Properties

Label 1050.2.d.a.1049.3
Level $1050$
Weight $2$
Character 1050.1049
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1049.3
Root \(0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 1050.1049
Dual form 1050.2.d.a.1049.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.618034 - 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} -1.00000 q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.618034 - 1.61803i) q^{3} +1.00000 q^{4} +(-0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} -1.00000 q^{8} +(-2.23607 - 2.00000i) q^{9} +4.47214i q^{11} +(0.618034 - 1.61803i) q^{12} +1.23607 q^{13} +(-0.381966 - 2.61803i) q^{14} +1.00000 q^{16} -5.23607i q^{17} +(2.23607 + 2.00000i) q^{18} +8.47214i q^{19} +(4.47214 + 1.00000i) q^{21} -4.47214i q^{22} -4.00000 q^{23} +(-0.618034 + 1.61803i) q^{24} -1.23607 q^{26} +(-4.61803 + 2.38197i) q^{27} +(0.381966 + 2.61803i) q^{28} +7.70820i q^{29} +2.76393i q^{31} -1.00000 q^{32} +(7.23607 + 2.76393i) q^{33} +5.23607i q^{34} +(-2.23607 - 2.00000i) q^{36} +0.763932i q^{37} -8.47214i q^{38} +(0.763932 - 2.00000i) q^{39} +2.47214 q^{41} +(-4.47214 - 1.00000i) q^{42} +4.94427i q^{43} +4.47214i q^{44} +4.00000 q^{46} +6.47214i q^{47} +(0.618034 - 1.61803i) q^{48} +(-6.70820 + 2.00000i) q^{49} +(-8.47214 - 3.23607i) q^{51} +1.23607 q^{52} +0.472136 q^{53} +(4.61803 - 2.38197i) q^{54} +(-0.381966 - 2.61803i) q^{56} +(13.7082 + 5.23607i) q^{57} -7.70820i q^{58} +4.47214 q^{59} -7.23607i q^{61} -2.76393i q^{62} +(4.38197 - 6.61803i) q^{63} +1.00000 q^{64} +(-7.23607 - 2.76393i) q^{66} -12.0000i q^{67} -5.23607i q^{68} +(-2.47214 + 6.47214i) q^{69} -7.23607i q^{71} +(2.23607 + 2.00000i) q^{72} +11.2361 q^{73} -0.763932i q^{74} +8.47214i q^{76} +(-11.7082 + 1.70820i) q^{77} +(-0.763932 + 2.00000i) q^{78} +8.94427 q^{79} +(1.00000 + 8.94427i) q^{81} -2.47214 q^{82} +14.6525i q^{83} +(4.47214 + 1.00000i) q^{84} -4.94427i q^{86} +(12.4721 + 4.76393i) q^{87} -4.47214i q^{88} -5.52786 q^{89} +(0.472136 + 3.23607i) q^{91} -4.00000 q^{92} +(4.47214 + 1.70820i) q^{93} -6.47214i q^{94} +(-0.618034 + 1.61803i) q^{96} +0.763932 q^{97} +(6.70820 - 2.00000i) q^{98} +(8.94427 - 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 2q^{3} + 4q^{4} + 2q^{6} + 6q^{7} - 4q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 2q^{3} + 4q^{4} + 2q^{6} + 6q^{7} - 4q^{8} - 2q^{12} - 4q^{13} - 6q^{14} + 4q^{16} - 16q^{23} + 2q^{24} + 4q^{26} - 14q^{27} + 6q^{28} - 4q^{32} + 20q^{33} + 12q^{39} - 8q^{41} + 16q^{46} - 2q^{48} - 16q^{51} - 4q^{52} - 16q^{53} + 14q^{54} - 6q^{56} + 28q^{57} + 22q^{63} + 4q^{64} - 20q^{66} + 8q^{69} + 36q^{73} - 20q^{77} - 12q^{78} + 4q^{81} + 8q^{82} + 32q^{87} - 40q^{89} - 16q^{91} - 16q^{92} + 2q^{96} + 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.618034 1.61803i 0.356822 0.934172i
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −0.618034 + 1.61803i −0.252311 + 0.660560i
\(7\) 0.381966 + 2.61803i 0.144370 + 0.989524i
\(8\) −1.00000 −0.353553
\(9\) −2.23607 2.00000i −0.745356 0.666667i
\(10\) 0 0
\(11\) 4.47214i 1.34840i 0.738549 + 0.674200i \(0.235511\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 0.618034 1.61803i 0.178411 0.467086i
\(13\) 1.23607 0.342824 0.171412 0.985199i \(-0.445167\pi\)
0.171412 + 0.985199i \(0.445167\pi\)
\(14\) −0.381966 2.61803i −0.102085 0.699699i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.23607i 1.26993i −0.772540 0.634967i \(-0.781014\pi\)
0.772540 0.634967i \(-0.218986\pi\)
\(18\) 2.23607 + 2.00000i 0.527046 + 0.471405i
\(19\) 8.47214i 1.94364i 0.235722 + 0.971821i \(0.424255\pi\)
−0.235722 + 0.971821i \(0.575745\pi\)
\(20\) 0 0
\(21\) 4.47214 + 1.00000i 0.975900 + 0.218218i
\(22\) 4.47214i 0.953463i
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −0.618034 + 1.61803i −0.126156 + 0.330280i
\(25\) 0 0
\(26\) −1.23607 −0.242413
\(27\) −4.61803 + 2.38197i −0.888741 + 0.458410i
\(28\) 0.381966 + 2.61803i 0.0721848 + 0.494762i
\(29\) 7.70820i 1.43138i 0.698419 + 0.715689i \(0.253887\pi\)
−0.698419 + 0.715689i \(0.746113\pi\)
\(30\) 0 0
\(31\) 2.76393i 0.496417i 0.968707 + 0.248208i \(0.0798418\pi\)
−0.968707 + 0.248208i \(0.920158\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.23607 + 2.76393i 1.25964 + 0.481139i
\(34\) 5.23607i 0.897978i
\(35\) 0 0
\(36\) −2.23607 2.00000i −0.372678 0.333333i
\(37\) 0.763932i 0.125590i 0.998026 + 0.0627948i \(0.0200014\pi\)
−0.998026 + 0.0627948i \(0.979999\pi\)
\(38\) 8.47214i 1.37436i
\(39\) 0.763932 2.00000i 0.122327 0.320256i
\(40\) 0 0
\(41\) 2.47214 0.386083 0.193041 0.981191i \(-0.438165\pi\)
0.193041 + 0.981191i \(0.438165\pi\)
\(42\) −4.47214 1.00000i −0.690066 0.154303i
\(43\) 4.94427i 0.753994i 0.926214 + 0.376997i \(0.123043\pi\)
−0.926214 + 0.376997i \(0.876957\pi\)
\(44\) 4.47214i 0.674200i
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) 6.47214i 0.944058i 0.881583 + 0.472029i \(0.156478\pi\)
−0.881583 + 0.472029i \(0.843522\pi\)
\(48\) 0.618034 1.61803i 0.0892055 0.233543i
\(49\) −6.70820 + 2.00000i −0.958315 + 0.285714i
\(50\) 0 0
\(51\) −8.47214 3.23607i −1.18634 0.453140i
\(52\) 1.23607 0.171412
\(53\) 0.472136 0.0648529 0.0324264 0.999474i \(-0.489677\pi\)
0.0324264 + 0.999474i \(0.489677\pi\)
\(54\) 4.61803 2.38197i 0.628435 0.324145i
\(55\) 0 0
\(56\) −0.381966 2.61803i −0.0510424 0.349850i
\(57\) 13.7082 + 5.23607i 1.81570 + 0.693534i
\(58\) 7.70820i 1.01214i
\(59\) 4.47214 0.582223 0.291111 0.956689i \(-0.405975\pi\)
0.291111 + 0.956689i \(0.405975\pi\)
\(60\) 0 0
\(61\) 7.23607i 0.926484i −0.886232 0.463242i \(-0.846686\pi\)
0.886232 0.463242i \(-0.153314\pi\)
\(62\) 2.76393i 0.351020i
\(63\) 4.38197 6.61803i 0.552076 0.833794i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −7.23607 2.76393i −0.890698 0.340217i
\(67\) 12.0000i 1.46603i −0.680211 0.733017i \(-0.738112\pi\)
0.680211 0.733017i \(-0.261888\pi\)
\(68\) 5.23607i 0.634967i
\(69\) −2.47214 + 6.47214i −0.297610 + 0.779154i
\(70\) 0 0
\(71\) 7.23607i 0.858763i −0.903123 0.429382i \(-0.858732\pi\)
0.903123 0.429382i \(-0.141268\pi\)
\(72\) 2.23607 + 2.00000i 0.263523 + 0.235702i
\(73\) 11.2361 1.31508 0.657541 0.753419i \(-0.271597\pi\)
0.657541 + 0.753419i \(0.271597\pi\)
\(74\) 0.763932i 0.0888053i
\(75\) 0 0
\(76\) 8.47214i 0.971821i
\(77\) −11.7082 + 1.70820i −1.33427 + 0.194668i
\(78\) −0.763932 + 2.00000i −0.0864983 + 0.226455i
\(79\) 8.94427 1.00631 0.503155 0.864196i \(-0.332173\pi\)
0.503155 + 0.864196i \(0.332173\pi\)
\(80\) 0 0
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) −2.47214 −0.273002
\(83\) 14.6525i 1.60832i 0.594414 + 0.804159i \(0.297384\pi\)
−0.594414 + 0.804159i \(0.702616\pi\)
\(84\) 4.47214 + 1.00000i 0.487950 + 0.109109i
\(85\) 0 0
\(86\) 4.94427i 0.533155i
\(87\) 12.4721 + 4.76393i 1.33715 + 0.510747i
\(88\) 4.47214i 0.476731i
\(89\) −5.52786 −0.585952 −0.292976 0.956120i \(-0.594646\pi\)
−0.292976 + 0.956120i \(0.594646\pi\)
\(90\) 0 0
\(91\) 0.472136 + 3.23607i 0.0494933 + 0.339232i
\(92\) −4.00000 −0.417029
\(93\) 4.47214 + 1.70820i 0.463739 + 0.177132i
\(94\) 6.47214i 0.667550i
\(95\) 0 0
\(96\) −0.618034 + 1.61803i −0.0630778 + 0.165140i
\(97\) 0.763932 0.0775655 0.0387828 0.999248i \(-0.487652\pi\)
0.0387828 + 0.999248i \(0.487652\pi\)
\(98\) 6.70820 2.00000i 0.677631 0.202031i
\(99\) 8.94427 10.0000i 0.898933 1.00504i
\(100\) 0 0
\(101\) 12.4721 1.24102 0.620512 0.784197i \(-0.286925\pi\)
0.620512 + 0.784197i \(0.286925\pi\)
\(102\) 8.47214 + 3.23607i 0.838866 + 0.320418i
\(103\) 14.6525 1.44375 0.721876 0.692023i \(-0.243280\pi\)
0.721876 + 0.692023i \(0.243280\pi\)
\(104\) −1.23607 −0.121206
\(105\) 0 0
\(106\) −0.472136 −0.0458579
\(107\) −11.4164 −1.10367 −0.551833 0.833955i \(-0.686071\pi\)
−0.551833 + 0.833955i \(0.686071\pi\)
\(108\) −4.61803 + 2.38197i −0.444371 + 0.229205i
\(109\) −4.47214 −0.428353 −0.214176 0.976795i \(-0.568707\pi\)
−0.214176 + 0.976795i \(0.568707\pi\)
\(110\) 0 0
\(111\) 1.23607 + 0.472136i 0.117322 + 0.0448132i
\(112\) 0.381966 + 2.61803i 0.0360924 + 0.247381i
\(113\) −2.94427 −0.276974 −0.138487 0.990364i \(-0.544224\pi\)
−0.138487 + 0.990364i \(0.544224\pi\)
\(114\) −13.7082 5.23607i −1.28389 0.490403i
\(115\) 0 0
\(116\) 7.70820i 0.715689i
\(117\) −2.76393 2.47214i −0.255526 0.228549i
\(118\) −4.47214 −0.411693
\(119\) 13.7082 2.00000i 1.25663 0.183340i
\(120\) 0 0
\(121\) −9.00000 −0.818182
\(122\) 7.23607i 0.655123i
\(123\) 1.52786 4.00000i 0.137763 0.360668i
\(124\) 2.76393i 0.248208i
\(125\) 0 0
\(126\) −4.38197 + 6.61803i −0.390377 + 0.589581i
\(127\) 0.291796i 0.0258927i −0.999916 0.0129464i \(-0.995879\pi\)
0.999916 0.0129464i \(-0.00412107\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.00000 + 3.05573i 0.704361 + 0.269042i
\(130\) 0 0
\(131\) −5.41641 −0.473234 −0.236617 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(132\) 7.23607 + 2.76393i 0.629819 + 0.240569i
\(133\) −22.1803 + 3.23607i −1.92328 + 0.280603i
\(134\) 12.0000i 1.03664i
\(135\) 0 0
\(136\) 5.23607i 0.448989i
\(137\) −3.52786 −0.301406 −0.150703 0.988579i \(-0.548154\pi\)
−0.150703 + 0.988579i \(0.548154\pi\)
\(138\) 2.47214 6.47214i 0.210442 0.550945i
\(139\) 11.5279i 0.977781i −0.872345 0.488890i \(-0.837402\pi\)
0.872345 0.488890i \(-0.162598\pi\)
\(140\) 0 0
\(141\) 10.4721 + 4.00000i 0.881913 + 0.336861i
\(142\) 7.23607i 0.607237i
\(143\) 5.52786i 0.462263i
\(144\) −2.23607 2.00000i −0.186339 0.166667i
\(145\) 0 0
\(146\) −11.2361 −0.929904
\(147\) −0.909830 + 12.0902i −0.0750415 + 0.997180i
\(148\) 0.763932i 0.0627948i
\(149\) 4.29180i 0.351598i 0.984426 + 0.175799i \(0.0562508\pi\)
−0.984426 + 0.175799i \(0.943749\pi\)
\(150\) 0 0
\(151\) 20.9443 1.70442 0.852210 0.523199i \(-0.175262\pi\)
0.852210 + 0.523199i \(0.175262\pi\)
\(152\) 8.47214i 0.687181i
\(153\) −10.4721 + 11.7082i −0.846622 + 0.946552i
\(154\) 11.7082 1.70820i 0.943474 0.137651i
\(155\) 0 0
\(156\) 0.763932 2.00000i 0.0611635 0.160128i
\(157\) −9.23607 −0.737118 −0.368559 0.929604i \(-0.620149\pi\)
−0.368559 + 0.929604i \(0.620149\pi\)
\(158\) −8.94427 −0.711568
\(159\) 0.291796 0.763932i 0.0231409 0.0605838i
\(160\) 0 0
\(161\) −1.52786 10.4721i −0.120413 0.825320i
\(162\) −1.00000 8.94427i −0.0785674 0.702728i
\(163\) 10.4721i 0.820241i 0.912031 + 0.410120i \(0.134513\pi\)
−0.912031 + 0.410120i \(0.865487\pi\)
\(164\) 2.47214 0.193041
\(165\) 0 0
\(166\) 14.6525i 1.13725i
\(167\) 0.944272i 0.0730700i 0.999332 + 0.0365350i \(0.0116320\pi\)
−0.999332 + 0.0365350i \(0.988368\pi\)
\(168\) −4.47214 1.00000i −0.345033 0.0771517i
\(169\) −11.4721 −0.882472
\(170\) 0 0
\(171\) 16.9443 18.9443i 1.29576 1.44870i
\(172\) 4.94427i 0.376997i
\(173\) 9.41641i 0.715916i −0.933738 0.357958i \(-0.883473\pi\)
0.933738 0.357958i \(-0.116527\pi\)
\(174\) −12.4721 4.76393i −0.945510 0.361153i
\(175\) 0 0
\(176\) 4.47214i 0.337100i
\(177\) 2.76393 7.23607i 0.207750 0.543896i
\(178\) 5.52786 0.414331
\(179\) 14.9443i 1.11699i 0.829509 + 0.558494i \(0.188620\pi\)
−0.829509 + 0.558494i \(0.811380\pi\)
\(180\) 0 0
\(181\) 16.1803i 1.20268i 0.798995 + 0.601338i \(0.205365\pi\)
−0.798995 + 0.601338i \(0.794635\pi\)
\(182\) −0.472136 3.23607i −0.0349970 0.239873i
\(183\) −11.7082 4.47214i −0.865495 0.330590i
\(184\) 4.00000 0.294884
\(185\) 0 0
\(186\) −4.47214 1.70820i −0.327913 0.125252i
\(187\) 23.4164 1.71238
\(188\) 6.47214i 0.472029i
\(189\) −8.00000 11.1803i −0.581914 0.813250i
\(190\) 0 0
\(191\) 7.23607i 0.523584i 0.965124 + 0.261792i \(0.0843134\pi\)
−0.965124 + 0.261792i \(0.915687\pi\)
\(192\) 0.618034 1.61803i 0.0446028 0.116772i
\(193\) 6.00000i 0.431889i 0.976406 + 0.215945i \(0.0692831\pi\)
−0.976406 + 0.215945i \(0.930717\pi\)
\(194\) −0.763932 −0.0548471
\(195\) 0 0
\(196\) −6.70820 + 2.00000i −0.479157 + 0.142857i
\(197\) −3.52786 −0.251350 −0.125675 0.992071i \(-0.540110\pi\)
−0.125675 + 0.992071i \(0.540110\pi\)
\(198\) −8.94427 + 10.0000i −0.635642 + 0.710669i
\(199\) 22.1803i 1.57232i −0.618021 0.786161i \(-0.712065\pi\)
0.618021 0.786161i \(-0.287935\pi\)
\(200\) 0 0
\(201\) −19.4164 7.41641i −1.36953 0.523113i
\(202\) −12.4721 −0.877536
\(203\) −20.1803 + 2.94427i −1.41638 + 0.206647i
\(204\) −8.47214 3.23607i −0.593168 0.226570i
\(205\) 0 0
\(206\) −14.6525 −1.02089
\(207\) 8.94427 + 8.00000i 0.621670 + 0.556038i
\(208\) 1.23607 0.0857059
\(209\) −37.8885 −2.62081
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 0.472136 0.0324264
\(213\) −11.7082 4.47214i −0.802233 0.306426i
\(214\) 11.4164 0.780410
\(215\) 0 0
\(216\) 4.61803 2.38197i 0.314217 0.162072i
\(217\) −7.23607 + 1.05573i −0.491216 + 0.0716675i
\(218\) 4.47214 0.302891
\(219\) 6.94427 18.1803i 0.469250 1.22851i
\(220\) 0 0
\(221\) 6.47214i 0.435363i
\(222\) −1.23607 0.472136i −0.0829595 0.0316877i
\(223\) −17.7082 −1.18583 −0.592915 0.805265i \(-0.702023\pi\)
−0.592915 + 0.805265i \(0.702023\pi\)
\(224\) −0.381966 2.61803i −0.0255212 0.174925i
\(225\) 0 0
\(226\) 2.94427 0.195850
\(227\) 0.763932i 0.0507039i −0.999679 0.0253520i \(-0.991929\pi\)
0.999679 0.0253520i \(-0.00807065\pi\)
\(228\) 13.7082 + 5.23607i 0.907848 + 0.346767i
\(229\) 8.76393i 0.579137i −0.957157 0.289568i \(-0.906488\pi\)
0.957157 0.289568i \(-0.0935118\pi\)
\(230\) 0 0
\(231\) −4.47214 + 20.0000i −0.294245 + 1.31590i
\(232\) 7.70820i 0.506068i
\(233\) 11.5279 0.755215 0.377608 0.925966i \(-0.376747\pi\)
0.377608 + 0.925966i \(0.376747\pi\)
\(234\) 2.76393 + 2.47214i 0.180684 + 0.161609i
\(235\) 0 0
\(236\) 4.47214 0.291111
\(237\) 5.52786 14.4721i 0.359073 0.940066i
\(238\) −13.7082 + 2.00000i −0.888571 + 0.129641i
\(239\) 0.180340i 0.0116652i −0.999983 0.00583261i \(-0.998143\pi\)
0.999983 0.00583261i \(-0.00185659\pi\)
\(240\) 0 0
\(241\) 17.8885i 1.15230i −0.817343 0.576151i \(-0.804554\pi\)
0.817343 0.576151i \(-0.195446\pi\)
\(242\) 9.00000 0.578542
\(243\) 15.0902 + 3.90983i 0.968035 + 0.250816i
\(244\) 7.23607i 0.463242i
\(245\) 0 0
\(246\) −1.52786 + 4.00000i −0.0974131 + 0.255031i
\(247\) 10.4721i 0.666326i
\(248\) 2.76393i 0.175510i
\(249\) 23.7082 + 9.05573i 1.50245 + 0.573883i
\(250\) 0 0
\(251\) 12.4721 0.787234 0.393617 0.919274i \(-0.371224\pi\)
0.393617 + 0.919274i \(0.371224\pi\)
\(252\) 4.38197 6.61803i 0.276038 0.416897i
\(253\) 17.8885i 1.12464i
\(254\) 0.291796i 0.0183089i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 14.1803i 0.884545i −0.896881 0.442273i \(-0.854172\pi\)
0.896881 0.442273i \(-0.145828\pi\)
\(258\) −8.00000 3.05573i −0.498058 0.190241i
\(259\) −2.00000 + 0.291796i −0.124274 + 0.0181313i
\(260\) 0 0
\(261\) 15.4164 17.2361i 0.954252 1.06689i
\(262\) 5.41641 0.334627
\(263\) −12.9443 −0.798178 −0.399089 0.916912i \(-0.630674\pi\)
−0.399089 + 0.916912i \(0.630674\pi\)
\(264\) −7.23607 2.76393i −0.445349 0.170108i
\(265\) 0 0
\(266\) 22.1803 3.23607i 1.35996 0.198416i
\(267\) −3.41641 + 8.94427i −0.209081 + 0.547381i
\(268\) 12.0000i 0.733017i
\(269\) 4.47214 0.272671 0.136335 0.990663i \(-0.456467\pi\)
0.136335 + 0.990663i \(0.456467\pi\)
\(270\) 0 0
\(271\) 31.7082i 1.92614i −0.269258 0.963068i \(-0.586778\pi\)
0.269258 0.963068i \(-0.413222\pi\)
\(272\) 5.23607i 0.317483i
\(273\) 5.52786 + 1.23607i 0.334562 + 0.0748102i
\(274\) 3.52786 0.213126
\(275\) 0 0
\(276\) −2.47214 + 6.47214i −0.148805 + 0.389577i
\(277\) 17.1246i 1.02892i −0.857515 0.514459i \(-0.827993\pi\)
0.857515 0.514459i \(-0.172007\pi\)
\(278\) 11.5279i 0.691395i
\(279\) 5.52786 6.18034i 0.330945 0.370007i
\(280\) 0 0
\(281\) 20.0000i 1.19310i 0.802576 + 0.596550i \(0.203462\pi\)
−0.802576 + 0.596550i \(0.796538\pi\)
\(282\) −10.4721 4.00000i −0.623607 0.238197i
\(283\) −13.2361 −0.786803 −0.393401 0.919367i \(-0.628702\pi\)
−0.393401 + 0.919367i \(0.628702\pi\)
\(284\) 7.23607i 0.429382i
\(285\) 0 0
\(286\) 5.52786i 0.326869i
\(287\) 0.944272 + 6.47214i 0.0557386 + 0.382038i
\(288\) 2.23607 + 2.00000i 0.131762 + 0.117851i
\(289\) −10.4164 −0.612730
\(290\) 0 0
\(291\) 0.472136 1.23607i 0.0276771 0.0724596i
\(292\) 11.2361 0.657541
\(293\) 2.58359i 0.150935i −0.997148 0.0754675i \(-0.975955\pi\)
0.997148 0.0754675i \(-0.0240449\pi\)
\(294\) 0.909830 12.0902i 0.0530624 0.705113i
\(295\) 0 0
\(296\) 0.763932i 0.0444026i
\(297\) −10.6525 20.6525i −0.618119 1.19838i
\(298\) 4.29180i 0.248617i
\(299\) −4.94427 −0.285935
\(300\) 0 0
\(301\) −12.9443 + 1.88854i −0.746095 + 0.108854i
\(302\) −20.9443 −1.20521
\(303\) 7.70820 20.1803i 0.442825 1.15933i
\(304\) 8.47214i 0.485910i
\(305\) 0 0
\(306\) 10.4721 11.7082i 0.598652 0.669313i
\(307\) −18.1803 −1.03761 −0.518803 0.854894i \(-0.673622\pi\)
−0.518803 + 0.854894i \(0.673622\pi\)
\(308\) −11.7082 + 1.70820i −0.667137 + 0.0973340i
\(309\) 9.05573 23.7082i 0.515162 1.34871i
\(310\) 0 0
\(311\) −17.5279 −0.993914 −0.496957 0.867775i \(-0.665549\pi\)
−0.496957 + 0.867775i \(0.665549\pi\)
\(312\) −0.763932 + 2.00000i −0.0432491 + 0.113228i
\(313\) 5.70820 0.322647 0.161323 0.986902i \(-0.448424\pi\)
0.161323 + 0.986902i \(0.448424\pi\)
\(314\) 9.23607 0.521221
\(315\) 0 0
\(316\) 8.94427 0.503155
\(317\) 10.9443 0.614692 0.307346 0.951598i \(-0.400559\pi\)
0.307346 + 0.951598i \(0.400559\pi\)
\(318\) −0.291796 + 0.763932i −0.0163631 + 0.0428392i
\(319\) −34.4721 −1.93007
\(320\) 0 0
\(321\) −7.05573 + 18.4721i −0.393812 + 1.03101i
\(322\) 1.52786 + 10.4721i 0.0851445 + 0.583589i
\(323\) 44.3607 2.46829
\(324\) 1.00000 + 8.94427i 0.0555556 + 0.496904i
\(325\) 0 0
\(326\) 10.4721i 0.579998i
\(327\) −2.76393 + 7.23607i −0.152846 + 0.400155i
\(328\) −2.47214 −0.136501
\(329\) −16.9443 + 2.47214i −0.934168 + 0.136293i
\(330\) 0 0
\(331\) 3.05573 0.167958 0.0839790 0.996468i \(-0.473237\pi\)
0.0839790 + 0.996468i \(0.473237\pi\)
\(332\) 14.6525i 0.804159i
\(333\) 1.52786 1.70820i 0.0837264 0.0936090i
\(334\) 0.944272i 0.0516683i
\(335\) 0 0
\(336\) 4.47214 + 1.00000i 0.243975 + 0.0545545i
\(337\) 21.4164i 1.16663i 0.812247 + 0.583313i \(0.198244\pi\)
−0.812247 + 0.583313i \(0.801756\pi\)
\(338\) 11.4721 0.624002
\(339\) −1.81966 + 4.76393i −0.0988304 + 0.258741i
\(340\) 0 0
\(341\) −12.3607 −0.669368
\(342\) −16.9443 + 18.9443i −0.916241 + 1.02439i
\(343\) −7.79837 16.7984i −0.421073 0.907027i
\(344\) 4.94427i 0.266577i
\(345\) 0 0
\(346\) 9.41641i 0.506229i
\(347\) −2.47214 −0.132711 −0.0663556 0.997796i \(-0.521137\pi\)
−0.0663556 + 0.997796i \(0.521137\pi\)
\(348\) 12.4721 + 4.76393i 0.668577 + 0.255374i
\(349\) 20.1803i 1.08023i 0.841592 + 0.540114i \(0.181619\pi\)
−0.841592 + 0.540114i \(0.818381\pi\)
\(350\) 0 0
\(351\) −5.70820 + 2.94427i −0.304681 + 0.157154i
\(352\) 4.47214i 0.238366i
\(353\) 27.7082i 1.47476i −0.675479 0.737379i \(-0.736063\pi\)
0.675479 0.737379i \(-0.263937\pi\)
\(354\) −2.76393 + 7.23607i −0.146901 + 0.384593i
\(355\) 0 0
\(356\) −5.52786 −0.292976
\(357\) 5.23607 23.4164i 0.277122 1.23933i
\(358\) 14.9443i 0.789829i
\(359\) 12.1803i 0.642854i 0.946934 + 0.321427i \(0.104162\pi\)
−0.946934 + 0.321427i \(0.895838\pi\)
\(360\) 0 0
\(361\) −52.7771 −2.77774
\(362\) 16.1803i 0.850420i
\(363\) −5.56231 + 14.5623i −0.291945 + 0.764323i
\(364\) 0.472136 + 3.23607i 0.0247466 + 0.169616i
\(365\) 0 0
\(366\) 11.7082 + 4.47214i 0.611998 + 0.233762i
\(367\) −8.18034 −0.427010 −0.213505 0.976942i \(-0.568488\pi\)
−0.213505 + 0.976942i \(0.568488\pi\)
\(368\) −4.00000 −0.208514
\(369\) −5.52786 4.94427i −0.287769 0.257389i
\(370\) 0 0
\(371\) 0.180340 + 1.23607i 0.00936278 + 0.0641735i
\(372\) 4.47214 + 1.70820i 0.231869 + 0.0885662i
\(373\) 32.1803i 1.66623i 0.553096 + 0.833117i \(0.313446\pi\)
−0.553096 + 0.833117i \(0.686554\pi\)
\(374\) −23.4164 −1.21083
\(375\) 0 0
\(376\) 6.47214i 0.333775i
\(377\) 9.52786i 0.490710i
\(378\) 8.00000 + 11.1803i 0.411476 + 0.575055i
\(379\) 17.8885 0.918873 0.459436 0.888211i \(-0.348051\pi\)
0.459436 + 0.888211i \(0.348051\pi\)
\(380\) 0 0
\(381\) −0.472136 0.180340i −0.0241883 0.00923909i
\(382\) 7.23607i 0.370229i
\(383\) 13.8885i 0.709671i −0.934929 0.354836i \(-0.884537\pi\)
0.934929 0.354836i \(-0.115463\pi\)
\(384\) −0.618034 + 1.61803i −0.0315389 + 0.0825700i
\(385\) 0 0
\(386\) 6.00000i 0.305392i
\(387\) 9.88854 11.0557i 0.502663 0.561994i
\(388\) 0.763932 0.0387828
\(389\) 30.1803i 1.53020i −0.643909 0.765102i \(-0.722689\pi\)
0.643909 0.765102i \(-0.277311\pi\)
\(390\) 0 0
\(391\) 20.9443i 1.05920i
\(392\) 6.70820 2.00000i 0.338815 0.101015i
\(393\) −3.34752 + 8.76393i −0.168860 + 0.442082i
\(394\) 3.52786 0.177731
\(395\) 0 0
\(396\) 8.94427 10.0000i 0.449467 0.502519i
\(397\) 23.1246 1.16059 0.580295 0.814406i \(-0.302937\pi\)
0.580295 + 0.814406i \(0.302937\pi\)
\(398\) 22.1803i 1.11180i
\(399\) −8.47214 + 37.8885i −0.424137 + 1.89680i
\(400\) 0 0
\(401\) 14.4721i 0.722704i 0.932429 + 0.361352i \(0.117685\pi\)
−0.932429 + 0.361352i \(0.882315\pi\)
\(402\) 19.4164 + 7.41641i 0.968402 + 0.369897i
\(403\) 3.41641i 0.170183i
\(404\) 12.4721 0.620512
\(405\) 0 0
\(406\) 20.1803 2.94427i 1.00153 0.146122i
\(407\) −3.41641 −0.169345
\(408\) 8.47214 + 3.23607i 0.419433 + 0.160209i
\(409\) 7.41641i 0.366718i 0.983046 + 0.183359i \(0.0586970\pi\)
−0.983046 + 0.183359i \(0.941303\pi\)
\(410\) 0 0
\(411\) −2.18034 + 5.70820i −0.107548 + 0.281565i
\(412\) 14.6525 0.721876
\(413\) 1.70820 + 11.7082i 0.0840552 + 0.576123i
\(414\) −8.94427 8.00000i −0.439587 0.393179i
\(415\) 0 0
\(416\) −1.23607 −0.0606032
\(417\) −18.6525 7.12461i −0.913416 0.348894i
\(418\) 37.8885 1.85319
\(419\) 36.8328 1.79940 0.899700 0.436508i \(-0.143785\pi\)
0.899700 + 0.436508i \(0.143785\pi\)
\(420\) 0 0
\(421\) −3.52786 −0.171938 −0.0859688 0.996298i \(-0.527399\pi\)
−0.0859688 + 0.996298i \(0.527399\pi\)
\(422\) 8.00000 0.389434
\(423\) 12.9443 14.4721i 0.629372 0.703659i
\(424\) −0.472136 −0.0229289
\(425\) 0 0
\(426\) 11.7082 + 4.47214i 0.567264 + 0.216676i
\(427\) 18.9443 2.76393i 0.916778 0.133756i
\(428\) −11.4164 −0.551833
\(429\) 8.94427 + 3.41641i 0.431834 + 0.164946i
\(430\) 0 0
\(431\) 39.5967i 1.90731i −0.300905 0.953654i \(-0.597289\pi\)
0.300905 0.953654i \(-0.402711\pi\)
\(432\) −4.61803 + 2.38197i −0.222185 + 0.114602i
\(433\) −26.6525 −1.28084 −0.640418 0.768026i \(-0.721239\pi\)
−0.640418 + 0.768026i \(0.721239\pi\)
\(434\) 7.23607 1.05573i 0.347342 0.0506766i
\(435\) 0 0
\(436\) −4.47214 −0.214176
\(437\) 33.8885i 1.62111i
\(438\) −6.94427 + 18.1803i −0.331810 + 0.868690i
\(439\) 10.1803i 0.485881i 0.970041 + 0.242941i \(0.0781120\pi\)
−0.970041 + 0.242941i \(0.921888\pi\)
\(440\) 0 0
\(441\) 19.0000 + 8.94427i 0.904762 + 0.425918i
\(442\) 6.47214i 0.307848i
\(443\) −18.4721 −0.877638 −0.438819 0.898576i \(-0.644603\pi\)
−0.438819 + 0.898576i \(0.644603\pi\)
\(444\) 1.23607 + 0.472136i 0.0586612 + 0.0224066i
\(445\) 0 0
\(446\) 17.7082 0.838508
\(447\) 6.94427 + 2.65248i 0.328453 + 0.125458i
\(448\) 0.381966 + 2.61803i 0.0180462 + 0.123690i
\(449\) 10.4721i 0.494211i 0.968989 + 0.247105i \(0.0794794\pi\)
−0.968989 + 0.247105i \(0.920521\pi\)
\(450\) 0 0
\(451\) 11.0557i 0.520594i
\(452\) −2.94427 −0.138487
\(453\) 12.9443 33.8885i 0.608175 1.59222i
\(454\) 0.763932i 0.0358531i
\(455\) 0 0
\(456\) −13.7082 5.23607i −0.641945 0.245201i
\(457\) 26.9443i 1.26040i 0.776433 + 0.630200i \(0.217027\pi\)
−0.776433 + 0.630200i \(0.782973\pi\)
\(458\) 8.76393i 0.409512i
\(459\) 12.4721 + 24.1803i 0.582149 + 1.12864i
\(460\) 0 0
\(461\) 6.94427 0.323427 0.161713 0.986838i \(-0.448298\pi\)
0.161713 + 0.986838i \(0.448298\pi\)
\(462\) 4.47214 20.0000i 0.208063 0.930484i
\(463\) 22.1803i 1.03081i 0.856947 + 0.515404i \(0.172358\pi\)
−0.856947 + 0.515404i \(0.827642\pi\)
\(464\) 7.70820i 0.357844i
\(465\) 0 0
\(466\) −11.5279 −0.534018
\(467\) 33.7082i 1.55983i 0.625886 + 0.779915i \(0.284738\pi\)
−0.625886 + 0.779915i \(0.715262\pi\)
\(468\) −2.76393 2.47214i −0.127763 0.114275i
\(469\) 31.4164 4.58359i 1.45067 0.211651i
\(470\) 0 0
\(471\) −5.70820 + 14.9443i −0.263020 + 0.688596i
\(472\) −4.47214 −0.205847
\(473\) −22.1115 −1.01669
\(474\) −5.52786 + 14.4721i −0.253903 + 0.664727i
\(475\) 0 0
\(476\) 13.7082 2.00000i 0.628314 0.0916698i
\(477\) −1.05573 0.944272i −0.0483385 0.0432352i
\(478\) 0.180340i 0.00824855i
\(479\) 37.8885 1.73117 0.865586 0.500761i \(-0.166946\pi\)
0.865586 + 0.500761i \(0.166946\pi\)
\(480\) 0 0
\(481\) 0.944272i 0.0430551i
\(482\) 17.8885i 0.814801i
\(483\) −17.8885 4.00000i −0.813957 0.182006i
\(484\) −9.00000 −0.409091
\(485\) 0 0
\(486\) −15.0902 3.90983i −0.684504 0.177353i
\(487\) 17.5967i 0.797385i 0.917085 + 0.398692i \(0.130536\pi\)
−0.917085 + 0.398692i \(0.869464\pi\)
\(488\) 7.23607i 0.327561i
\(489\) 16.9443 + 6.47214i 0.766246 + 0.292680i
\(490\) 0 0
\(491\) 13.4164i 0.605474i 0.953074 + 0.302737i \(0.0979004\pi\)
−0.953074 + 0.302737i \(0.902100\pi\)
\(492\) 1.52786 4.00000i 0.0688814 0.180334i
\(493\) 40.3607 1.81775
\(494\) 10.4721i 0.471164i
\(495\) 0 0
\(496\) 2.76393i 0.124104i
\(497\) 18.9443 2.76393i 0.849767 0.123979i
\(498\) −23.7082 9.05573i −1.06239 0.405797i
\(499\) −17.8885 −0.800801 −0.400401 0.916340i \(-0.631129\pi\)
−0.400401 + 0.916340i \(0.631129\pi\)
\(500\) 0 0
\(501\) 1.52786 + 0.583592i 0.0682599 + 0.0260730i
\(502\) −12.4721 −0.556659
\(503\) 28.3607i 1.26454i −0.774748 0.632270i \(-0.782123\pi\)
0.774748 0.632270i \(-0.217877\pi\)
\(504\) −4.38197 + 6.61803i −0.195188 + 0.294791i
\(505\) 0 0
\(506\) 17.8885i 0.795243i
\(507\) −7.09017 + 18.5623i −0.314886 + 0.824381i
\(508\) 0.291796i 0.0129464i
\(509\) 15.5279 0.688260 0.344130 0.938922i \(-0.388174\pi\)
0.344130 + 0.938922i \(0.388174\pi\)
\(510\) 0 0
\(511\) 4.29180 + 29.4164i 0.189858 + 1.30131i
\(512\) −1.00000 −0.0441942
\(513\) −20.1803 39.1246i −0.890984 1.72739i
\(514\) 14.1803i 0.625468i
\(515\) 0 0
\(516\) 8.00000 + 3.05573i 0.352180 + 0.134521i
\(517\) −28.9443 −1.27297
\(518\) 2.00000 0.291796i 0.0878750 0.0128208i
\(519\) −15.2361 5.81966i −0.668789 0.255455i
\(520\) 0 0
\(521\) 36.9443 1.61856 0.809279 0.587425i \(-0.199858\pi\)
0.809279 + 0.587425i \(0.199858\pi\)
\(522\) −15.4164 + 17.2361i −0.674758 + 0.754402i
\(523\) 42.5410 1.86019 0.930094 0.367320i \(-0.119725\pi\)
0.930094 + 0.367320i \(0.119725\pi\)
\(524\) −5.41641 −0.236617
\(525\) 0 0
\(526\) 12.9443 0.564397
\(527\) 14.4721 0.630416
\(528\) 7.23607 + 2.76393i 0.314909 + 0.120285i
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) −10.0000 8.94427i −0.433963 0.388148i
\(532\) −22.1803 + 3.23607i −0.961640 + 0.140301i
\(533\) 3.05573 0.132358
\(534\) 3.41641 8.94427i 0.147842 0.387056i
\(535\) 0 0
\(536\) 12.0000i 0.518321i
\(537\) 24.1803 + 9.23607i 1.04346 + 0.398566i
\(538\) −4.47214 −0.192807
\(539\) −8.94427 30.0000i −0.385257 1.29219i
\(540\) 0 0
\(541\) 30.9443 1.33040 0.665199 0.746666i \(-0.268347\pi\)
0.665199 + 0.746666i \(0.268347\pi\)
\(542\) 31.7082i 1.36198i
\(543\) 26.1803 + 10.0000i 1.12351 + 0.429141i
\(544\) 5.23607i 0.224495i
\(545\) 0 0
\(546\) −5.52786 1.23607i −0.236571 0.0528988i
\(547\) 35.4164i 1.51430i −0.653243 0.757148i \(-0.726592\pi\)
0.653243 0.757148i \(-0.273408\pi\)
\(548\) −3.52786 −0.150703
\(549\) −14.4721 + 16.1803i −0.617656 + 0.690560i
\(550\) 0 0
\(551\) −65.3050 −2.78208
\(552\) 2.47214 6.47214i 0.105221 0.275472i
\(553\) 3.41641 + 23.4164i 0.145280 + 0.995767i
\(554\) 17.1246i 0.727555i
\(555\) 0 0
\(556\) 11.5279i 0.488890i
\(557\) 7.52786 0.318966 0.159483 0.987201i \(-0.449017\pi\)
0.159483 + 0.987201i \(0.449017\pi\)
\(558\) −5.52786 + 6.18034i −0.234013 + 0.261635i
\(559\) 6.11146i 0.258487i
\(560\) 0 0
\(561\) 14.4721 37.8885i 0.611014 1.59966i
\(562\) 20.0000i 0.843649i
\(563\) 40.1803i 1.69340i 0.532071 + 0.846700i \(0.321414\pi\)
−0.532071 + 0.846700i \(0.678586\pi\)
\(564\) 10.4721 + 4.00000i 0.440956 + 0.168430i
\(565\) 0 0
\(566\) 13.2361 0.556353
\(567\) −23.0344 + 6.03444i −0.967356 + 0.253423i
\(568\) 7.23607i 0.303619i
\(569\) 9.52786i 0.399429i −0.979854 0.199714i \(-0.935999\pi\)
0.979854 0.199714i \(-0.0640014\pi\)
\(570\) 0 0
\(571\) 18.8328 0.788129 0.394064 0.919083i \(-0.371069\pi\)
0.394064 + 0.919083i \(0.371069\pi\)
\(572\) 5.52786i 0.231132i
\(573\) 11.7082 + 4.47214i 0.489117 + 0.186826i
\(574\) −0.944272 6.47214i −0.0394131 0.270142i
\(575\) 0 0
\(576\) −2.23607 2.00000i −0.0931695 0.0833333i
\(577\) −8.18034 −0.340552 −0.170276 0.985396i \(-0.554466\pi\)
−0.170276 + 0.985396i \(0.554466\pi\)
\(578\) 10.4164 0.433265
\(579\) 9.70820 + 3.70820i 0.403459 + 0.154108i
\(580\) 0 0
\(581\) −38.3607 + 5.59675i −1.59147 + 0.232192i
\(582\) −0.472136 + 1.23607i −0.0195707 + 0.0512367i
\(583\) 2.11146i 0.0874476i
\(584\) −11.2361 −0.464952
\(585\) 0 0
\(586\) 2.58359i 0.106727i
\(587\) 10.2918i 0.424788i 0.977184 + 0.212394i \(0.0681260\pi\)
−0.977184 + 0.212394i \(0.931874\pi\)
\(588\) −0.909830 + 12.0902i −0.0375208 + 0.498590i
\(589\) −23.4164 −0.964856
\(590\) 0 0
\(591\) −2.18034 + 5.70820i −0.0896872 + 0.234804i
\(592\) 0.763932i 0.0313974i
\(593\) 29.0132i 1.19143i −0.803197 0.595714i \(-0.796869\pi\)
0.803197 0.595714i \(-0.203131\pi\)
\(594\) 10.6525 + 20.6525i 0.437076 + 0.847381i
\(595\) 0 0
\(596\) 4.29180i 0.175799i
\(597\) −35.8885 13.7082i −1.46882 0.561039i
\(598\) 4.94427 0.202186
\(599\) 36.7639i 1.50213i −0.660226 0.751067i \(-0.729540\pi\)
0.660226 0.751067i \(-0.270460\pi\)
\(600\) 0 0
\(601\) 5.52786i 0.225486i −0.993624 0.112743i \(-0.964036\pi\)
0.993624 0.112743i \(-0.0359637\pi\)
\(602\) 12.9443 1.88854i 0.527569 0.0769713i
\(603\) −24.0000 + 26.8328i −0.977356 + 1.09272i
\(604\) 20.9443 0.852210
\(605\) 0 0
\(606\) −7.70820 + 20.1803i −0.313124 + 0.819770i
\(607\) −19.2361 −0.780768 −0.390384 0.920652i \(-0.627658\pi\)
−0.390384 + 0.920652i \(0.627658\pi\)
\(608\) 8.47214i 0.343590i
\(609\) −7.70820 + 34.4721i −0.312352 + 1.39688i
\(610\) 0 0
\(611\) 8.00000i 0.323645i
\(612\) −10.4721 + 11.7082i −0.423311 + 0.473276i
\(613\) 38.0689i 1.53759i −0.639497 0.768794i \(-0.720857\pi\)
0.639497 0.768794i \(-0.279143\pi\)
\(614\) 18.1803 0.733699
\(615\) 0 0
\(616\) 11.7082 1.70820i 0.471737 0.0688255i
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) −9.05573 + 23.7082i −0.364275 + 0.953684i
\(619\) 14.0000i 0.562708i 0.959604 + 0.281354i \(0.0907834\pi\)
−0.959604 + 0.281354i \(0.909217\pi\)
\(620\) 0 0
\(621\) 18.4721 9.52786i 0.741261 0.382340i
\(622\) 17.5279 0.702803
\(623\) −2.11146 14.4721i −0.0845937 0.579814i
\(624\) 0.763932 2.00000i 0.0305818 0.0800641i
\(625\) 0 0
\(626\) −5.70820 −0.228146
\(627\) −23.4164 + 61.3050i −0.935161 + 2.44828i
\(628\) −9.23607 −0.368559
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −5.88854 −0.234419 −0.117210 0.993107i \(-0.537395\pi\)
−0.117210 + 0.993107i \(0.537395\pi\)
\(632\) −8.94427 −0.355784
\(633\) −4.94427 + 12.9443i −0.196517 + 0.514489i
\(634\) −10.9443 −0.434653
\(635\) 0 0
\(636\) 0.291796 0.763932i 0.0115705 0.0302919i
\(637\) −8.29180 + 2.47214i −0.328533 + 0.0979496i
\(638\) 34.4721 1.36476
\(639\) −14.4721 + 16.1803i −0.572509 + 0.640084i
\(640\) 0 0
\(641\) 23.4164i 0.924893i 0.886647 + 0.462446i \(0.153028\pi\)
−0.886647 + 0.462446i \(0.846972\pi\)
\(642\) 7.05573 18.4721i 0.278467 0.729037i
\(643\) 12.2918 0.484741 0.242371 0.970184i \(-0.422075\pi\)
0.242371 + 0.970184i \(0.422075\pi\)
\(644\) −1.52786 10.4721i −0.0602063 0.412660i
\(645\) 0 0
\(646\) −44.3607 −1.74535
\(647\) 34.8328i 1.36942i −0.728816 0.684710i \(-0.759929\pi\)
0.728816 0.684710i \(-0.240071\pi\)
\(648\) −1.00000 8.94427i −0.0392837 0.351364i
\(649\) 20.0000i 0.785069i
\(650\) 0 0
\(651\) −2.76393 + 12.3607i −0.108327 + 0.484453i
\(652\) 10.4721i 0.410120i
\(653\) 23.8885 0.934831 0.467415 0.884038i \(-0.345185\pi\)
0.467415 + 0.884038i \(0.345185\pi\)
\(654\) 2.76393 7.23607i 0.108078 0.282953i
\(655\) 0 0
\(656\) 2.47214 0.0965207
\(657\) −25.1246 22.4721i −0.980204 0.876722i
\(658\) 16.9443 2.47214i 0.660556 0.0963739i
\(659\) 31.5279i 1.22815i 0.789247 + 0.614076i \(0.210471\pi\)
−0.789247 + 0.614076i \(0.789529\pi\)
\(660\) 0 0
\(661\) 18.2918i 0.711468i −0.934587 0.355734i \(-0.884231\pi\)
0.934587 0.355734i \(-0.115769\pi\)
\(662\) −3.05573 −0.118764
\(663\) −10.4721 4.00000i −0.406704 0.155347i
\(664\) 14.6525i 0.568626i
\(665\) 0 0
\(666\) −1.52786 + 1.70820i −0.0592035 + 0.0661916i
\(667\) 30.8328i 1.19385i
\(668\) 0.944272i 0.0365350i
\(669\) −10.9443 + 28.6525i −0.423130 + 1.10777i
\(670\) 0 0
\(671\) 32.3607 1.24927
\(672\) −4.47214 1.00000i −0.172516 0.0385758i
\(673\) 19.5279i 0.752744i −0.926469 0.376372i \(-0.877171\pi\)
0.926469 0.376372i \(-0.122829\pi\)
\(674\) 21.4164i 0.824929i
\(675\) 0 0
\(676\) −11.4721 −0.441236
\(677\) 18.0000i 0.691796i −0.938272 0.345898i \(-0.887574\pi\)
0.938272 0.345898i \(-0.112426\pi\)
\(678\) 1.81966 4.76393i 0.0698836 0.182958i
\(679\) 0.291796 + 2.00000i 0.0111981 + 0.0767530i
\(680\) 0 0
\(681\) −1.23607 0.472136i −0.0473662 0.0180923i
\(682\) 12.3607 0.473315
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 16.9443 18.9443i 0.647880 0.724352i
\(685\) 0 0
\(686\) 7.79837 + 16.7984i 0.297743 + 0.641365i
\(687\) −14.1803 5.41641i −0.541014 0.206649i
\(688\) 4.94427i 0.188499i
\(689\) 0.583592 0.0222331
\(690\) 0 0
\(691\) 21.0557i 0.800998i 0.916297 + 0.400499i \(0.131163\pi\)
−0.916297 + 0.400499i \(0.868837\pi\)
\(692\) 9.41641i 0.357958i
\(693\) 29.5967 + 19.5967i 1.12429 + 0.744419i
\(694\) 2.47214 0.0938410
\(695\) 0 0
\(696\) −12.4721 4.76393i −0.472755 0.180576i
\(697\) 12.9443i 0.490299i
\(698\) 20.1803i 0.763837i
\(699\) 7.12461 18.6525i 0.269478 0.705501i
\(700\) 0 0
\(701\) 44.0689i 1.66446i −0.554431 0.832229i \(-0.687064\pi\)
0.554431 0.832229i \(-0.312936\pi\)
\(702\) 5.70820 2.94427i 0.215442 0.111124i
\(703\) −6.47214 −0.244101
\(704\) 4.47214i 0.168550i
\(705\) 0 0
\(706\) 27.7082i 1.04281i
\(707\) 4.76393 + 32.6525i 0.179166 + 1.22802i
\(708\) 2.76393 7.23607i 0.103875 0.271948i
\(709\) 15.5279 0.583161 0.291581 0.956546i \(-0.405819\pi\)
0.291581 + 0.956546i \(0.405819\pi\)
\(710\) 0 0
\(711\) −20.0000 17.8885i −0.750059 0.670873i
\(712\) 5.52786 0.207165
\(713\) 11.0557i 0.414040i
\(714\) −5.23607 + 23.4164i −0.195955 + 0.876337i
\(715\) 0 0
\(716\) 14.9443i 0.558494i
\(717\) −0.291796 0.111456i −0.0108973 0.00416241i
\(718\) 12.1803i 0.454566i
\(719\) −34.4721 −1.28559 −0.642797 0.766037i \(-0.722226\pi\)
−0.642797 + 0.766037i \(0.722226\pi\)
\(720\) 0 0
\(721\) 5.59675 + 38.3607i 0.208434 + 1.42863i
\(722\) 52.7771 1.96416
\(723\) −28.9443 11.0557i −1.07645 0.411167i
\(724\) 16.1803i 0.601338i
\(725\) 0 0
\(726\) 5.56231 14.5623i 0.206437 0.540458i
\(727\) 26.2918 0.975109 0.487554 0.873093i \(-0.337889\pi\)
0.487554 + 0.873093i \(0.337889\pi\)
\(728\) −0.472136 3.23607i −0.0174985 0.119937i
\(729\) 15.6525 22.0000i 0.579721 0.814815i
\(730\) 0 0
\(731\) 25.8885 0.957522
\(732\) −11.7082 4.47214i −0.432748 0.165295i
\(733\) −20.0689 −0.741261 −0.370631 0.928780i \(-0.620858\pi\)
−0.370631 + 0.928780i \(0.620858\pi\)
\(734\) 8.18034 0.301942
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 53.6656 1.97680
\(738\) 5.52786 + 4.94427i 0.203483 + 0.182001i
\(739\) −8.94427 −0.329020 −0.164510 0.986375i \(-0.552604\pi\)
−0.164510 + 0.986375i \(0.552604\pi\)
\(740\) 0 0
\(741\) 16.9443 + 6.47214i 0.622463 + 0.237760i
\(742\) −0.180340 1.23607i −0.00662049 0.0453775i
\(743\) 10.4721 0.384185 0.192093 0.981377i \(-0.438473\pi\)
0.192093 + 0.981377i \(0.438473\pi\)
\(744\) −4.47214 1.70820i −0.163956 0.0626258i
\(745\) 0 0
\(746\) 32.1803i 1.17821i
\(747\) 29.3050 32.7639i 1.07221 1.19877i
\(748\) 23.4164 0.856189
\(749\) −4.36068 29.8885i −0.159336 1.09210i
\(750\) 0 0
\(751\) 8.58359 0.313220 0.156610 0.987661i \(-0.449943\pi\)
0.156610 + 0.987661i \(0.449943\pi\)
\(752\) 6.47214i 0.236015i
\(753\) 7.70820 20.1803i 0.280903 0.735412i
\(754\) 9.52786i 0.346984i
\(755\) 0 0
\(756\) −8.00000 11.1803i −0.290957 0.406625i
\(757\) 2.65248i 0.0964059i −0.998838 0.0482029i \(-0.984651\pi\)
0.998838 0.0482029i \(-0.0153494\pi\)
\(758\) −17.8885 −0.649741
\(759\) −28.9443 11.0557i −1.05061 0.401298i
\(760\) 0 0
\(761\) 5.88854 0.213460 0.106730 0.994288i \(-0.465962\pi\)
0.106730 + 0.994288i \(0.465962\pi\)
\(762\) 0.472136 + 0.180340i 0.0171037 + 0.00653302i
\(763\) −1.70820 11.7082i −0.0618411 0.423865i
\(764\) 7.23607i 0.261792i
\(765\) 0 0
\(766\) 13.8885i 0.501813i
\(767\) 5.52786 0.199600
\(768\) 0.618034 1.61803i 0.0223014 0.0583858i
\(769\) 36.0000i 1.29819i −0.760706 0.649097i \(-0.775147\pi\)
0.760706 0.649097i \(-0.224853\pi\)
\(770\) 0 0
\(771\) −22.9443 8.76393i −0.826318 0.315625i
\(772\) 6.00000i 0.215945i
\(773\) 10.5836i 0.380665i 0.981720 + 0.190333i \(0.0609567\pi\)
−0.981720 + 0.190333i \(0.939043\pi\)
\(774\) −9.88854 + 11.0557i −0.355436 + 0.397390i
\(775\) 0 0
\(776\) −0.763932 −0.0274236
\(777\) −0.763932 + 3.41641i −0.0274059 + 0.122563i
\(778\) 30.1803i 1.08202i
\(779\) 20.9443i 0.750406i
\(780\) 0 0
\(781\) 32.3607 1.15796
\(782\) 20.9443i 0.748966i
\(783\) −18.3607 35.5967i −0.656157 1.27212i
\(784\) −6.70820 + 2.00000i −0.239579 + 0.0714286i
\(785\) 0 0
\(786\) 3.34752 8.76393i 0.119402 0.312599i
\(787\) 36.2918 1.29366 0.646831 0.762633i \(-0.276094\pi\)
0.646831 + 0.762633i \(0.276094\pi\)
\(788\) −3.52786 −0.125675
\(789\) −8.00000 <