Properties

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

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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.d.1049.4

$q$-expansion

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

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 \(-0.575745\pi\)
0.235722 0.971821i \(-0.424255\pi\)
\(20\) 0 0
\(21\) −4.00000 2.23607i −0.872872 0.487950i
\(22\) 4.47214i 0.953463i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 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 \(-0.920158\pi\)
0.968707 0.248208i \(-0.0798418\pi\)
\(32\) 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 \(-0.979999\pi\)
0.998026 0.0627948i \(-0.0200014\pi\)
\(38\) 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 \(-0.561835\pi\)
−0.193041 + 0.981191i \(0.561835\pi\)
\(42\) −4.00000 2.23607i −0.617213 0.345033i
\(43\) 4.94427i 0.753994i −0.926214 0.376997i \(-0.876957\pi\)
0.926214 0.376997i \(-0.123043\pi\)
\(44\) 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 \(-0.510323\pi\)
−0.0324264 + 0.999474i \(0.510323\pi\)
\(54\) −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 \(-0.594025\pi\)
−0.291111 + 0.956689i \(0.594025\pi\)
\(60\) 0 0
\(61\) 7.23607i 0.926484i 0.886232 + 0.463242i \(0.153314\pi\)
−0.886232 + 0.463242i \(0.846686\pi\)
\(62\) 2.76393i 0.351020i
\(63\) −6.09017 + 5.09017i −0.767289 + 0.641301i
\(64\) 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 \(0.261888\pi\)
−0.680211 + 0.733017i \(0.738112\pi\)
\(68\) 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 \(0.702616\pi\)
\(84\) −4.00000 2.23607i −0.436436 0.243975i
\(85\) 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 \(-0.405354\pi\)
0.292976 + 0.956120i \(0.405354\pi\)
\(90\) 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 \(-0.713075\pi\)
−0.620512 + 0.784197i \(0.713075\pi\)
\(102\) −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 \(-0.313929\pi\)
0.551833 + 0.833955i \(0.313929\pi\)
\(108\) −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 \(-0.455776\pi\)
0.138487 + 0.990364i \(0.455776\pi\)
\(114\) −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
\(126\) −6.09017 + 5.09017i −0.542555 + 0.453468i
\(127\) 0.291796i 0.0258927i 0.999916 + 0.0129464i \(0.00412107\pi\)
−0.999916 + 0.0129464i \(0.995879\pi\)
\(128\) 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 \(-0.423961\pi\)
0.236617 + 0.971603i \(0.423961\pi\)
\(132\) 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 \(-0.451846\pi\)
0.150703 + 0.988579i \(0.451846\pi\)
\(138\) 2.47214 6.47214i 0.210442 0.550945i
\(139\) 11.5279i 0.977781i 0.872345 + 0.488890i \(0.162598\pi\)
−0.872345 + 0.488890i \(0.837402\pi\)
\(140\) 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
\(147\) −7.38197 + 9.61803i −0.608854 + 0.793282i
\(148\) 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 \(-0.865487\pi\)
0.912031 0.410120i \(-0.134513\pi\)
\(164\) −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 \(0.988368\pi\)
\(168\) −4.00000 2.23607i −0.308607 0.172516i
\(169\) −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 \(-0.794635\pi\)
0.798995 0.601338i \(-0.205365\pi\)
\(182\) 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
\(189\) 4.47214 + 13.0000i 0.325300 + 0.945611i
\(190\) 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 \(-0.930717\pi\)
0.976406 0.215945i \(-0.0692831\pi\)
\(194\) 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 \(-0.459890\pi\)
0.125675 + 0.992071i \(0.459890\pi\)
\(198\) 8.94427 10.0000i 0.635642 0.710669i
\(199\) 22.1803i 1.57232i 0.618021 + 0.786161i \(0.287935\pi\)
−0.618021 + 0.786161i \(0.712065\pi\)
\(200\) 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 \(0.0935118\pi\)
−0.957157 + 0.289568i \(0.906488\pi\)
\(230\) 0 0
\(231\) 10.0000 17.8885i 0.657952 1.17698i
\(232\) 7.70820i 0.506068i
\(233\) −11.5279 −0.755215 −0.377608 0.925966i \(-0.623253\pi\)
−0.377608 + 0.925966i \(0.623253\pi\)
\(234\) −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 \(0.195446\pi\)
−0.817343 + 0.576151i \(0.804554\pi\)
\(242\) −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 \(-0.628776\pi\)
−0.393617 + 0.919274i \(0.628776\pi\)
\(252\) −6.09017 + 5.09017i −0.383645 + 0.320651i
\(253\) 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 \(-0.369326\pi\)
0.399089 + 0.916912i \(0.369326\pi\)
\(264\) 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 \(-0.543533\pi\)
−0.136335 + 0.990663i \(0.543533\pi\)
\(270\) 0 0
\(271\) 31.7082i 1.92614i 0.269258 + 0.963068i \(0.413222\pi\)
−0.269258 + 0.963068i \(0.586778\pi\)
\(272\) 5.23607i 0.317483i
\(273\) −4.94427 2.76393i −0.299241 0.167281i
\(274\) 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 \(0.172007\pi\)
−0.857515 + 0.514459i \(0.827993\pi\)
\(278\) 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 \(-0.0240449\pi\)
\(294\) −7.38197 + 9.61803i −0.430525 + 0.560935i
\(295\) 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 \(-0.334451\pi\)
0.496957 + 0.867775i \(0.334451\pi\)
\(312\) 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 \(-0.599441\pi\)
−0.307346 + 0.951598i \(0.599441\pi\)
\(318\) −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
\(336\) −4.00000 2.23607i −0.218218 0.121988i
\(337\) 21.4164i 1.16663i −0.812247 0.583313i \(-0.801756\pi\)
0.812247 0.583313i \(-0.198244\pi\)
\(338\) −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 \(-0.478863\pi\)
0.0663556 + 0.997796i \(0.478863\pi\)
\(348\) 12.4721 + 4.76393i 0.668577 + 0.255374i
\(349\) 20.1803i 1.08023i −0.841592 0.540114i \(-0.818381\pi\)
0.841592 0.540114i \(-0.181619\pi\)
\(350\) 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
\(357\) −11.7082 + 20.9443i −0.619664 + 1.10849i
\(358\) 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 \(-0.686554\pi\)
0.553096 0.833117i \(-0.313446\pi\)
\(374\) 23.4164 1.21083
\(375\) 0 0
\(376\) 6.47214i 0.333775i
\(377\) 9.52786i 0.490710i
\(378\) 4.47214 + 13.0000i 0.230022 + 0.668648i
\(379\) 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
\(399\) −18.9443 + 33.8885i −0.948400 + 1.69655i
\(400\) 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 \(-0.941303\pi\)
0.983046 0.183359i \(-0.0586970\pi\)
\(410\) 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 \(-0.856215\pi\)
−0.899700 + 0.436508i \(0.856215\pi\)
\(420\) 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 \(-0.921888\pi\)
0.970041 0.242941i \(-0.0781120\pi\)
\(440\) 0 0
\(441\) 11.0000 + 17.8885i 0.523810 + 0.851835i
\(442\) 6.47214i 0.307848i
\(443\) 18.4721 0.877638 0.438819 0.898576i \(-0.355397\pi\)
0.438819 + 0.898576i \(0.355397\pi\)
\(444\) −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 \(-0.782973\pi\)
0.776433 0.630200i \(-0.217027\pi\)
\(458\) 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 \(-0.551702\pi\)
−0.161713 + 0.986838i \(0.551702\pi\)
\(462\) 10.0000 17.8885i 0.465242 0.832250i
\(463\) 22.1803i 1.03081i −0.856947 0.515404i \(-0.827642\pi\)
0.856947 0.515404i \(-0.172358\pi\)
\(464\) 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 \(-0.833054\pi\)
−0.865586 + 0.500761i \(0.833054\pi\)
\(480\) 0 0
\(481\) 0.944272i 0.0430551i
\(482\) 17.8885i 0.814801i
\(483\) −16.0000 8.94427i −0.728025 0.406978i
\(484\) −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 \(-0.869464\pi\)
0.917085 0.398692i \(-0.130536\pi\)
\(488\) 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 \(-0.217877\pi\)
\(504\) −6.09017 + 5.09017i −0.271278 + 0.226734i
\(505\) 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 \(-0.611826\pi\)
−0.344130 + 0.938922i \(0.611826\pi\)
\(510\) 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 \(-0.800142\pi\)
−0.809279 + 0.587425i \(0.800142\pi\)
\(522\) 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
\(546\) −4.94427 2.76393i −0.211595 0.118285i
\(547\) 35.4164i 1.51430i 0.653243 + 0.757148i \(0.273408\pi\)
−0.653243 + 0.757148i \(0.726592\pi\)
\(548\) 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 \(-0.550983\pi\)
−0.159483 + 0.987201i \(0.550983\pi\)
\(558\) −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
\(567\) 23.7984 + 0.798374i 0.999438 + 0.0335286i
\(568\) 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 \(0.931874\pi\)
\(588\) −7.38197 + 9.61803i −0.304427 + 0.396641i
\(589\) −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 \(0.0359637\pi\)
−0.993624 + 0.112743i \(0.964036\pi\)
\(602\) −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
\(609\) 17.2361 30.8328i 0.698441 1.24941i
\(610\) 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 \(0.279143\pi\)
−0.639497 + 0.768794i \(0.720857\pi\)
\(614\) −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 \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 9.05573 23.7082i 0.364275 0.953684i
\(619\) 14.0000i 0.562708i −0.959604 0.281354i \(-0.909217\pi\)
0.959604 0.281354i \(-0.0907834\pi\)
\(620\) 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
\(651\) −6.18034 + 11.0557i −0.242227 + 0.433308i
\(652\) 10.4721i 0.410120i
\(653\) −23.8885 −0.934831 −0.467415 0.884038i \(-0.654815\pi\)
−0.467415 + 0.884038i \(0.654815\pi\)
\(654\) −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 \(0.115769\pi\)
−0.934587 + 0.355734i \(0.884231\pi\)
\(662\) 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
\(672\) −4.00000 2.23607i −0.154303 0.0862582i
\(673\) 19.5279i 0.752744i 0.926469 + 0.376372i \(0.122829\pi\)
−0.926469 + 0.376372i \(0.877171\pi\)
\(674\) 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 \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) −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 \(-0.868837\pi\)
0.916297 0.400499i \(-0.131163\pi\)
\(692\) 9.41641i 0.357958i
\(693\) −22.7639 27.2361i −0.864730 1.03461i
\(694\) 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
\(714\) −11.7082 + 20.9443i −0.438169 + 0.783820i
\(715\) 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 \(-0.277774\pi\)
0.642797 + 0.766037i \(0.277774\pi\)
\(720\) 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 \(-0.561527\pi\)
−0.192093 + 0.981377i \(0.561527\pi\)
\(744\) −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
\(756\) 4.47214 + 13.0000i 0.162650 + 0.472805i
\(757\) 2.65248i 0.0964059i 0.998838 + 0.0482029i \(0.0153494\pi\)
−0.998838 + 0.0482029i \(0.984651\pi\)
\(758\) 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 \(-0.534038\pi\)
−0.106730 + 0.994288i \(0.534038\pi\)
\(762\) 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 \(0.224853\pi\)
−0.760706 + 0.649097i \(0.775147\pi\)
\(770\) 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
\(777\) −1.70820 + 3.05573i −0.0612815 + 0.109624i
\(778\) 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