.617213i
\(43\) −4.94427 −0.753994 −0.376997 0.926214i \(-0.623043\pi\)
−0.376997 + 0.926214i \(0.623043\pi\)
\(44\) 4.47214i 0.674200i
\(45\) 2.23607 + 2.00000i 0.333333 + 0.298142i
\(46\) 4.00000 0.589768
\(47\) −6.47214 −0.944058 −0.472029 0.881583i \(-0.656478\pi\)
−0.472029 + 0.881583i \(0.656478\pi\)
\(48\) −1.61803 0.618034i −0.233543 0.0892055i
\(49\) 6.70820 + 2.00000i 0.958315 + 0.285714i
\(50\) 1.00000i 0.141421i
\(51\) −8.47214 3.23607i −1.18634 0.453140i
\(52\) 1.23607i 0.171412i
\(53\) 0.472136i 0.0648529i 0.999474 + 0.0324264i \(0.0103235\pi\)
−0.999474 + 0.0324264i \(0.989677\pi\)
\(54\) 4.61803 2.38197i 0.628435 0.324145i
\(55\) 4.47214i 0.603023i
\(56\) 0.381966 2.61803i 0.0510424 0.349850i
\(57\) 5.23607 13.7082i 0.693534 1.81570i
\(58\) 7.70820 1.01214
\(59\) 4.47214 0.582223 0.291111 0.956689i \(-0.405975\pi\)
0.291111 + 0.956689i \(0.405975\pi\)
\(60\) 1.61803 + 0.618034i 0.208887 + 0.0797878i
\(61\) 7.23607i 0.926484i 0.886232 + 0.463242i \(0.153314\pi\)
−0.886232 + 0.463242i \(0.846686\pi\)
\(62\) 2.76393 0.351020
\(63\) 5.09017 + 6.09017i 0.641301 + 0.767289i
\(64\) −1.00000 −0.125000
\(65\) 1.23607i 0.153315i
\(66\) 7.23607 + 2.76393i 0.890698 + 0.340217i
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) −5.23607 −0.634967
\(69\) −2.47214 + 6.47214i −0.297610 + 0.779154i
\(70\) −0.381966 + 2.61803i −0.0456537 + 0.312915i
\(71\) 7.23607i 0.858763i −0.903123 0.429382i \(-0.858732\pi\)
0.903123 0.429382i \(-0.141268\pi\)
\(72\) 2.00000 2.23607i 0.235702 0.263523i
\(73\) 11.2361i 1.31508i −0.753419 0.657541i \(-0.771597\pi\)
0.753419 0.657541i \(-0.228403\pi\)
\(74\) 0.763932i 0.0888053i
\(75\) −1.61803 0.618034i −0.186834 0.0713644i
\(76\) 8.47214i 0.971821i
\(77\) −1.70820 + 11.7082i −0.194668 + 1.33427i
\(78\) −2.00000 0.763932i −0.226455 0.0864983i
\(79\) −8.94427 −1.00631 −0.503155 0.864196i \(-0.667827\pi\)
−0.503155 + 0.864196i \(0.667827\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 2.47214i 0.273002i
\(83\) 14.6525 1.60832 0.804159 0.594414i \(-0.202616\pi\)
0.804159 + 0.594414i \(0.202616\pi\)
\(84\) 4.00000 + 2.23607i 0.436436 + 0.243975i
\(85\) 5.23607 0.567931
\(86\) 4.94427i 0.533155i
\(87\) −4.76393 + 12.4721i −0.510747 + 1.33715i
\(88\) 4.47214 0.476731
\(89\) −5.52786 −0.585952 −0.292976 0.956120i \(-0.594646\pi\)
−0.292976 + 0.956120i \(0.594646\pi\)
\(90\) −2.00000 + 2.23607i −0.210819 + 0.235702i
\(91\) 0.472136 3.23607i 0.0494933 0.339232i
\(92\) 4.00000i 0.417029i
\(93\) −1.70820 + 4.47214i −0.177132 + 0.463739i
\(94\) 6.47214i 0.667550i
\(95\) 8.47214i 0.869223i
\(96\) 0.618034 1.61803i 0.0630778 0.165140i
\(97\) 0.763932i 0.0775655i 0.999248 + 0.0387828i \(0.0123480\pi\)
−0.999248 + 0.0387828i \(0.987652\pi\)
\(98\) −2.00000 + 6.70820i −0.202031 + 0.677631i
\(99\) −8.94427 + 10.0000i −0.898933 + 1.00504i
\(100\) −1.00000 −0.100000
\(101\) −12.4721 −1.24102 −0.620512 0.784197i \(-0.713075\pi\)
−0.620512 + 0.784197i \(0.713075\pi\)
\(102\) 3.23607 8.47214i 0.320418 0.838866i
\(103\) 14.6525i 1.44375i −0.692023 0.721876i \(-0.743280\pi\)
0.692023 0.721876i \(-0.256720\pi\)
\(104\) −1.23607 −0.121206
\(105\) −4.00000 2.23607i −0.390360 0.218218i
\(106\) −0.472136 −0.0458579
\(107\) 11.4164i 1.10367i 0.833955 + 0.551833i \(0.186071\pi\)
−0.833955 + 0.551833i \(0.813929\pi\)
\(108\) 2.38197 + 4.61803i 0.229205 + 0.444371i
\(109\) 4.47214 0.428353 0.214176 0.976795i \(-0.431293\pi\)
0.214176 + 0.976795i \(0.431293\pi\)
\(110\) −4.47214 −0.426401
\(111\) −1.23607 0.472136i −0.117322 0.0448132i
\(112\) 2.61803 + 0.381966i 0.247381 + 0.0360924i
\(113\) 2.94427i 0.276974i −0.990364 0.138487i \(-0.955776\pi\)
0.990364 0.138487i \(-0.0442239\pi\)
\(114\) 13.7082 + 5.23607i 1.28389 + 0.490403i
\(115\) 4.00000i 0.373002i
\(116\) 7.70820i 0.715689i
\(117\) 2.47214 2.76393i 0.228549 0.255526i
\(118\) 4.47214i 0.411693i
\(119\) 13.7082 + 2.00000i 1.25663 + 0.183340i
\(120\) −0.618034 + 1.61803i −0.0564185 + 0.147706i
\(121\) −9.00000 −0.818182
\(122\) −7.23607 −0.655123
\(123\) 4.00000 + 1.52786i 0.360668 + 0.137763i
\(124\) 2.76393i 0.248208i
\(125\) 1.00000 0.0894427
\(126\) −6.09017 + 5.09017i −0.542555 + 0.453468i
\(127\) −0.291796 −0.0258927 −0.0129464 0.999916i \(-0.504121\pi\)
−0.0129464 + 0.999916i \(0.504121\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.00000 + 3.05573i 0.704361 + 0.269042i
\(130\) 1.23607 0.108410
\(131\) 5.41641 0.473234 0.236617 0.971603i \(-0.423961\pi\)
0.236617 + 0.971603i \(0.423961\pi\)
\(132\) −2.76393 + 7.23607i −0.240569 + 0.629819i
\(133\) −3.23607 + 22.1803i −0.280603 + 1.92328i
\(134\) 12.0000i 1.03664i
\(135\) −2.38197 4.61803i −0.205007 0.397457i
\(136\) 5.23607i 0.448989i
\(137\) 3.52786i 0.301406i 0.988579 + 0.150703i \(0.0481537\pi\)
−0.988579 + 0.150703i \(0.951846\pi\)
\(138\) −6.47214 2.47214i −0.550945 0.210442i
\(139\) 11.5279i 0.977781i −0.872345 0.488890i \(-0.837402\pi\)
0.872345 0.488890i \(-0.162598\pi\)
\(140\) −2.61803 0.381966i −0.221264 0.0322820i
\(141\) 10.4721 + 4.00000i 0.881913 + 0.336861i
\(142\) 7.23607 0.607237
\(143\) 5.52786 0.462263
\(144\) 2.23607 + 2.00000i 0.186339 + 0.166667i
\(145\) 7.70820i 0.640131i
\(146\) 11.2361 0.929904
\(147\) −9.61803 7.38197i −0.793282 0.608854i
\(148\) −0.763932 −0.0627948
\(149\) 4.29180i 0.351598i −0.984426 0.175799i \(-0.943749\pi\)
0.984426 0.175799i \(-0.0562508\pi\)
\(150\) 0.618034 1.61803i 0.0504623 0.132112i
\(151\) 20.9443 1.70442 0.852210 0.523199i \(-0.175262\pi\)
0.852210 + 0.523199i \(0.175262\pi\)
\(152\) 8.47214 0.687181
\(153\) 11.7082 + 10.4721i 0.946552 + 0.846622i
\(154\) −11.7082 1.70820i −0.943474 0.137651i
\(155\) 2.76393i 0.222004i
\(156\) 0.763932 2.00000i 0.0611635 0.160128i
\(157\) 9.23607i 0.737118i −0.929604 0.368559i \(-0.879851\pi\)
0.929604 0.368559i \(-0.120149\pi\)
\(158\) 8.94427i 0.711568i
\(159\) 0.291796 0.763932i 0.0231409 0.0605838i
\(160\) 1.00000i 0.0790569i
\(161\) 1.52786 10.4721i 0.120413 0.825320i
\(162\) −8.94427 + 1.00000i −0.702728 + 0.0785674i
\(163\) −10.4721 −0.820241 −0.410120 0.912031i \(-0.634513\pi\)
−0.410120 + 0.912031i \(0.634513\pi\)
\(164\) 2.47214 0.193041
\(165\) 2.76393 7.23607i 0.215172 0.563327i
\(166\) 14.6525i 1.13725i
\(167\) −0.944272 −0.0730700 −0.0365350 0.999332i \(-0.511632\pi\)
−0.0365350 + 0.999332i \(0.511632\pi\)
\(168\) −2.23607 + 4.00000i −0.172516 + 0.308607i
\(169\) 11.4721 0.882472
\(170\) 5.23607i 0.401588i
\(171\) −16.9443 + 18.9443i −1.29576 + 1.44870i
\(172\) 4.94427 0.376997
\(173\) −9.41641 −0.715916 −0.357958 0.933738i \(-0.616527\pi\)
−0.357958 + 0.933738i \(0.616527\pi\)
\(174\) −12.4721 4.76393i −0.945510 0.361153i
\(175\) 2.61803 + 0.381966i 0.197905 + 0.0288739i
\(176\) 4.47214i 0.337100i
\(177\) −7.23607 2.76393i −0.543896 0.207750i
\(178\) 5.52786i 0.414331i
\(179\) 14.9443i 1.11699i −0.829509 0.558494i \(-0.811380\pi\)
0.829509 0.558494i \(-0.188620\pi\)
\(180\) −2.23607 2.00000i −0.166667 0.149071i
\(181\) 16.1803i 1.20268i −0.798995 0.601338i \(-0.794635\pi\)
0.798995 0.601338i \(-0.205365\pi\)
\(182\) 3.23607 + 0.472136i 0.239873 + 0.0349970i
\(183\) 4.47214 11.7082i 0.330590 0.865495i
\(184\) −4.00000 −0.294884
\(185\) 0.763932 0.0561654
\(186\) −4.47214 1.70820i −0.327913 0.125252i
\(187\) 23.4164i 1.71238i
\(188\) 6.47214 0.472029
\(189\) −4.47214 13.0000i −0.325300 0.945611i
\(190\) −8.47214 −0.614633
\(191\) 7.23607i 0.523584i 0.965124 + 0.261792i \(0.0843134\pi\)
−0.965124 + 0.261792i \(0.915687\pi\)
\(192\) 1.61803 + 0.618034i 0.116772 + 0.0446028i
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) −0.763932 −0.0548471
\(195\) −0.763932 + 2.00000i −0.0547063 + 0.143223i
\(196\) −6.70820 2.00000i −0.479157 0.142857i
\(197\) 3.52786i 0.251350i 0.992071 + 0.125675i \(0.0401096\pi\)
−0.992071 + 0.125675i \(0.959890\pi\)
\(198\) −10.0000 8.94427i −0.710669 0.635642i
\(199\) 22.1803i 1.57232i −0.618021 0.786161i \(-0.712065\pi\)
0.618021 0.786161i \(-0.287935\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 19.4164 + 7.41641i 1.36953 + 0.523113i
\(202\) 12.4721i 0.877536i
\(203\) 2.94427 20.1803i 0.206647 1.41638i
\(204\) 8.47214 + 3.23607i 0.593168 + 0.226570i
\(205\) −2.47214 −0.172661
\(206\) 14.6525 1.02089
\(207\) 8.00000 8.94427i 0.556038 0.621670i
\(208\) 1.23607i 0.0857059i
\(209\) −37.8885 −2.62081
\(210\) 2.23607 4.00000i 0.154303 0.276026i
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 0.472136i 0.0324264i
\(213\) −4.47214 + 11.7082i −0.306426 + 0.802233i
\(214\) −11.4164 −0.780410
\(215\) −4.94427 −0.337197
\(216\) −4.61803 + 2.38197i −0.314217 + 0.162072i
\(217\) 1.05573 7.23607i 0.0716675 0.491216i
\(218\) 4.47214i 0.302891i
\(219\) −6.94427 + 18.1803i −0.469250 + 1.22851i
\(220\) 4.47214i 0.301511i
\(221\) 6.47214i 0.435363i
\(222\) 0.472136 1.23607i 0.0316877 0.0829595i
\(223\) 17.7082i 1.18583i 0.805265 + 0.592915i \(0.202023\pi\)
−0.805265 + 0.592915i \(0.797977\pi\)
\(224\) −0.381966 + 2.61803i −0.0255212 + 0.174925i
\(225\) 2.23607 + 2.00000i 0.149071 + 0.133333i
\(226\) 2.94427 0.195850
\(227\) 0.763932 0.0507039 0.0253520 0.999679i \(-0.491929\pi\)
0.0253520 + 0.999679i \(0.491929\pi\)
\(228\) −5.23607 + 13.7082i −0.346767 + 0.907848i
\(229\) 8.76393i 0.579137i −0.957157 0.289568i \(-0.906488\pi\)
0.957157 0.289568i \(-0.0935118\pi\)
\(230\) 4.00000 0.263752
\(231\) 10.0000 17.8885i 0.657952 1.17698i
\(232\) −7.70820 −0.506068
\(233\) 11.5279i 0.755215i 0.925966 + 0.377608i \(0.123253\pi\)
−0.925966 + 0.377608i \(0.876747\pi\)
\(234\) 2.76393 + 2.47214i 0.180684 + 0.161609i
\(235\) −6.47214 −0.422196
\(236\) −4.47214 −0.291111
\(237\) 14.4721 + 5.52786i 0.940066 + 0.359073i
\(238\) −2.00000 + 13.7082i −0.129641 + 0.888571i
\(239\) 0.180340i 0.0116652i 0.999983 + 0.00583261i \(0.00185659\pi\)
−0.999983 + 0.00583261i \(0.998143\pi\)
\(240\) −1.61803 0.618034i −0.104444 0.0398939i
\(241\) 17.8885i 1.15230i 0.817343 + 0.576151i \(0.195446\pi\)
−0.817343 + 0.576151i \(0.804554\pi\)
\(242\) 9.00000i 0.578542i
\(243\) 3.90983 15.0902i 0.250816 0.968035i
\(244\) 7.23607i 0.463242i
\(245\) 6.70820 + 2.00000i 0.428571 + 0.127775i
\(246\) −1.52786 + 4.00000i −0.0974131 + 0.255031i
\(247\) 10.4721 0.666326
\(248\) −2.76393 −0.175510
\(249\) −23.7082 9.05573i −1.50245 0.573883i
\(250\) 1.00000i 0.0632456i
\(251\) −12.4721 −0.787234 −0.393617 0.919274i \(-0.628776\pi\)
−0.393617 + 0.919274i \(0.628776\pi\)
\(252\) −5.09017 6.09017i −0.320651 0.383645i
\(253\) 17.8885 1.12464
\(254\) 0.291796i 0.0183089i
\(255\) −8.47214 3.23607i −0.530546 0.202650i
\(256\) 1.00000 0.0625000
\(257\) 14.1803 0.884545 0.442273 0.896881i \(-0.354172\pi\)
0.442273 + 0.896881i \(0.354172\pi\)
\(258\) −3.05573 + 8.00000i −0.190241 + 0.498058i
\(259\) 2.00000 + 0.291796i 0.124274 + 0.0181313i
\(260\) 1.23607i 0.0766577i
\(261\) 15.4164 17.2361i 0.954252 1.06689i
\(262\) 5.41641i 0.334627i
\(263\) 12.9443i 0.798178i −0.916912 0.399089i \(-0.869326\pi\)
0.916912 0.399089i \(-0.130674\pi\)
\(264\) −7.23607 2.76393i −0.445349 0.170108i
\(265\) 0.472136i 0.0290031i
\(266\) −22.1803 3.23607i −1.35996 0.198416i
\(267\) 8.94427 + 3.41641i 0.547381 + 0.209081i
\(268\) 12.0000 0.733017
\(269\) 4.47214 0.272671 0.136335 0.990663i \(-0.456467\pi\)
0.136335 + 0.990663i \(0.456467\pi\)
\(270\) 4.61803 2.38197i 0.281045 0.144962i
\(271\) 31.7082i 1.92614i 0.269258 + 0.963068i \(0.413222\pi\)
−0.269258 + 0.963068i \(0.586778\pi\)
\(272\) 5.23607 0.317483
\(273\) −2.76393 + 4.94427i −0.167281 + 0.299241i
\(274\) −3.52786 −0.213126
\(275\) 4.47214i 0.269680i
\(276\) 2.47214 6.47214i 0.148805 0.389577i
\(277\) −17.1246 −1.02892 −0.514459 0.857515i \(-0.672007\pi\)
−0.514459 + 0.857515i \(0.672007\pi\)
\(278\) 11.5279 0.691395
\(279\) 5.52786 6.18034i 0.330945 0.370007i
\(280\) 0.381966 2.61803i 0.0228268 0.156457i
\(281\) 20.0000i 1.19310i 0.802576 + 0.596550i \(0.203462\pi\)
−0.802576 + 0.596550i \(0.796538\pi\)
\(282\) −4.00000 + 10.4721i −0.238197 + 0.623607i
\(283\) 13.2361i 0.786803i 0.919367 + 0.393401i \(0.128702\pi\)
−0.919367 + 0.393401i \(0.871298\pi\)
\(284\) 7.23607i 0.429382i
\(285\) 5.23607 13.7082i 0.310158 0.812004i
\(286\) 5.52786i 0.326869i
\(287\) −6.47214 0.944272i −0.382038 0.0557386i
\(288\) −2.00000 + 2.23607i −0.117851 + 0.131762i
\(289\) 10.4164 0.612730
\(290\) 7.70820 0.452641
\(291\) 0.472136 1.23607i 0.0276771 0.0724596i
\(292\) 11.2361i 0.657541i
\(293\) −2.58359 −0.150935 −0.0754675 0.997148i \(-0.524045\pi\)
−0.0754675 + 0.997148i \(0.524045\pi\)
\(294\) 7.38197 9.61803i 0.430525 0.560935i
\(295\) 4.47214 0.260378
\(296\) 0.763932i 0.0444026i
\(297\) 20.6525 10.6525i 1.19838 0.618119i
\(298\) 4.29180 0.248617
\(299\) −4.94427 −0.285935
\(300\) 1.61803 + 0.618034i 0.0934172 + 0.0356822i
\(301\) −12.9443 1.88854i −0.746095 0.108854i
\(302\) 20.9443i 1.20521i
\(303\) 20.1803 + 7.70820i 1.15933 + 0.442825i
\(304\) 8.47214i 0.485910i
\(305\) 7.23607i 0.414336i
\(306\) −10.4721 + 11.7082i −0.598652 + 0.669313i
\(307\) 18.1803i 1.03761i −0.854894 0.518803i \(-0.826378\pi\)
0.854894 0.518803i \(-0.173622\pi\)
\(308\) 1.70820 11.7082i 0.0973340 0.667137i
\(309\) −9.05573 + 23.7082i −0.515162 + 1.34871i
\(310\) 2.76393 0.156981
\(311\) 17.5279 0.993914 0.496957 0.867775i \(-0.334451\pi\)
0.496957 + 0.867775i \(0.334451\pi\)
\(312\) 2.00000 + 0.763932i 0.113228 + 0.0432491i
\(313\) 5.70820i 0.322647i −0.986902 0.161323i \(-0.948424\pi\)
0.986902 0.161323i \(-0.0515762\pi\)
\(314\) 9.23607 0.521221
\(315\) 5.09017 + 6.09017i 0.286799 + 0.343142i
\(316\) 8.94427 0.503155
\(317\) 10.9443i 0.614692i −0.951598 0.307346i \(-0.900559\pi\)
0.951598 0.307346i \(-0.0994408\pi\)
\(318\) 0.763932 + 0.291796i 0.0428392 + 0.0163631i
\(319\) 34.4721 1.93007
\(320\) −1.00000 −0.0559017
\(321\) 7.05573 18.4721i 0.393812 1.03101i
\(322\) 10.4721 + 1.52786i 0.583589 + 0.0851445i
\(323\) 44.3607i 2.46829i
\(324\) −1.00000 8.94427i −0.0555556 0.496904i
\(325\) 1.23607i 0.0685647i
\(326\) 10.4721i 0.579998i
\(327\) −7.23607 2.76393i −0.400155 0.152846i
\(328\) 2.47214i 0.136501i
\(329\) −16.9443 2.47214i −0.934168 0.136293i
\(330\) 7.23607 + 2.76393i 0.398332 + 0.152149i
\(331\) 3.05573 0.167958 0.0839790 0.996468i \(-0.473237\pi\)
0.0839790 + 0.996468i \(0.473237\pi\)
\(332\) −14.6525 −0.804159
\(333\) 1.70820 + 1.52786i 0.0936090 + 0.0837264i
\(334\) 0.944272i 0.0516683i
\(335\) −12.0000 −0.655630
\(336\) −4.00000 2.23607i −0.218218 0.121988i
\(337\) 21.4164 1.16663 0.583313 0.812247i \(-0.301756\pi\)
0.583313 + 0.812247i \(0.301756\pi\)
\(338\) 11.4721i 0.624002i
\(339\) −1.81966 + 4.76393i −0.0988304 + 0.258741i
\(340\) −5.23607 −0.283966
\(341\) 12.3607 0.669368
\(342\) −18.9443 16.9443i −1.02439 0.916241i
\(343\) 16.7984 + 7.79837i 0.907027 + 0.421073i
\(344\) 4.94427i 0.266577i
\(345\) −2.47214 + 6.47214i −0.133095 + 0.348448i
\(346\) 9.41641i 0.506229i
\(347\) 2.47214i 0.132711i 0.997796 + 0.0663556i \(0.0211372\pi\)
−0.997796 + 0.0663556i \(0.978863\pi\)
\(348\) 4.76393 12.4721i 0.255374 0.668577i
\(349\) 20.1803i 1.08023i 0.841592 + 0.540114i \(0.181619\pi\)
−0.841592 + 0.540114i \(0.818381\pi\)
\(350\) −0.381966 + 2.61803i −0.0204169 + 0.139940i
\(351\) −5.70820 + 2.94427i −0.304681 + 0.157154i
\(352\) −4.47214 −0.238366
\(353\) −27.7082 −1.47476 −0.737379 0.675479i \(-0.763937\pi\)
−0.737379 + 0.675479i \(0.763937\pi\)
\(354\) 2.76393 7.23607i 0.146901 0.384593i
\(355\) 7.23607i 0.384051i
\(356\) 5.52786 0.292976
\(357\) −20.9443 11.7082i −1.10849 0.619664i
\(358\) 14.9443 0.789829
\(359\) 12.1803i 0.642854i −0.946934 0.321427i \(-0.895838\pi\)
0.946934 0.321427i \(-0.104162\pi\)
\(360\) 2.00000 2.23607i 0.105409 0.117851i
\(361\) −52.7771 −2.77774
\(362\) 16.1803 0.850420
\(363\) 14.5623 + 5.56231i 0.764323 + 0.291945i
\(364\) −0.472136 + 3.23607i −0.0247466 + 0.169616i
\(365\) 11.2361i 0.588123i
\(366\) 11.7082 + 4.47214i 0.611998 + 0.233762i
\(367\) 8.18034i 0.427010i −0.976942 0.213505i \(-0.931512\pi\)
0.976942 0.213505i \(-0.0684880\pi\)
\(368\) 4.00000i 0.208514i
\(369\) −5.52786 4.94427i −0.287769 0.257389i
\(370\) 0.763932i 0.0397149i
\(371\) −0.180340 + 1.23607i −0.00936278 + 0.0641735i
\(372\) 1.70820 4.47214i 0.0885662 0.231869i
\(373\) −32.1803 −1.66623 −0.833117 0.553096i \(-0.813446\pi\)
−0.833117 + 0.553096i \(0.813446\pi\)
\(374\) −23.4164 −1.21083
\(375\) −1.61803 0.618034i −0.0835549 0.0319151i
\(376\) 6.47214i 0.333775i
\(377\) −9.52786 −0.490710
\(378\) 13.0000 4.47214i 0.668648 0.230022i
\(379\) −17.8885 −0.918873 −0.459436 0.888211i \(-0.651949\pi\)
−0.459436 + 0.888211i \(0.651949\pi\)
\(380\) 8.47214i 0.434611i
\(381\) 0.472136 + 0.180340i 0.0241883 + 0.00923909i
\(382\) −7.23607 −0.370229
\(383\) −13.8885 −0.709671 −0.354836 0.934929i \(-0.615463\pi\)
−0.354836 + 0.934929i \(0.615463\pi\)
\(384\) −0.618034 + 1.61803i −0.0315389 + 0.0825700i
\(385\) −1.70820 + 11.7082i −0.0870581 + 0.596705i
\(386\) 6.00000i 0.305392i
\(387\) −11.0557 9.88854i −0.561994 0.502663i
\(388\) 0.763932i 0.0387828i
\(389\) 30.1803i 1.53020i 0.643909 + 0.765102i \(0.277311\pi\)
−0.643909 + 0.765102i \(0.722689\pi\)
\(390\) −2.00000 0.763932i −0.101274 0.0386832i
\(391\) 20.9443i 1.05920i
\(392\) 2.00000 6.70820i 0.101015 0.338815i
\(393\) −8.76393 3.34752i −0.442082 0.168860i
\(394\) −3.52786 −0.177731
\(395\) −8.94427 −0.450035
\(396\) 8.94427 10.0000i 0.449467 0.502519i
\(397\) 23.1246i 1.16059i 0.814406 + 0.580295i \(0.197063\pi\)
−0.814406 + 0.580295i \(0.802937\pi\)
\(398\) 22.1803 1.11180
\(399\) 18.9443 33.8885i 0.948400 1.69655i
\(400\) 1.00000 0.0500000
\(401\) 14.4721i 0.722704i 0.932429 + 0.361352i \(0.117685\pi\)
−0.932429 + 0.361352i \(0.882315\pi\)
\(402\) −7.41641 + 19.4164i −0.369897 + 0.968402i
\(403\) −3.41641 −0.170183
\(404\) 12.4721 0.620512
\(405\) 1.00000 + 8.94427i 0.0496904 + 0.444444i
\(406\) 20.1803 + 2.94427i 1.00153 + 0.146122i
\(407\) 3.41641i 0.169345i
\(408\) −3.23607 + 8.47214i −0.160209 + 0.419433i
\(409\) 7.41641i 0.366718i 0.983046 + 0.183359i \(0.0586970\pi\)
−0.983046 + 0.183359i \(0.941303\pi\)
\(410\) 2.47214i 0.122090i
\(411\) 2.18034 5.70820i 0.107548 0.281565i
\(412\) 14.6525i 0.721876i
\(413\) 11.7082 + 1.70820i 0.576123 + 0.0840552i
\(414\) 8.94427 + 8.00000i 0.439587 + 0.393179i
\(415\) 14.6525 0.719262
\(416\) 1.23607 0.0606032
\(417\) −7.12461 + 18.6525i −0.348894 + 0.913416i
\(418\) 37.8885i 1.85319i
\(419\) 36.8328 1.79940 0.899700 0.436508i \(-0.143785\pi\)
0.899700 + 0.436508i \(0.143785\pi\)
\(420\) 4.00000 + 2.23607i 0.195180 + 0.109109i
\(421\) −3.52786 −0.171938 −0.0859688 0.996298i \(-0.527399\pi\)
−0.0859688 + 0.996298i \(0.527399\pi\)
\(422\) 8.00000i 0.389434i
\(423\) −14.4721 12.9443i −0.703659 0.629372i
\(424\) 0.472136 0.0229289
\(425\) 5.23607 0.253987
\(426\) −11.7082 4.47214i −0.567264 0.216676i
\(427\) −2.76393 + 18.9443i −0.133756 + 0.916778i
\(428\) 11.4164i 0.551833i
\(429\) −8.94427 3.41641i −0.431834 0.164946i
\(430\) 4.94427i 0.238434i
\(431\) 39.5967i 1.90731i −0.300905 0.953654i \(-0.597289\pi\)
0.300905 0.953654i \(-0.402711\pi\)
\(432\) −2.38197 4.61803i −0.114602 0.222185i
\(433\) 26.6525i 1.28084i 0.768026 + 0.640418i \(0.221239\pi\)
−0.768026 + 0.640418i \(0.778761\pi\)
\(434\) 7.23607 + 1.05573i 0.347342 + 0.0506766i
\(435\) −4.76393 + 12.4721i −0.228413 + 0.597993i
\(436\) −4.47214 −0.214176
\(437\) 33.8885 1.62111
\(438\) −18.1803 6.94427i −0.868690 0.331810i
\(439\) 10.1803i 0.485881i 0.970041 + 0.242941i \(0.0781120\pi\)
−0.970041 + 0.242941i \(0.921888\pi\)
\(440\) 4.47214 0.213201
\(441\) 11.0000 + 17.8885i 0.523810 + 0.851835i
\(442\) 6.47214 0.307848
\(443\) 18.4721i 0.877638i −0.898576 0.438819i \(-0.855397\pi\)
0.898576 0.438819i \(-0.144603\pi\)
\(444\) 1.23607 + 0.472136i 0.0586612 + 0.0224066i
\(445\) −5.52786 −0.262046
\(446\) −17.7082 −0.838508
\(447\) −2.65248 + 6.94427i −0.125458 + 0.328453i
\(448\) −2.61803 0.381966i −0.123690 0.0180462i
\(449\) 10.4721i 0.494211i −0.968989 0.247105i \(-0.920521\pi\)
0.968989 0.247105i \(-0.0794794\pi\)
\(450\) −2.00000 + 2.23607i −0.0942809 + 0.105409i
\(451\) 11.0557i 0.520594i
\(452\) 2.94427i 0.138487i
\(453\) −33.8885 12.9443i −1.59222 0.608175i
\(454\) 0.763932i 0.0358531i
\(455\) 0.472136 3.23607i 0.0221341 0.151709i
\(456\) −13.7082 5.23607i −0.641945 0.245201i
\(457\) 26.9443 1.26040 0.630200 0.776433i \(-0.282973\pi\)
0.630200 + 0.776433i \(0.282973\pi\)
\(458\) 8.76393 0.409512
\(459\) −12.4721 24.1803i −0.582149 1.12864i
\(460\) 4.00000i 0.186501i
\(461\) −6.94427 −0.323427 −0.161713 0.986838i \(-0.551702\pi\)
−0.161713 + 0.986838i \(0.551702\pi\)
\(462\) 17.8885 + 10.0000i 0.832250 + 0.465242i
\(463\) −22.1803 −1.03081 −0.515404 0.856947i \(-0.672358\pi\)
−0.515404 + 0.856947i \(0.672358\pi\)
\(464\) 7.70820i 0.357844i
\(465\) −1.70820 + 4.47214i −0.0792161 + 0.207390i
\(466\) −11.5279 −0.534018
\(467\) −33.7082 −1.55983 −0.779915 0.625886i \(-0.784738\pi\)
−0.779915 + 0.625886i \(0.784738\pi\)
\(468\) −2.47214 + 2.76393i −0.114275 + 0.127763i
\(469\) −31.4164 4.58359i −1.45067 0.211651i
\(470\) 6.47214i 0.298537i
\(471\) −5.70820 + 14.9443i −0.263020 + 0.688596i
\(472\) 4.47214i 0.205847i
\(473\) 22.1115i 1.01669i
\(474\) −5.52786 + 14.4721i −0.253903 + 0.664727i
\(475\) 8.47214i 0.388728i
\(476\) −13.7082 2.00000i −0.628314 0.0916698i
\(477\) −0.944272 + 1.05573i −0.0432352 + 0.0483385i
\(478\) −0.180340 −0.00824855
\(479\) 37.8885 1.73117 0.865586 0.500761i \(-0.166946\pi\)
0.865586 + 0.500761i \(0.166946\pi\)
\(480\) 0.618034 1.61803i 0.0282093 0.0738528i
\(481\) 0.944272i 0.0430551i
\(482\) −17.8885 −0.814801
\(483\) −8.94427 + 16.0000i −0.406978 + 0.728025i
\(484\) 9.00000 0.409091
\(485\) 0.763932i 0.0346884i
\(486\) 15.0902 + 3.90983i 0.684504 + 0.177353i
\(487\) 17.5967 0.797385 0.398692 0.917085i \(-0.369464\pi\)
0.398692 + 0.917085i \(0.369464\pi\)
\(488\) 7.23607 0.327561
\(489\) 16.9443 + 6.47214i 0.766246 + 0.292680i
\(490\) −2.00000 + 6.70820i −0.0903508 + 0.303046i
\(491\) 13.4164i 0.605474i 0.953074 + 0.302737i \(0.0979004\pi\)
−0.953074 + 0.302737i \(0.902100\pi\)
\(492\) −4.00000 1.52786i −0.180334 0.0688814i
\(493\) 40.3607i 1.81775i
\(494\) 10.4721i 0.471164i
\(495\) −8.94427 + 10.0000i −0.402015 + 0.449467i
\(496\) 2.76393i 0.124104i
\(497\) 2.76393 18.9443i 0.123979 0.849767i
\(498\) 9.05573 23.7082i 0.405797 1.06239i
\(499\) 17.8885 0.800801 0.400401 0.916340i \(-0.368871\pi\)
0.400401 + 0.916340i \(0.368871\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 1.52786 + 0.583592i 0.0682599 + 0.0260730i
\(502\) 12.4721i 0.556659i
\(503\) −28.3607 −1.26454 −0.632270 0.774748i \(-0.717877\pi\)
−0.632270 + 0.774748i \(0.717877\pi\)
\(504\) 6.09017 5.09017i 0.271278 0.226734i
\(505\) −12.4721 −0.555003
\(506\) 17.8885i 0.795243i
\(507\) −18.5623 7.09017i −0.824381 0.314886i
\(508\) 0.291796 0.0129464
\(509\) 15.5279 0.688260 0.344130 0.938922i \(-0.388174\pi\)
0.344130 + 0.938922i \(0.388174\pi\)
\(510\) 3.23607 8.47214i 0.143295 0.375152i
\(511\) 4.29180 29.4164i 0.189858 1.30131i
\(512\) 1.00000i 0.0441942i
\(513\) 39.1246 20.1803i 1.72739 0.890984i
\(514\) 14.1803i 0.625468i
\(515\) 14.6525i 0.645665i
\(516\) −8.00000 3.05573i −0.352180 0.134521i
\(517\) 28.9443i 1.27297i
\(518\) −0.291796 + 2.00000i −0.0128208 + 0.0878750i
\(519\) 15.2361 + 5.81966i 0.668789 + 0.255455i
\(520\) −1.23607 −0.0542052
\(521\) −36.9443 −1.61856 −0.809279 0.587425i \(-0.800142\pi\)
−0.809279 + 0.587425i \(0.800142\pi\)
\(522\) 17.2361 + 15.4164i 0.754402 + 0.674758i
\(523\) 42.5410i 1.86019i −0.367320 0.930094i \(-0.619725\pi\)
0.367320 0.930094i \(-0.380275\pi\)
\(524\) −5.41641 −0.236617
\(525\) −4.00000 2.23607i −0.174574 0.0975900i
\(526\) 12.9443 0.564397
\(527\) 14.4721i 0.630416i
\(528\) 2.76393 7.23607i 0.120285 0.314909i
\(529\) 7.00000 0.304348
\(530\) −0.472136 −0.0205083
\(531\) 10.0000 + 8.94427i 0.433963 + 0.388148i
\(532\) 3.23607 22.1803i 0.140301 0.961640i
\(533\) 3.05573i 0.132358i
\(534\) −3.41641 + 8.94427i −0.147842 + 0.387056i
\(535\) 11.4164i 0.493574i
\(536\) 12.0000i 0.518321i
\(537\) −9.23607 + 24.1803i −0.398566 + 1.04346i
\(538\) 4.47214i 0.192807i
\(539\) −8.94427 + 30.0000i −0.385257 + 1.29219i
\(540\) 2.38197 + 4.61803i 0.102503 + 0.198729i
\(541\) 30.9443 1.33040 0.665199 0.746666i \(-0.268347\pi\)
0.665199 + 0.746666i \(0.268347\pi\)
\(542\) −31.7082 −1.36198
\(543\) −10.0000 + 26.1803i −0.429141 + 1.12351i
\(544\) 5.23607i 0.224495i
\(545\) 4.47214 0.191565
\(546\) −4.94427 2.76393i −0.211595 0.118285i
\(547\) −35.4164 −1.51430 −0.757148 0.653243i \(-0.773408\pi\)
−0.757148 + 0.653243i \(0.773408\pi\)
\(548\) 3.52786i 0.150703i
\(549\) −14.4721 + 16.1803i −0.617656 + 0.690560i
\(550\) −4.47214 −0.190693
\(551\) 65.3050 2.78208
\(552\) 6.47214 + 2.47214i 0.275472 + 0.105221i
\(553\) −23.4164 3.41641i −0.995767 0.145280i
\(554\) 17.1246i 0.727555i
\(555\) −1.23607 0.472136i −0.0524682 0.0200411i
\(556\) 11.5279i 0.488890i
\(557\) 7.52786i 0.318966i −0.987201 0.159483i \(-0.949017\pi\)
0.987201 0.159483i \(-0.0509827\pi\)
\(558\) 6.18034 + 5.52786i 0.261635 + 0.234013i
\(559\) 6.11146i 0.258487i
\(560\) 2.61803 + 0.381966i 0.110632 + 0.0161410i
\(561\) 14.4721 37.8885i 0.611014 1.59966i
\(562\) −20.0000 −0.843649
\(563\) 40.1803 1.69340 0.846700 0.532071i \(-0.178586\pi\)
0.846700 + 0.532071i \(0.178586\pi\)
\(564\) −10.4721 4.00000i −0.440956 0.168430i
\(565\) 2.94427i 0.123866i
\(566\) −13.2361 −0.556353
\(567\) −0.798374 + 23.7984i −0.0335286 + 0.999438i
\(568\) −7.23607 −0.303619
\(569\) 9.52786i 0.399429i 0.979854 + 0.199714i \(0.0640014\pi\)
−0.979854 + 0.199714i \(0.935999\pi\)
\(570\) 13.7082 + 5.23607i 0.574173 + 0.219315i
\(571\) 18.8328 0.788129 0.394064 0.919083i \(-0.371069\pi\)
0.394064 + 0.919083i \(0.371069\pi\)
\(572\) −5.52786 −0.231132
\(573\) 4.47214 11.7082i 0.186826 0.489117i
\(574\) 0.944272 6.47214i 0.0394131 0.270142i
\(575\) 4.00000i 0.166812i
\(576\) −2.23607 2.00000i −0.0931695 0.0833333i
\(577\) 8.18034i 0.340552i −0.985396 0.170276i \(-0.945534\pi\)
0.985396 0.170276i \(-0.0544659\pi\)
\(578\) 10.4164i 0.433265i
\(579\) 9.70820 + 3.70820i 0.403459 + 0.154108i
\(580\) 7.70820i 0.320066i
\(581\) 38.3607 + 5.59675i 1.59147 + 0.232192i
\(582\) 1.23607 + 0.472136i 0.0512367 + 0.0195707i
\(583\) −2.11146 −0.0874476
\(584\) −11.2361 −0.464952
\(585\) 2.47214 2.76393i 0.102210 0.114275i
\(586\) 2.58359i 0.106727i
\(587\) −10.2918 −0.424788 −0.212394 0.977184i \(-0.568126\pi\)
−0.212394 + 0.977184i \(0.568126\pi\)
\(588\) 9.61803 + 7.38197i 0.396641 + 0.304427i
\(589\) 23.4164 0.964856
\(590\) 4.47214i 0.184115i
\(591\) 2.18034 5.70820i 0.0896872 0.234804i
\(592\) 0.763932 0.0313974
\(593\) −29.0132 −1.19143 −0.595714 0.803197i \(-0.703131\pi\)
−0.595714 + 0.803197i \(0.703131\pi\)
\(594\) 10.6525 + 20.6525i 0.437076 + 0.847381i
\(595\) 13.7082 + 2.00000i 0.561982 + 0.0819920i
\(596\) 4.29180i 0.175799i
\(597\) −13.7082 + 35.8885i −0.561039 + 1.46882i
\(598\) 4.94427i 0.202186i
\(599\) 36.7639i 1.50213i 0.660226 + 0.751067i \(0.270460\pi\)
−0.660226 + 0.751067i \(0.729540\pi\)
\(600\) −0.618034 + 1.61803i −0.0252311 + 0.0660560i
\(601\) 5.52786i 0.225486i 0.993624 + 0.112743i \(0.0359637\pi\)
−0.993624 + 0.112743i \(0.964036\pi\)
\(602\) 1.88854 12.9443i 0.0769713 0.527569i
\(603\) −26.8328 24.0000i −1.09272 0.977356i
\(604\) −20.9443 −0.852210
\(605\) −9.00000 −0.365902
\(606\) −7.70820 + 20.1803i −0.313124 + 0.819770i
\(607\) 19.2361i 0.780768i −0.920652 0.390384i \(-0.872342\pi\)
0.920652 0.390384i \(-0.127658\pi\)
\(608\) −8.47214 −0.343590
\(609\) −17.2361 + 30.8328i −0.698441 + 1.24941i
\(610\) −7.23607 −0.292980
\(611\) 8.00000i 0.323645i
\(612\) −11.7082 10.4721i −0.473276 0.423311i
\(613\) 38.0689 1.53759 0.768794 0.639497i \(-0.220857\pi\)
0.768794 + 0.639497i \(0.220857\pi\)
\(614\) 18.1803 0.733699
\(615\) 4.00000 + 1.52786i 0.161296 + 0.0616094i
\(616\) 11.7082 + 1.70820i 0.471737 + 0.0688255i
\(617\) 2.00000i 0.0805170i −0.999189 0.0402585i \(-0.987182\pi\)
0.999189 0.0402585i \(-0.0128181\pi\)
\(618\) −23.7082 9.05573i −0.953684 0.364275i
\(619\) 14.0000i 0.562708i 0.959604 + 0.281354i \(0.0907834\pi\)
−0.959604 + 0.281354i \(0.909217\pi\)
\(620\) 2.76393i 0.111002i
\(621\) −18.4721 + 9.52786i −0.741261 + 0.382340i
\(622\) 17.5279i 0.702803i
\(623\) −14.4721 2.11146i −0.579814 0.0845937i
\(624\) −0.763932 + 2.00000i −0.0305818 + 0.0800641i
\(625\) 1.00000 0.0400000
\(626\) 5.70820 0.228146
\(627\) 61.3050 + 23.4164i 2.44828 + 0.935161i
\(628\) 9.23607i 0.368559i
\(629\) 4.00000 0.159490
\(630\) −6.09017 + 5.09017i −0.242638 + 0.202797i
\(631\) −5.88854 −0.234419 −0.117210 0.993107i \(-0.537395\pi\)
−0.117210 + 0.993107i \(0.537395\pi\)
\(632\) 8.94427i 0.355784i
\(633\) 12.9443 + 4.94427i 0.514489 + 0.196517i
\(634\) 10.9443 0.434653
\(635\) −0.291796 −0.0115796
\(636\) −0.291796 + 0.763932i −0.0115705 + 0.0302919i
\(637\) 2.47214 8.29180i 0.0979496 0.328533i
\(638\) 34.4721i 1.36476i
\(639\) 14.4721 16.1803i 0.572509 0.640084i
\(640\) 1.00000i 0.0395285i
\(641\) 23.4164i 0.924893i 0.886647 + 0.462446i \(0.153028\pi\)
−0.886647 + 0.462446i \(0.846972\pi\)
\(642\) 18.4721 + 7.05573i 0.729037 + 0.278467i
\(643\) 12.2918i 0.484741i −0.970184 0.242371i \(-0.922075\pi\)
0.970184 0.242371i \(-0.0779250\pi\)
\(644\) −1.52786 + 10.4721i −0.0602063 + 0.412660i
\(645\) 8.00000 + 3.05573i 0.315000 + 0.120319i
\(646\) −44.3607 −1.74535
\(647\) 34.8328 1.36942 0.684710 0.728816i \(-0.259929\pi\)
0.684710 + 0.728816i \(0.259929\pi\)
\(648\) 8.94427 1.00000i 0.351364 0.0392837i
\(649\) 20.0000i 0.785069i
\(650\) 1.23607 0.0484826
\(651\) −6.18034 + 11.0557i −0.242227 + 0.433308i
\(652\) 10.4721 0.410120
\(653\) 23.8885i 0.934831i 0.884038 + 0.467415i \(0.154815\pi\)
−0.884038 + 0.467415i \(0.845185\pi\)
\(654\) 2.76393 7.23607i 0.108078 0.282953i
\(655\) 5.41641 0.211637
\(656\) −2.47214 −0.0965207
\(657\) 22.4721 25.1246i 0.876722 0.980204i
\(658\) 2.47214 16.9443i 0.0963739 0.660556i
\(659\) 31.5279i 1.22815i −0.789247 0.614076i \(-0.789529\pi\)
0.789247 0.614076i \(-0.210471\pi\)
\(660\) −2.76393 + 7.23607i −0.107586 + 0.281664i
\(661\) 18.2918i 0.711468i 0.934587 + 0.355734i \(0.115769\pi\)
−0.934587 + 0.355734i \(0.884231\pi\)
\(662\) 3.05573i 0.118764i
\(663\) −4.00000 + 10.4721i −0.155347 + 0.406704i
\(664\) 14.6525i 0.568626i
\(665\) −3.23607 + 22.1803i −0.125489 + 0.860117i
\(666\) −1.52786 + 1.70820i −0.0592035 + 0.0661916i
\(667\) −30.8328 −1.19385
\(668\) 0.944272 0.0365350
\(669\) 10.9443 28.6525i 0.423130 1.10777i
\(670\) 12.0000i 0.463600i
\(671\) −32.3607 −1.24927
\(672\) 2.23607 4.00000i 0.0862582 0.154303i
\(673\) 19.5279 0.752744 0.376372 0.926469i \(-0.377171\pi\)
0.376372 + 0.926469i \(0.377171\pi\)
\(674\) 21.4164i 0.824929i
\(675\) −2.38197 4.61803i −0.0916819 0.177748i
\(676\) −11.4721 −0.441236
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −4.76393 1.81966i −0.182958 0.0698836i
\(679\) −0.291796 + 2.00000i −0.0111981 + 0.0767530i
\(680\) 5.23607i 0.200794i
\(681\) −1.23607 0.472136i −0.0473662 0.0180923i
\(682\) 12.3607i 0.473315i
\(683\) 36.0000i 1.37750i 0.724998 + 0.688751i \(0.241841\pi\)
−0.724998 + 0.688751i \(0.758159\pi\)
\(684\) 16.9443 18.9443i 0.647880 0.724352i
\(685\) 3.52786i 0.134793i
\(686\) −7.79837 + 16.7984i −0.297743 + 0.641365i
\(687\) −5.41641 + 14.1803i −0.206649 + 0.541014i
\(688\) −4.94427 −0.188499
\(689\) 0.583592 0.0222331
\(690\) −6.47214 2.47214i −0.246390 0.0941126i
\(691\) 21.0557i 0.800998i −0.916297 0.400499i \(-0.868837\pi\)
0.916297 0.400499i \(-0.131163\pi\)
\(692\) 9.41641 0.357958
\(693\) −27.2361 + 22.7639i −1.03461 + 0.864730i
\(694\) −2.47214 −0.0938410
\(695\) 11.5279i 0.437277i
\(696\) 12.4721 + 4.76393i 0.472755 + 0.180576i
\(697\) −12.9443 −0.490299
\(698\) −20.1803 −0.763837
\(699\) 7.12461 18.6525i 0.269478 0.705501i
\(700\) −2.61803 0.381966i −0.0989524 0.0144370i
\(701\) 44.0689i 1.66446i −0.554431 0.832229i \(-0.687064\pi\)
0.554431 0.832229i \(-0.312936\pi\)
\(702\) −2.94427 5.70820i −0.111124 0.215442i
\(703\) 6.47214i 0.244101i
\(704\) 4.47214i 0.168550i
\(705\) 10.4721 + 4.00000i 0.394403 + 0.150649i
\(706\) 27.7082i 1.04281i
\(707\) −32.6525 4.76393i −1.22802 0.179166i
\(708\) 7.23607 + 2.76393i 0.271948 + 0.103875i
\(709\) −15.5279 −0.583161 −0.291581 0.956546i \(-0.594181\pi\)
−0.291581 + 0.956546i \(0.594181\pi\)
\(710\) 7.23607 0.271565
\(711\) −20.0000 17.8885i −0.750059 0.670873i
\(712\) 5.52786i 0.207165i
\(713\) −11.0557 −0.414040
\(714\) 11.7082 20.9443i 0.438169 0.783820i
\(715\) 5.52786 0.206730
\(716\) 14.9443i 0.558494i
\(717\) 0.111456 0.291796i 0.00416241 0.0108973i
\(718\) 12.1803 0.454566
\(719\) −34.4721 −1.28559 −0.642797 0.766037i \(-0.722226\pi\)
−0.642797 + 0.766037i \(0.722226\pi\)
\(720\) 2.23607 + 2.00000i 0.0833333 + 0.0745356i
\(721\) 5.59675 38.3607i 0.208434 1.42863i
\(722\) 52.7771i 1.96416i
\(723\) 11.0557 28.9443i 0.411167 1.07645i
\(724\) 16.1803i 0.601338i
\(725\) 7.70820i 0.286276i
\(726\) −5.56231 + 14.5623i −0.206437 + 0.540458i
\(727\) 26.2918i 0.975109i 0.873093 + 0.487554i \(0.162111\pi\)
−0.873093 + 0.487554i \(0.837889\pi\)
\(728\) −3.23607 0.472136i −0.119937 0.0174985i
\(729\) −15.6525 + 22.0000i −0.579721 + 0.814815i
\(730\) 11.2361 0.415866
\(731\) −25.8885 −0.957522
\(732\) −4.47214 + 11.7082i −0.165295 + 0.432748i
\(733\) 20.0689i 0.741261i 0.928780 + 0.370631i \(0.120858\pi\)
−0.928780 + 0.370631i \(0.879142\pi\)
\(734\) 8.18034 0.301942
\(735\) −9.61803 7.38197i −0.354767 0.272288i
\(736\) 4.00000 0.147442
\(737\) 53.6656i 1.97680i
\(738\) 4.94427 5.52786i 0.182001 0.203483i
\(739\) 8.94427 0.329020 0.164510 0.986375i \(-0.447396\pi\)
0.164510 + 0.986375i \(0.447396\pi\)
\(740\) −0.763932 −0.0280827
\(741\) −16.9443 6.47214i −0.622463 0.237760i
\(742\) −1.23607 0.180340i −0.0453775 0.00662049i
\(743\) 10.4721i 0.384185i 0.981377 + 0.192093i \(0.0615274\pi\)
−0.981377 + 0.192093i \(0.938473\pi\)
\(744\) 4.47214 + 1.70820i 0.163956 + 0.0626258i
\(745\) 4.29180i 0.157239i
\(746\) 32.1803i 1.17821i
\(747\) 32.7639 + 29.3050i 1.19877 + 1.07221i
\(748\) 23.4164i 0.856189i
\(749\) −4.36068 + 29.8885i −0.159336 + 1.09210i
\(750\) 0.618034 1.61803i 0.0225674 0.0590822i
\(751\) 8.58359 0.313220 0.156610 0.987661i \(-0.449943\pi\)
0.156610 + 0.987661i \(0.449943\pi\)
\(752\) −6.47214 −0.236015
\(753\) 20.1803 + 7.70820i 0.735412 + 0.280903i
\(754\) 9.52786i 0.346984i
\(755\) 20.9443 0.762240
\(756\) 4.47214 + 13.0000i 0.162650 + 0.472805i
\(757\) −2.65248 −0.0964059 −0.0482029 0.998838i \(-0.515349\pi\)
−0.0482029 + 0.998838i \(0.515349\pi\)
\(758\) 17.8885i 0.649741i
\(759\) −28.9443 11.0557i −1.05061 0.401298i
\(760\) 8.47214 0.307317
\(761\) −5.88854 −0.213460 −0.106730 0.994288i \(-0.534038\pi\)
−0.106730 + 0.994288i \(0.534038\pi\)
\(762\) −0.180340 + 0.472136i −0.00653302 + 0.0171037i
\(763\) 11.7082 + 1.70820i 0.423865 + 0.0618411i
\(764\) 7.23607i 0.261792i
\(765\) 11.7082 + 10.4721i 0.423311 + 0.378621i
\(766\) 13.8885i 0.501813i
\(767\) 5.52786i 0.199600i
\(768\) −1.61803 0.618034i −0.0583858 0.0223014i
\(769\) 36.0000i 1.29819i −0.760706 0.649097i \(-0.775147\pi\)
0.760706 0.649097i \(-0.224853\pi\)
\(770\) −11.7082 1.70820i −0.421934 0.0615594i
\(771\) −22.9443 8.76393i −0.826318 0.315625i
\(772\) 6.00000 0.215945
\(773\) 10.5836 0.380665 0.190333 0.981720i \(-0.439043\pi\)
0.190333 + 0.981720i \(0.439043\pi\)
\(774\) 9.88854 11.0557i 0.355436 0.397390i
\(775\) 2.76393i 0.0992834i
\(776\) 0.763932 0.0274236
\(777\) −3.05573 1.70820i −0.109624 0.0612815i
\(778\) −30.1803 −1.08202
\(779\) 20.9443i 0.750406i
\(780\) 0.763932 2.00000i 0.0273532 0.0716115i
\(781\) 32.3607 1.15796
\(782\) 20.9443 0.748966