Properties

Label 1050.2.b.a.251.1
Level 1050
Weight 2
Character 1050.251
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.b (of order \(2\), degree \(1\), 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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.1
Root \(-0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 1050.251
Dual form 1050.2.b.a.251.3

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.61803 0.618034i −0.934172 0.356822i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) −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
\(10\) 0 0
\(11\) 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
\(15\) 0 0
\(16\) 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 \(-0.575745\pi\)
0.235722 0.971821i \(-0.424255\pi\)
\(20\) 0 0
\(21\) 4.47214 + 1.00000i 0.975900 + 0.218218i
\(22\) 4.47214 0.953463
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 0.618034 1.61803i 0.126156 0.330280i
\(25\) 0 0
\(26\) −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 0
\(31\) 2.76393i 0.496417i 0.968707 + 0.248208i \(0.0798418\pi\)
−0.968707 + 0.248208i \(0.920158\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.76393 7.23607i 0.481139 1.25964i
\(34\) 5.23607i 0.897978i
\(35\) 0 0
\(36\) −2.23607 2.00000i −0.372678 0.333333i
\(37\) −0.763932 −0.125590 −0.0627948 0.998026i \(-0.520001\pi\)
−0.0627948 + 0.998026i \(0.520001\pi\)
\(38\) −8.47214 −1.37436
\(39\) −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 \(0.438165\pi\)
\(42\) 1.00000 4.47214i 0.154303 0.690066i
\(43\) 4.94427 0.753994 0.376997 0.926214i \(-0.376957\pi\)
0.376997 + 0.926214i \(0.376957\pi\)
\(44\) 4.47214i 0.674200i
\(45\) 0 0
\(46\) 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
\(50\) 0 0
\(51\) −8.47214 3.23607i −1.18634 0.453140i
\(52\) 1.23607i 0.171412i
\(53\) 0.472136i 0.0648529i −0.999474 0.0324264i \(-0.989677\pi\)
0.999474 0.0324264i \(-0.0103235\pi\)
\(54\) −4.61803 + 2.38197i −0.628435 + 0.324145i
\(55\) 0 0
\(56\) −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 \(-0.594025\pi\)
−0.291111 + 0.956689i \(0.594025\pi\)
\(60\) 0 0
\(61\) 7.23607i 0.926484i −0.886232 0.463242i \(-0.846686\pi\)
0.886232 0.463242i \(-0.153314\pi\)
\(62\) 2.76393 0.351020
\(63\) −6.61803 4.38197i −0.833794 0.552076i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −7.23607 2.76393i −0.890698 0.340217i
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −5.23607 −0.634967
\(69\) 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 \(-0.141268\pi\)
\(72\) −2.00000 + 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
\(75\) 0 0
\(76\) 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 \(0.667827\pi\)
\(80\) 0 0
\(81\) 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 \(0.202616\pi\)
\(84\) −4.47214 1.00000i −0.487950 0.109109i
\(85\) 0 0
\(86\) 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 \(-0.405354\pi\)
0.292976 + 0.956120i \(0.405354\pi\)
\(90\) 0 0
\(91\) 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
\(95\) 0 0
\(96\) −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
\(100\) 0 0
\(101\) 12.4721 1.24102 0.620512 0.784197i \(-0.286925\pi\)
0.620512 + 0.784197i \(0.286925\pi\)
\(102\) −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
\(105\) 0 0
\(106\) −0.472136 −0.0458579
\(107\) 11.4164i 1.10367i −0.833955 0.551833i \(-0.813929\pi\)
0.833955 0.551833i \(-0.186071\pi\)
\(108\) 2.38197 + 4.61803i 0.229205 + 0.444371i
\(109\) 4.47214 0.428353 0.214176 0.976795i \(-0.431293\pi\)
0.214176 + 0.976795i \(0.431293\pi\)
\(110\) 0 0
\(111\) 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 \(0.0442239\pi\)
−0.990364 + 0.138487i \(0.955776\pi\)
\(114\) 13.7082 + 5.23607i 1.28389 + 0.490403i
\(115\) 0 0
\(116\) 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 0
\(121\) −9.00000 −0.818182
\(122\) −7.23607 −0.655123
\(123\) −4.00000 1.52786i −0.360668 0.137763i
\(124\) 2.76393i 0.248208i
\(125\) 0 0
\(126\) −4.38197 + 6.61803i −0.390377 + 0.589581i
\(127\) 0.291796 0.0258927 0.0129464 0.999916i \(-0.495879\pi\)
0.0129464 + 0.999916i \(0.495879\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −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 \(0.576039\pi\)
\(132\) −2.76393 + 7.23607i −0.240569 + 0.629819i
\(133\) 3.23607 + 22.1803i 0.280603 + 1.92328i
\(134\) 12.0000i 1.03664i
\(135\) 0 0
\(136\) 5.23607i 0.448989i
\(137\) 3.52786i 0.301406i −0.988579 0.150703i \(-0.951846\pi\)
0.988579 0.150703i \(-0.0481537\pi\)
\(138\) −6.47214 2.47214i −0.550945 0.210442i
\(139\) 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
\(142\) −7.23607 −0.607237
\(143\) 5.52786 0.462263
\(144\) 2.23607 + 2.00000i 0.186339 + 0.166667i
\(145\) 0 0
\(146\) −11.2361 −0.929904
\(147\) −12.0902 0.909830i −0.997180 0.0750415i
\(148\) 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 0
\(151\) 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
\(155\) 0 0
\(156\) 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
\(160\) 0 0
\(161\) −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 \(-0.365487\pi\)
0.410120 + 0.912031i \(0.365487\pi\)
\(164\) −2.47214 −0.193041
\(165\) 0 0
\(166\) 14.6525i 1.13725i
\(167\) −0.944272 −0.0730700 −0.0365350 0.999332i \(-0.511632\pi\)
−0.0365350 + 0.999332i \(0.511632\pi\)
\(168\) −1.00000 + 4.47214i −0.0771517 + 0.345033i
\(169\) 11.4721 0.882472
\(170\) 0 0
\(171\) 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
\(175\) 0 0
\(176\) 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 \(-0.188620\pi\)
\(180\) 0 0
\(181\) 16.1803i 1.20268i 0.798995 + 0.601338i \(0.205365\pi\)
−0.798995 + 0.601338i \(0.794635\pi\)
\(182\) 3.23607 0.472136i 0.239873 0.0349970i
\(183\) −4.47214 + 11.7082i −0.330590 + 0.865495i
\(184\) −4.00000 −0.294884
\(185\) 0 0
\(186\) −4.47214 1.70820i −0.327913 0.125252i
\(187\) 23.4164i 1.71238i
\(188\) 6.47214 0.472029
\(189\) 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 \(0.915687\pi\)
\(192\) 1.61803 + 0.618034i 0.116772 + 0.0446028i
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 0.763932 0.0548471
\(195\) 0 0
\(196\) −6.70820 + 2.00000i −0.479157 + 0.142857i
\(197\) 3.52786i 0.251350i −0.992071 0.125675i \(-0.959890\pi\)
0.992071 0.125675i \(-0.0401096\pi\)
\(198\) 10.0000 + 8.94427i 0.710669 + 0.635642i
\(199\) 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
\(202\) 12.4721i 0.877536i
\(203\) 2.94427 + 20.1803i 0.206647 + 1.41638i
\(204\) 8.47214 + 3.23607i 0.593168 + 0.226570i
\(205\) 0 0
\(206\) −14.6525 −1.02089
\(207\) −8.00000 + 8.94427i −0.556038 + 0.621670i
\(208\) 1.23607i 0.0857059i
\(209\) 37.8885 2.62081
\(210\) 0 0
\(211\) −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
\(215\) 0 0
\(216\) 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
\(220\) 0 0
\(221\) 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
\(225\) 0 0
\(226\) 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 \(0.0935118\pi\)
−0.957157 + 0.289568i \(0.906488\pi\)
\(230\) 0 0
\(231\) −4.47214 + 20.0000i −0.294245 + 1.31590i
\(232\) 7.70820 0.506068
\(233\) 11.5279i 0.755215i −0.925966 0.377608i \(-0.876747\pi\)
0.925966 0.377608i \(-0.123253\pi\)
\(234\) −2.76393 2.47214i −0.180684 0.161609i
\(235\) 0 0
\(236\) 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 \(0.998143\pi\)
\(240\) 0 0
\(241\) 17.8885i 1.15230i −0.817343 0.576151i \(-0.804554\pi\)
0.817343 0.576151i \(-0.195446\pi\)
\(242\) 9.00000i 0.578542i
\(243\) 3.90983 15.0902i 0.250816 0.968035i
\(244\) 7.23607i 0.463242i
\(245\) 0 0
\(246\) −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
\(250\) 0 0
\(251\) 12.4721 0.787234 0.393617 0.919274i \(-0.371224\pi\)
0.393617 + 0.919274i \(0.371224\pi\)
\(252\) 6.61803 + 4.38197i 0.416897 + 0.276038i
\(253\) −17.8885 −1.12464
\(254\) 0.291796i 0.0183089i
\(255\) 0 0
\(256\) 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
\(260\) 0 0
\(261\) 15.4164 17.2361i 0.954252 1.06689i
\(262\) 5.41641i 0.334627i
\(263\) 12.9443i 0.798178i 0.916912 + 0.399089i \(0.130674\pi\)
−0.916912 + 0.399089i \(0.869326\pi\)
\(264\) 7.23607 + 2.76393i 0.445349 + 0.170108i
\(265\) 0 0
\(266\) 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 \(-0.543533\pi\)
−0.136335 + 0.990663i \(0.543533\pi\)
\(270\) 0 0
\(271\) 31.7082i 1.92614i −0.269258 0.963068i \(-0.586778\pi\)
0.269258 0.963068i \(-0.413222\pi\)
\(272\) 5.23607 0.317483
\(273\) 1.23607 5.52786i 0.0748102 0.334562i
\(274\) −3.52786 −0.213126
\(275\) 0 0
\(276\) −2.47214 + 6.47214i −0.148805 + 0.389577i
\(277\) 17.1246 1.02892 0.514459 0.857515i \(-0.327993\pi\)
0.514459 + 0.857515i \(0.327993\pi\)
\(278\) 11.5279 0.691395
\(279\) −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 \(0.796538\pi\)
\(282\) 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
\(285\) 0 0
\(286\) 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
\(290\) 0 0
\(291\) 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 \(0.524045\pi\)
\(294\) −0.909830 + 12.0902i −0.0530624 + 0.705113i
\(295\) 0 0
\(296\) 0.763932i 0.0444026i
\(297\) 20.6525 10.6525i 1.19838 0.618119i
\(298\) −4.29180 −0.248617
\(299\) 4.94427 0.285935
\(300\) 0 0
\(301\) −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
\(305\) 0 0
\(306\) 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
\(310\) 0 0
\(311\) −17.5279 −0.993914 −0.496957 0.867775i \(-0.665549\pi\)
−0.496957 + 0.867775i \(0.665549\pi\)
\(312\) −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
\(315\) 0 0
\(316\) 8.94427 0.503155
\(317\) 10.9443i 0.614692i 0.951598 + 0.307346i \(0.0994408\pi\)
−0.951598 + 0.307346i \(0.900559\pi\)
\(318\) 0.763932 + 0.291796i 0.0428392 + 0.0163631i
\(319\) 34.4721 1.93007
\(320\) 0 0
\(321\) −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
\(325\) 0 0
\(326\) 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
\(330\) 0 0
\(331\) 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
\(335\) 0 0
\(336\) 4.47214 + 1.00000i 0.243975 + 0.0545545i
\(337\) −21.4164 −1.16663 −0.583313 0.812247i \(-0.698244\pi\)
−0.583313 + 0.812247i \(0.698244\pi\)
\(338\) 11.4721i 0.624002i
\(339\) 1.81966 4.76393i 0.0988304 0.258741i
\(340\) 0 0
\(341\) −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
\(345\) 0 0
\(346\) 9.41641i 0.506229i
\(347\) 2.47214i 0.132711i −0.997796 0.0663556i \(-0.978863\pi\)
0.997796 0.0663556i \(-0.0211372\pi\)
\(348\) 4.76393 12.4721i 0.255374 0.668577i
\(349\) 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
\(352\) 4.47214 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
\(355\) 0 0
\(356\) −5.52786 −0.292976
\(357\) 23.4164 + 5.23607i 1.23933 + 0.277122i
\(358\) −14.9443 −0.789829
\(359\) 12.1803i 0.642854i −0.946934 0.321427i \(-0.895838\pi\)
0.946934 0.321427i \(-0.104162\pi\)
\(360\) 0 0
\(361\) −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
\(365\) 0 0
\(366\) 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 0
\(371\) 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 \(-0.186554\pi\)
0.833117 + 0.553096i \(0.186554\pi\)
\(374\) 23.4164 1.21083
\(375\) 0 0
\(376\) 6.47214i 0.333775i
\(377\) −9.52786 −0.490710
\(378\) 11.1803 8.00000i 0.575055 0.411476i
\(379\) −17.8885 −0.918873 −0.459436 0.888211i \(-0.651949\pi\)
−0.459436 + 0.888211i \(0.651949\pi\)
\(380\) 0 0
\(381\) −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
\(385\) 0 0
\(386\) 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 \(0.722689\pi\)
\(390\) 0 0
\(391\) 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
\(395\) 0 0
\(396\) 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
\(399\) 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 \(0.882315\pi\)
\(402\) −7.41641 + 19.4164i −0.369897 + 0.968402i
\(403\) 3.41641 0.170183
\(404\) −12.4721 −0.620512
\(405\) 0 0
\(406\) 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 \(-0.941303\pi\)
0.983046 0.183359i \(-0.0586970\pi\)
\(410\) 0 0
\(411\) −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
\(415\) 0 0
\(416\) −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 \(-0.856215\pi\)
−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 \(0.527399\pi\)
\(422\) 8.00000i 0.389434i
\(423\) −14.4721 12.9443i −0.703659 0.629372i
\(424\) 0.472136 0.0229289
\(425\) 0 0
\(426\) 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
\(430\) 0 0
\(431\) 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
\(435\) 0 0
\(436\) −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 \(-0.921888\pi\)
0.970041 0.242941i \(-0.0781120\pi\)
\(440\) 0 0
\(441\) 19.0000 + 8.94427i 0.904762 + 0.425918i
\(442\) −6.47214 −0.307848
\(443\) 18.4721i 0.877638i 0.898576 + 0.438819i \(0.144603\pi\)
−0.898576 + 0.438819i \(0.855397\pi\)
\(444\) −1.23607 0.472136i −0.0586612 0.0224066i
\(445\) 0 0
\(446\) 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 \(-0.0794794\pi\)
\(450\) 0 0
\(451\) 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 0
\(456\) −13.7082 5.23607i −0.641945 0.245201i
\(457\) −26.9443 −1.26040 −0.630200 0.776433i \(-0.717027\pi\)
−0.630200 + 0.776433i \(0.717027\pi\)
\(458\) 8.76393 0.409512
\(459\) −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 \(0.448298\pi\)
\(462\) 20.0000 + 4.47214i 0.930484 + 0.208063i
\(463\) 22.1803 1.03081 0.515404 0.856947i \(-0.327642\pi\)
0.515404 + 0.856947i \(0.327642\pi\)
\(464\) 7.70820i 0.357844i
\(465\) 0 0
\(466\) −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
\(470\) 0 0
\(471\) −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
\(475\) 0 0
\(476\) 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 \(-0.833054\pi\)
−0.865586 + 0.500761i \(0.833054\pi\)
\(480\) 0 0
\(481\) 0.944272i 0.0430551i
\(482\) −17.8885 −0.814801
\(483\) −4.00000 + 17.8885i −0.182006 + 0.813957i
\(484\) 9.00000 0.409091
\(485\) 0 0
\(486\) −15.0902 3.90983i −0.684504 0.177353i
\(487\) −17.5967 −0.797385 −0.398692 0.917085i \(-0.630536\pi\)
−0.398692 + 0.917085i \(0.630536\pi\)
\(488\) 7.23607 0.327561
\(489\) −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 \(0.902100\pi\)
\(492\) 4.00000 + 1.52786i 0.180334 + 0.0688814i
\(493\) 40.3607i 1.81775i
\(494\) 10.4721i 0.471164i
\(495\) 0 0
\(496\) 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 \(0.368871\pi\)
\(500\) 0 0
\(501\) 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 \(0.717877\pi\)
\(504\) 4.38197 6.61803i 0.195188 0.294791i
\(505\) 0 0
\(506\) 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 \(-0.611826\pi\)
−0.344130 + 0.938922i \(0.611826\pi\)
\(510\) 0 0
\(511\) 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
\(515\) 0 0
\(516\) 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
\(520\) 0 0
\(521\) 36.9443 1.61856 0.809279 0.587425i \(-0.199858\pi\)
0.809279 + 0.587425i \(0.199858\pi\)
\(522\) −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
\(525\) 0 0
\(526\) 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 0
\(531\) −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
\(535\) 0 0
\(536\) 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
\(540\) 0 0
\(541\) 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
\(545\) 0 0
\(546\) −5.52786 1.23607i −0.236571 0.0528988i
\(547\) 35.4164 1.51430 0.757148 0.653243i \(-0.226592\pi\)
0.757148 + 0.653243i \(0.226592\pi\)
\(548\) 3.52786i 0.150703i
\(549\) 14.4721 16.1803i 0.617656 0.690560i
\(550\) 0 0
\(551\) −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
\(555\) 0 0
\(556\) 11.5279i 0.488890i
\(557\) 7.52786i 0.318966i 0.987201 + 0.159483i \(0.0509827\pi\)
−0.987201 + 0.159483i \(0.949017\pi\)
\(558\) 6.18034 + 5.52786i 0.261635 + 0.234013i
\(559\) 6.11146i 0.258487i
\(560\) 0 0
\(561\) 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
\(565\) 0 0
\(566\) 13.2361 0.556353
\(567\) −6.03444 23.0344i −0.253423 0.967356i
\(568\) 7.23607 0.303619
\(569\) 9.52786i 0.399429i 0.979854 + 0.199714i \(0.0640014\pi\)
−0.979854 + 0.199714i \(0.935999\pi\)
\(570\) 0 0
\(571\) 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
\(575\) 0 0
\(576\) −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
\(580\) 0 0
\(581\) −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
\(585\) 0 0
\(586\) 2.58359i 0.106727i
\(587\) −10.2918 −0.424788 −0.212394 0.977184i \(-0.568126\pi\)
−0.212394 + 0.977184i \(0.568126\pi\)
\(588\) 12.0902 + 0.909830i 0.498590 + 0.0375208i
\(589\) 23.4164 0.964856
\(590\) 0 0
\(591\) −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
\(595\) 0 0
\(596\) 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 0
\(601\) 5.52786i 0.225486i −0.993624 0.112743i \(-0.964036\pi\)
0.993624 0.112743i \(-0.0359637\pi\)
\(602\) 1.88854 + 12.9443i 0.0769713 + 0.527569i
\(603\) 26.8328 + 24.0000i 1.09272 + 0.977356i
\(604\) −20.9443 −0.852210
\(605\) 0 0
\(606\) −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
\(609\) 7.70820 34.4721i 0.312352 1.39688i
\(610\) 0 0
\(611\) 8.00000i 0.323645i
\(612\) −11.7082 10.4721i −0.473276 0.423311i
\(613\) −38.0689 −1.53759 −0.768794 0.639497i \(-0.779143\pi\)
−0.768794 + 0.639497i \(0.779143\pi\)
\(614\) −18.1803 −0.733699
\(615\) 0 0
\(616\) 11.7082 1.70820i 0.471737 0.0688255i
\(617\) 2.00000i 0.0805170i 0.999189 + 0.0402585i \(0.0128181\pi\)
−0.999189 + 0.0402585i \(0.987182\pi\)
\(618\) 23.7082 + 9.05573i 0.953684 + 0.364275i
\(619\) 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
\(622\) 17.5279i 0.702803i
\(623\) −14.4721 + 2.11146i −0.579814 + 0.0845937i
\(624\) −0.763932 + 2.00000i −0.0305818 + 0.0800641i
\(625\) 0 0
\(626\) −5.70820 −0.228146
\(627\) −61.3050 23.4164i −2.44828 0.935161i
\(628\) 9.23607i 0.368559i
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) −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 0
\(636\) 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
\(640\) 0 0
\(641\) 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
\(645\) 0 0
\(646\) −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
\(650\) 0 0
\(651\) −2.76393 + 12.3607i −0.108327 + 0.484453i
\(652\) −10.4721 −0.410120
\(653\) 23.8885i 0.934831i −0.884038 0.467415i \(-0.845185\pi\)
0.884038 0.467415i \(-0.154815\pi\)
\(654\) −2.76393 + 7.23607i −0.108078 + 0.282953i
\(655\) 0 0
\(656\) 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 \(-0.210471\pi\)
\(660\) 0 0
\(661\) 18.2918i 0.711468i −0.934587 0.355734i \(-0.884231\pi\)
0.934587 0.355734i \(-0.115769\pi\)
\(662\) 3.05573i 0.118764i
\(663\) −4.00000 + 10.4721i −0.155347 + 0.406704i
\(664\) 14.6525i 0.568626i
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) 32.3607 1.24927
\(672\) 1.00000 4.47214i 0.0385758 0.172516i
\(673\) −19.5279 −0.752744 −0.376372 0.926469i \(-0.622829\pi\)
−0.376372 + 0.926469i \(0.622829\pi\)
\(674\) 21.4164i 0.824929i
\(675\) 0 0
\(676\) −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
\(680\) 0 0
\(681\) −1.23607 0.472136i −0.0473662 0.0180923i
\(682\) 12.3607i 0.473315i
\(683\) 36.0000i 1.37750i −0.724998 0.688751i \(-0.758159\pi\)
0.724998 0.688751i \(-0.241841\pi\)
\(684\) −16.9443 + 18.9443i −0.647880 + 0.724352i
\(685\) 0 0
\(686\) 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
\(690\) 0 0
\(691\) 21.0557i 0.800998i 0.916297 + 0.400499i \(0.131163\pi\)
−0.916297 + 0.400499i \(0.868837\pi\)
\(692\) 9.41641 0.357958
\(693\) 19.5967 29.5967i 0.744419 1.12429i
\(694\) −2.47214 −0.0938410
\(695\) 0 0
\(696\) −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
\(700\) 0 0
\(701\) 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
\(705\) 0 0
\(706\) 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 \(0.594181\pi\)
\(710\) 0 0
\(711\) −20.0000 17.8885i −0.750059 0.670873i
\(712\) 5.52786i 0.207165i
\(713\) −11.0557 −0.414040
\(714\) 5.23607 23.4164i 0.195955 0.876337i
\(715\) 0 0
\(716\) 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 \(-0.277774\pi\)
0.642797 + 0.766037i \(0.277774\pi\)
\(720\) 0 0
\(721\) 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
\(725\) 0 0
\(726\) 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
\(730\) 0 0
\(731\) 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
\(735\) 0 0
\(736\) 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 0
\(741\) 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 \(-0.938473\pi\)
0.981377 0.192093i \(-0.0615274\pi\)
\(744\) 4.47214 + 1.70820i 0.163956 + 0.0626258i
\(745\) 0 0
\(746\) 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 0
\(751\) 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
\(755\) 0 0
\(756\) −8.00000 11.1803i −0.290957 0.406625i
\(757\) 2.65248 0.0964059 0.0482029 0.998838i \(-0.484651\pi\)
0.0482029 + 0.998838i \(0.484651\pi\)
\(758\) 17.8885i 0.649741i
\(759\) 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 \(0.465962\pi\)
\(762\) −0.180340 + 0.472136i −0.00653302 + 0.0171037i
\(763\) −11.7082 + 1.70820i −0.423865 + 0.0618411i
\(764\) 7.23607i 0.261792i
\(765\) 0 0
\(766\) 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 \(0.224853\pi\)
−0.760706 + 0.649097i \(0.775147\pi\)
\(770\) 0 0
\(771\) −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
\(775\) 0 0
\(776\) −0.763932 −0.0274236
\(777\) −3.41641 0.763932i −0.122563 0.0274059i
\(778\) 30.1803 1.08202
\(779\) 20.9443i 0.750406i
\(780\) 0 0
\(781\) 32.3607 1.15796
\(782\) 20.9443 0.748966
\(783\) −35.5967 + 18.3607i −1.27212 + 0.656157i
\(784\) 6.70820 2.00000i 0.239579 0.0714286i
\(785\) 0 0
\(786\) 3.34752 8.76393i 0.119402 0.312599i
\(787\) 36.2918i 1.29366i 0.762633 + 0.646831i \(0.223906\pi\)
−0.762633 + 0.646831i \(0.776094\pi\)
\(788\) 3.52786i 0.125675i
\(789\) 8.00000 20.9443i 0.284808 0.745636i
\(790\) 0 0
\(791\) −1.12461 7.70820i −0.0399866 0.274072i
\(792\) −10.0000 8.94427i −0.355335 0.317821i
\(793\) −8.94427 −0.317620
\(794\) 23.1246 0.820662
\(795\) 0 0
\(796\) 22.1803i 0.786161i
\(797\) 21.4164