Properties

Label 1050.2.bc.a.607.2
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.2
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.a.493.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-2.63896 - 0.189469i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-2.63896 - 0.189469i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(0.258819 + 0.965926i) q^{12} +(4.05317 + 4.05317i) q^{13} +(-2.59808 + 0.500000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(7.20977 + 1.93185i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-1.13397 + 1.96410i) q^{19} +(0.866025 - 2.50000i) q^{21} +(-0.707107 - 0.707107i) q^{22} +(1.53433 + 5.72620i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.96410 + 2.86603i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.38014 + 1.15539i) q^{28} +6.92820i q^{29} +(6.46410 - 3.73205i) q^{31} +(0.258819 - 0.965926i) q^{32} +(0.965926 - 0.258819i) q^{33} +7.46410 q^{34} -1.00000 q^{36} +(3.79435 - 1.01669i) q^{37} +(-0.586988 + 2.19067i) q^{38} +(-4.96410 + 2.86603i) q^{39} -2.26795i q^{41} +(0.189469 - 2.63896i) q^{42} +(-6.31319 + 6.31319i) q^{43} +(-0.866025 - 0.500000i) q^{44} +(2.96410 + 5.13397i) q^{46} +(0.309587 + 1.15539i) q^{47} +(0.707107 + 0.707107i) q^{48} +(6.92820 + 1.00000i) q^{49} +(-3.73205 + 6.46410i) q^{51} +(5.53674 + 1.48356i) q^{52} +(0.965926 + 0.258819i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} +(-1.60368 - 1.60368i) q^{57} +(1.79315 + 6.69213i) q^{58} +(-5.73205 - 9.92820i) q^{59} +(-9.92820 - 5.73205i) q^{61} +(5.27792 - 5.27792i) q^{62} +(2.19067 + 1.48356i) q^{63} -1.00000i q^{64} +(0.866025 - 0.500000i) q^{66} +(0.517638 - 1.93185i) q^{67} +(7.20977 - 1.93185i) q^{68} -5.92820 q^{69} -8.92820 q^{71} +(-0.965926 + 0.258819i) q^{72} +(-1.03528 + 3.86370i) q^{73} +(3.40192 - 1.96410i) q^{74} +2.26795i q^{76} +(1.15539 + 2.38014i) q^{77} +(-4.05317 + 4.05317i) q^{78} +(2.66025 + 1.53590i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.586988 - 2.19067i) q^{82} +(-7.34847 - 7.34847i) q^{83} +(-0.500000 - 2.59808i) q^{84} +(-4.46410 + 7.73205i) q^{86} +(-6.69213 - 1.79315i) q^{87} +(-0.965926 - 0.258819i) q^{88} +(-3.46410 + 6.00000i) q^{89} +(-9.92820 - 11.4641i) q^{91} +(4.19187 + 4.19187i) q^{92} +(1.93185 + 7.20977i) q^{93} +(0.598076 + 1.03590i) q^{94} +(0.866025 + 0.500000i) q^{96} +(2.07055 - 2.07055i) q^{97} +(6.95095 - 0.827225i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 4q^{11} + 4q^{16} - 16q^{19} + 4q^{24} + 12q^{26} + 24q^{31} + 32q^{34} - 8q^{36} - 12q^{39} - 4q^{46} - 16q^{51} + 4q^{54} - 16q^{56} - 32q^{59} - 24q^{61} + 8q^{69} - 16q^{71} + 48q^{74} - 48q^{79} + 4q^{81} - 4q^{84} - 8q^{86} - 24q^{91} - 16q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) −0.258819 + 0.965926i −0.149429 + 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) −2.63896 0.189469i −0.997433 0.0716124i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0.258819 + 0.965926i 0.0747146 + 0.278839i
\(13\) 4.05317 + 4.05317i 1.12415 + 1.12415i 0.991111 + 0.133037i \(0.0424728\pi\)
0.133037 + 0.991111i \(0.457527\pi\)
\(14\) −2.59808 + 0.500000i −0.694365 + 0.133631i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 7.20977 + 1.93185i 1.74863 + 0.468543i 0.984332 0.176325i \(-0.0564211\pi\)
0.764294 + 0.644868i \(0.223088\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) −1.13397 + 1.96410i −0.260152 + 0.450596i −0.966282 0.257486i \(-0.917106\pi\)
0.706130 + 0.708082i \(0.250439\pi\)
\(20\) 0 0
\(21\) 0.866025 2.50000i 0.188982 0.545545i
\(22\) −0.707107 0.707107i −0.150756 0.150756i
\(23\) 1.53433 + 5.72620i 0.319930 + 1.19400i 0.919311 + 0.393532i \(0.128747\pi\)
−0.599381 + 0.800464i \(0.704586\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) 4.96410 + 2.86603i 0.973540 + 0.562074i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −2.38014 + 1.15539i −0.449804 + 0.218349i
\(29\) 6.92820i 1.28654i 0.765641 + 0.643268i \(0.222422\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(30\) 0 0
\(31\) 6.46410 3.73205i 1.16099 0.670296i 0.209447 0.977820i \(-0.432834\pi\)
0.951540 + 0.307524i \(0.0995004\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 0.965926 0.258819i 0.168146 0.0450546i
\(34\) 7.46410 1.28008
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 3.79435 1.01669i 0.623788 0.167143i 0.0669387 0.997757i \(-0.478677\pi\)
0.556849 + 0.830614i \(0.312010\pi\)
\(38\) −0.586988 + 2.19067i −0.0952221 + 0.355374i
\(39\) −4.96410 + 2.86603i −0.794892 + 0.458931i
\(40\) 0 0
\(41\) 2.26795i 0.354194i −0.984193 0.177097i \(-0.943329\pi\)
0.984193 0.177097i \(-0.0566707\pi\)
\(42\) 0.189469 2.63896i 0.0292357 0.407200i
\(43\) −6.31319 + 6.31319i −0.962753 + 0.962753i −0.999331 0.0365779i \(-0.988354\pi\)
0.0365779 + 0.999331i \(0.488354\pi\)
\(44\) −0.866025 0.500000i −0.130558 0.0753778i
\(45\) 0 0
\(46\) 2.96410 + 5.13397i 0.437033 + 0.756963i
\(47\) 0.309587 + 1.15539i 0.0451579 + 0.168532i 0.984822 0.173566i \(-0.0555292\pi\)
−0.939664 + 0.342098i \(0.888862\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(50\) 0 0
\(51\) −3.73205 + 6.46410i −0.522592 + 0.905155i
\(52\) 5.53674 + 1.48356i 0.767807 + 0.205733i
\(53\) 0.965926 + 0.258819i 0.132680 + 0.0355515i 0.324548 0.945869i \(-0.394788\pi\)
−0.191868 + 0.981421i \(0.561454\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) −1.60368 1.60368i −0.212413 0.212413i
\(58\) 1.79315 + 6.69213i 0.235452 + 0.878720i
\(59\) −5.73205 9.92820i −0.746249 1.29254i −0.949609 0.313438i \(-0.898519\pi\)
0.203359 0.979104i \(-0.434814\pi\)
\(60\) 0 0
\(61\) −9.92820 5.73205i −1.27118 0.733914i −0.295967 0.955198i \(-0.595642\pi\)
−0.975209 + 0.221284i \(0.928975\pi\)
\(62\) 5.27792 5.27792i 0.670296 0.670296i
\(63\) 2.19067 + 1.48356i 0.275999 + 0.186911i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0.866025 0.500000i 0.106600 0.0615457i
\(67\) 0.517638 1.93185i 0.0632396 0.236013i −0.927071 0.374887i \(-0.877682\pi\)
0.990310 + 0.138874i \(0.0443482\pi\)
\(68\) 7.20977 1.93185i 0.874313 0.234271i
\(69\) −5.92820 −0.713672
\(70\) 0 0
\(71\) −8.92820 −1.05958 −0.529791 0.848128i \(-0.677730\pi\)
−0.529791 + 0.848128i \(0.677730\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) −1.03528 + 3.86370i −0.121170 + 0.452212i −0.999674 0.0255221i \(-0.991875\pi\)
0.878504 + 0.477734i \(0.158542\pi\)
\(74\) 3.40192 1.96410i 0.395466 0.228322i
\(75\) 0 0
\(76\) 2.26795i 0.260152i
\(77\) 1.15539 + 2.38014i 0.131669 + 0.271242i
\(78\) −4.05317 + 4.05317i −0.458931 + 0.458931i
\(79\) 2.66025 + 1.53590i 0.299302 + 0.172802i 0.642129 0.766596i \(-0.278051\pi\)
−0.342827 + 0.939398i \(0.611385\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −0.586988 2.19067i −0.0648220 0.241919i
\(83\) −7.34847 7.34847i −0.806599 0.806599i 0.177518 0.984118i \(-0.443193\pi\)
−0.984118 + 0.177518i \(0.943193\pi\)
\(84\) −0.500000 2.59808i −0.0545545 0.283473i
\(85\) 0 0
\(86\) −4.46410 + 7.73205i −0.481376 + 0.833768i
\(87\) −6.69213 1.79315i −0.717472 0.192246i
\(88\) −0.965926 0.258819i −0.102968 0.0275902i
\(89\) −3.46410 + 6.00000i −0.367194 + 0.635999i −0.989126 0.147073i \(-0.953015\pi\)
0.621932 + 0.783072i \(0.286348\pi\)
\(90\) 0 0
\(91\) −9.92820 11.4641i −1.04076 1.20176i
\(92\) 4.19187 + 4.19187i 0.437033 + 0.437033i
\(93\) 1.93185 + 7.20977i 0.200324 + 0.747618i
\(94\) 0.598076 + 1.03590i 0.0616869 + 0.106845i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) 2.07055 2.07055i 0.210233 0.210233i −0.594134 0.804366i \(-0.702505\pi\)
0.804366 + 0.594134i \(0.202505\pi\)
\(98\) 6.95095 0.827225i 0.702152 0.0835624i
\(99\) 1.00000i 0.100504i
\(100\) 0 0
\(101\) 0.928203 0.535898i 0.0923597 0.0533239i −0.453109 0.891455i \(-0.649685\pi\)
0.545468 + 0.838131i \(0.316352\pi\)
\(102\) −1.93185 + 7.20977i −0.191282 + 0.713873i
\(103\) 17.7656 4.76028i 1.75050 0.469044i 0.765765 0.643121i \(-0.222361\pi\)
0.984732 + 0.174077i \(0.0556941\pi\)
\(104\) 5.73205 0.562074
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 14.4195 3.86370i 1.39399 0.373518i 0.517807 0.855498i \(-0.326749\pi\)
0.876183 + 0.481979i \(0.160082\pi\)
\(108\) 0.258819 0.965926i 0.0249049 0.0929463i
\(109\) 14.6603 8.46410i 1.40420 0.810714i 0.409378 0.912365i \(-0.365746\pi\)
0.994820 + 0.101651i \(0.0324126\pi\)
\(110\) 0 0
\(111\) 3.92820i 0.372849i
\(112\) −1.48356 + 2.19067i −0.140184 + 0.206999i
\(113\) −9.14162 + 9.14162i −0.859971 + 0.859971i −0.991334 0.131363i \(-0.958065\pi\)
0.131363 + 0.991334i \(0.458065\pi\)
\(114\) −1.96410 1.13397i −0.183955 0.106206i
\(115\) 0 0
\(116\) 3.46410 + 6.00000i 0.321634 + 0.557086i
\(117\) −1.48356 5.53674i −0.137156 0.511871i
\(118\) −8.10634 8.10634i −0.746249 0.746249i
\(119\) −18.6603 6.46410i −1.71058 0.592563i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) −11.0735 2.96713i −1.00255 0.268631i
\(123\) 2.19067 + 0.586988i 0.197526 + 0.0529270i
\(124\) 3.73205 6.46410i 0.335148 0.580493i
\(125\) 0 0
\(126\) 2.50000 + 0.866025i 0.222718 + 0.0771517i
\(127\) −3.53553 3.53553i −0.313728 0.313728i 0.532624 0.846352i \(-0.321206\pi\)
−0.846352 + 0.532624i \(0.821206\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) −4.46410 7.73205i −0.393042 0.680769i
\(130\) 0 0
\(131\) 3.57180 + 2.06218i 0.312069 + 0.180173i 0.647852 0.761766i \(-0.275667\pi\)
−0.335783 + 0.941939i \(0.609001\pi\)
\(132\) 0.707107 0.707107i 0.0615457 0.0615457i
\(133\) 3.36465 4.96833i 0.291752 0.430809i
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) 6.46410 3.73205i 0.554292 0.320021i
\(137\) −4.89898 + 18.2832i −0.418548 + 1.56204i 0.359073 + 0.933309i \(0.383093\pi\)
−0.777621 + 0.628733i \(0.783574\pi\)
\(138\) −5.72620 + 1.53433i −0.487447 + 0.130611i
\(139\) 10.3923 0.881464 0.440732 0.897639i \(-0.354719\pi\)
0.440732 + 0.897639i \(0.354719\pi\)
\(140\) 0 0
\(141\) −1.19615 −0.100734
\(142\) −8.62398 + 2.31079i −0.723708 + 0.193917i
\(143\) 1.48356 5.53674i 0.124062 0.463005i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 4.00000i 0.331042i
\(147\) −2.75908 + 6.43331i −0.227565 + 0.530611i
\(148\) 2.77766 2.77766i 0.228322 0.228322i
\(149\) 0.803848 + 0.464102i 0.0658538 + 0.0380207i 0.532565 0.846389i \(-0.321228\pi\)
−0.466712 + 0.884410i \(0.654561\pi\)
\(150\) 0 0
\(151\) 1.92820 + 3.33975i 0.156915 + 0.271785i 0.933755 0.357914i \(-0.116512\pi\)
−0.776840 + 0.629698i \(0.783178\pi\)
\(152\) 0.586988 + 2.19067i 0.0476110 + 0.177687i
\(153\) −5.27792 5.27792i −0.426694 0.426694i
\(154\) 1.73205 + 2.00000i 0.139573 + 0.161165i
\(155\) 0 0
\(156\) −2.86603 + 4.96410i −0.229466 + 0.397446i
\(157\) 4.50146 + 1.20616i 0.359256 + 0.0962622i 0.433932 0.900946i \(-0.357126\pi\)
−0.0746765 + 0.997208i \(0.523792\pi\)
\(158\) 2.96713 + 0.795040i 0.236052 + 0.0632499i
\(159\) −0.500000 + 0.866025i −0.0396526 + 0.0686803i
\(160\) 0 0
\(161\) −2.96410 15.4019i −0.233604 1.21384i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) −3.10583 11.5911i −0.243267 0.907886i −0.974246 0.225486i \(-0.927603\pi\)
0.730979 0.682400i \(-0.239064\pi\)
\(164\) −1.13397 1.96410i −0.0885485 0.153371i
\(165\) 0 0
\(166\) −9.00000 5.19615i −0.698535 0.403300i
\(167\) −4.81105 + 4.81105i −0.372290 + 0.372290i −0.868311 0.496021i \(-0.834794\pi\)
0.496021 + 0.868311i \(0.334794\pi\)
\(168\) −1.15539 2.38014i −0.0891406 0.183632i
\(169\) 19.8564i 1.52742i
\(170\) 0 0
\(171\) 1.96410 1.13397i 0.150199 0.0867172i
\(172\) −2.31079 + 8.62398i −0.176196 + 0.657572i
\(173\) −7.32989 + 1.96404i −0.557281 + 0.149323i −0.526457 0.850202i \(-0.676480\pi\)
−0.0308241 + 0.999525i \(0.509813\pi\)
\(174\) −6.92820 −0.525226
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 11.0735 2.96713i 0.832333 0.223023i
\(178\) −1.79315 + 6.69213i −0.134402 + 0.501596i
\(179\) −7.79423 + 4.50000i −0.582568 + 0.336346i −0.762153 0.647397i \(-0.775858\pi\)
0.179585 + 0.983742i \(0.442524\pi\)
\(180\) 0 0
\(181\) 14.3923i 1.06977i −0.844924 0.534886i \(-0.820355\pi\)
0.844924 0.534886i \(-0.179645\pi\)
\(182\) −12.5570 8.50386i −0.930789 0.630348i
\(183\) 8.10634 8.10634i 0.599238 0.599238i
\(184\) 5.13397 + 2.96410i 0.378482 + 0.218516i
\(185\) 0 0
\(186\) 3.73205 + 6.46410i 0.273647 + 0.473971i
\(187\) −1.93185 7.20977i −0.141271 0.527230i
\(188\) 0.845807 + 0.845807i 0.0616869 + 0.0616869i
\(189\) −2.00000 + 1.73205i −0.145479 + 0.125988i
\(190\) 0 0
\(191\) −1.46410 + 2.53590i −0.105939 + 0.183491i −0.914121 0.405441i \(-0.867118\pi\)
0.808183 + 0.588932i \(0.200451\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) −22.0082 5.89709i −1.58419 0.424482i −0.643969 0.765052i \(-0.722713\pi\)
−0.940219 + 0.340570i \(0.889380\pi\)
\(194\) 1.46410 2.53590i 0.105116 0.182067i
\(195\) 0 0
\(196\) 6.50000 2.59808i 0.464286 0.185577i
\(197\) −11.9193 11.9193i −0.849213 0.849213i 0.140822 0.990035i \(-0.455026\pi\)
−0.990035 + 0.140822i \(0.955026\pi\)
\(198\) 0.258819 + 0.965926i 0.0183935 + 0.0686454i
\(199\) −6.26795 10.8564i −0.444323 0.769590i 0.553682 0.832728i \(-0.313222\pi\)
−0.998005 + 0.0631382i \(0.979889\pi\)
\(200\) 0 0
\(201\) 1.73205 + 1.00000i 0.122169 + 0.0705346i
\(202\) 0.757875 0.757875i 0.0533239 0.0533239i
\(203\) 1.31268 18.2832i 0.0921319 1.28323i
\(204\) 7.46410i 0.522592i
\(205\) 0 0
\(206\) 15.9282 9.19615i 1.10977 0.640726i
\(207\) 1.53433 5.72620i 0.106643 0.397999i
\(208\) 5.53674 1.48356i 0.383904 0.102867i
\(209\) 2.26795 0.156877
\(210\) 0 0
\(211\) −19.7846 −1.36203 −0.681014 0.732270i \(-0.738461\pi\)
−0.681014 + 0.732270i \(0.738461\pi\)
\(212\) 0.965926 0.258819i 0.0663401 0.0177758i
\(213\) 2.31079 8.62398i 0.158333 0.590906i
\(214\) 12.9282 7.46410i 0.883754 0.510235i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −17.7656 + 8.62398i −1.20601 + 0.585434i
\(218\) 11.9700 11.9700i 0.810714 0.810714i
\(219\) −3.46410 2.00000i −0.234082 0.135147i
\(220\) 0 0
\(221\) 21.3923 + 37.0526i 1.43900 + 2.49242i
\(222\) 1.01669 + 3.79435i 0.0682360 + 0.254660i
\(223\) 6.59059 + 6.59059i 0.441339 + 0.441339i 0.892462 0.451123i \(-0.148976\pi\)
−0.451123 + 0.892462i \(0.648976\pi\)
\(224\) −0.866025 + 2.50000i −0.0578638 + 0.167038i
\(225\) 0 0
\(226\) −6.46410 + 11.1962i −0.429986 + 0.744757i
\(227\) −3.34607 0.896575i −0.222086 0.0595078i 0.146060 0.989276i \(-0.453341\pi\)
−0.368146 + 0.929768i \(0.620007\pi\)
\(228\) −2.19067 0.586988i −0.145081 0.0388743i
\(229\) 1.46410 2.53590i 0.0967506 0.167577i −0.813587 0.581443i \(-0.802488\pi\)
0.910338 + 0.413866i \(0.135822\pi\)
\(230\) 0 0
\(231\) −2.59808 + 0.500000i −0.170941 + 0.0328976i
\(232\) 4.89898 + 4.89898i 0.321634 + 0.321634i
\(233\) −0.480473 1.79315i −0.0314769 0.117473i 0.948400 0.317077i \(-0.102701\pi\)
−0.979877 + 0.199603i \(0.936035\pi\)
\(234\) −2.86603 4.96410i −0.187358 0.324513i
\(235\) 0 0
\(236\) −9.92820 5.73205i −0.646271 0.373125i
\(237\) −2.17209 + 2.17209i −0.141092 + 0.141092i
\(238\) −19.6975 1.41421i −1.27680 0.0916698i
\(239\) 24.0000i 1.55243i −0.630468 0.776215i \(-0.717137\pi\)
0.630468 0.776215i \(-0.282863\pi\)
\(240\) 0 0
\(241\) 19.2846 11.1340i 1.24223 0.717202i 0.272683 0.962104i \(-0.412089\pi\)
0.969548 + 0.244902i \(0.0787557\pi\)
\(242\) 2.58819 9.65926i 0.166375 0.620921i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) −11.4641 −0.733914
\(245\) 0 0
\(246\) 2.26795 0.144599
\(247\) −12.5570 + 3.36465i −0.798985 + 0.214087i
\(248\) 1.93185 7.20977i 0.122673 0.457821i
\(249\) 9.00000 5.19615i 0.570352 0.329293i
\(250\) 0 0
\(251\) 7.33975i 0.463281i 0.972801 + 0.231640i \(0.0744092\pi\)
−0.972801 + 0.231640i \(0.925591\pi\)
\(252\) 2.63896 + 0.189469i 0.166239 + 0.0119354i
\(253\) 4.19187 4.19187i 0.263541 0.263541i
\(254\) −4.33013 2.50000i −0.271696 0.156864i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.619174 + 2.31079i 0.0386230 + 0.144143i 0.982545 0.186026i \(-0.0595609\pi\)
−0.943922 + 0.330169i \(0.892894\pi\)
\(258\) −6.31319 6.31319i −0.393042 0.393042i
\(259\) −10.2058 + 1.96410i −0.634156 + 0.122043i
\(260\) 0 0
\(261\) 3.46410 6.00000i 0.214423 0.371391i
\(262\) 3.98382 + 1.06746i 0.246121 + 0.0659480i
\(263\) −28.8391 7.72741i −1.77829 0.476492i −0.788023 0.615646i \(-0.788895\pi\)
−0.990271 + 0.139154i \(0.955562\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) 0 0
\(266\) 1.96410 5.66987i 0.120427 0.347642i
\(267\) −4.89898 4.89898i −0.299813 0.299813i
\(268\) −0.517638 1.93185i −0.0316198 0.118007i
\(269\) 12.6603 + 21.9282i 0.771909 + 1.33699i 0.936515 + 0.350627i \(0.114031\pi\)
−0.164606 + 0.986359i \(0.552635\pi\)
\(270\) 0 0
\(271\) 6.92820 + 4.00000i 0.420858 + 0.242983i 0.695444 0.718580i \(-0.255208\pi\)
−0.274586 + 0.961563i \(0.588541\pi\)
\(272\) 5.27792 5.27792i 0.320021 0.320021i
\(273\) 13.6431 6.62278i 0.825717 0.400829i
\(274\) 18.9282i 1.14349i
\(275\) 0 0
\(276\) −5.13397 + 2.96410i −0.309029 + 0.178418i
\(277\) 5.69402 21.2504i 0.342120 1.27681i −0.553820 0.832636i \(-0.686830\pi\)
0.895940 0.444174i \(-0.146503\pi\)
\(278\) 10.0382 2.68973i 0.602051 0.161319i
\(279\) −7.46410 −0.446864
\(280\) 0 0
\(281\) −27.9282 −1.66606 −0.833028 0.553230i \(-0.813395\pi\)
−0.833028 + 0.553230i \(0.813395\pi\)
\(282\) −1.15539 + 0.309587i −0.0688027 + 0.0184356i
\(283\) 3.24453 12.1087i 0.192867 0.719790i −0.799941 0.600078i \(-0.795136\pi\)
0.992809 0.119712i \(-0.0381972\pi\)
\(284\) −7.73205 + 4.46410i −0.458813 + 0.264896i
\(285\) 0 0
\(286\) 5.73205i 0.338943i
\(287\) −0.429705 + 5.98502i −0.0253647 + 0.353285i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 33.5263 + 19.3564i 1.97213 + 1.13861i
\(290\) 0 0
\(291\) 1.46410 + 2.53590i 0.0858272 + 0.148657i
\(292\) 1.03528 + 3.86370i 0.0605850 + 0.226106i
\(293\) −1.22474 1.22474i −0.0715504 0.0715504i 0.670426 0.741976i \(-0.266111\pi\)
−0.741976 + 0.670426i \(0.766111\pi\)
\(294\) −1.00000 + 6.92820i −0.0583212 + 0.404061i
\(295\) 0 0
\(296\) 1.96410 3.40192i 0.114161 0.197733i
\(297\) −0.965926 0.258819i −0.0560487 0.0150182i
\(298\) 0.896575 + 0.240237i 0.0519372 + 0.0139165i
\(299\) −16.9904 + 29.4282i −0.982579 + 1.70188i
\(300\) 0 0
\(301\) 17.8564 15.4641i 1.02923 0.891336i
\(302\) 2.72689 + 2.72689i 0.156915 + 0.156915i
\(303\) 0.277401 + 1.03528i 0.0159363 + 0.0594751i
\(304\) 1.13397 + 1.96410i 0.0650379 + 0.112649i
\(305\) 0 0
\(306\) −6.46410 3.73205i −0.369528 0.213347i
\(307\) −15.8338 + 15.8338i −0.903680 + 0.903680i −0.995752 0.0920724i \(-0.970651\pi\)
0.0920724 + 0.995752i \(0.470651\pi\)
\(308\) 2.19067 + 1.48356i 0.124825 + 0.0845339i
\(309\) 18.3923i 1.04630i
\(310\) 0 0
\(311\) 17.7846 10.2679i 1.00847 0.582242i 0.0977286 0.995213i \(-0.468842\pi\)
0.910744 + 0.412971i \(0.135509\pi\)
\(312\) −1.48356 + 5.53674i −0.0839903 + 0.313456i
\(313\) 30.1146 8.06918i 1.70218 0.456097i 0.728691 0.684843i \(-0.240129\pi\)
0.973486 + 0.228746i \(0.0734624\pi\)
\(314\) 4.66025 0.262993
\(315\) 0 0
\(316\) 3.07180 0.172802
\(317\) −13.5230 + 3.62347i −0.759525 + 0.203514i −0.617739 0.786383i \(-0.711951\pi\)
−0.141786 + 0.989897i \(0.545285\pi\)
\(318\) −0.258819 + 0.965926i −0.0145139 + 0.0541664i
\(319\) 6.00000 3.46410i 0.335936 0.193952i
\(320\) 0 0
\(321\) 14.9282i 0.833211i
\(322\) −6.84941 14.1100i −0.381703 0.786317i
\(323\) −11.9700 + 11.9700i −0.666031 + 0.666031i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) −6.00000 10.3923i −0.332309 0.575577i
\(327\) 4.38134 + 16.3514i 0.242289 + 0.904234i
\(328\) −1.60368 1.60368i −0.0885485 0.0885485i
\(329\) −0.598076 3.10770i −0.0329730 0.171333i
\(330\) 0 0
\(331\) −12.8923 + 22.3301i −0.708625 + 1.22737i 0.256742 + 0.966480i \(0.417351\pi\)
−0.965367 + 0.260895i \(0.915982\pi\)
\(332\) −10.0382 2.68973i −0.550918 0.147618i
\(333\) −3.79435 1.01669i −0.207929 0.0557145i
\(334\) −3.40192 + 5.89230i −0.186145 + 0.322413i
\(335\) 0 0
\(336\) −1.73205 2.00000i −0.0944911 0.109109i
\(337\) 7.82894 + 7.82894i 0.426470 + 0.426470i 0.887424 0.460954i \(-0.152493\pi\)
−0.460954 + 0.887424i \(0.652493\pi\)
\(338\) 5.13922 + 19.1798i 0.279537 + 1.04324i
\(339\) −6.46410 11.1962i −0.351082 0.608092i
\(340\) 0 0
\(341\) −6.46410 3.73205i −0.350051 0.202102i
\(342\) 1.60368 1.60368i 0.0867172 0.0867172i
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 8.92820i 0.481376i
\(345\) 0 0
\(346\) −6.57180 + 3.79423i −0.353302 + 0.203979i
\(347\) 0.757875 2.82843i 0.0406848 0.151838i −0.942595 0.333937i \(-0.891623\pi\)
0.983280 + 0.182099i \(0.0582893\pi\)
\(348\) −6.69213 + 1.79315i −0.358736 + 0.0961230i
\(349\) −1.85641 −0.0993712 −0.0496856 0.998765i \(-0.515822\pi\)
−0.0496856 + 0.998765i \(0.515822\pi\)
\(350\) 0 0
\(351\) 5.73205 0.305954
\(352\) −0.965926 + 0.258819i −0.0514840 + 0.0137951i
\(353\) −1.79315 + 6.69213i −0.0954398 + 0.356186i −0.997086 0.0762887i \(-0.975693\pi\)
0.901646 + 0.432475i \(0.142360\pi\)
\(354\) 9.92820 5.73205i 0.527678 0.304655i
\(355\) 0 0
\(356\) 6.92820i 0.367194i
\(357\) 11.0735 16.3514i 0.586070 0.865407i
\(358\) −6.36396 + 6.36396i −0.336346 + 0.336346i
\(359\) 4.39230 + 2.53590i 0.231817 + 0.133840i 0.611410 0.791314i \(-0.290603\pi\)
−0.379593 + 0.925154i \(0.623936\pi\)
\(360\) 0 0
\(361\) 6.92820 + 12.0000i 0.364642 + 0.631579i
\(362\) −3.72500 13.9019i −0.195782 0.730668i
\(363\) 7.07107 + 7.07107i 0.371135 + 0.371135i
\(364\) −14.3301 4.96410i −0.751103 0.260190i
\(365\) 0 0
\(366\) 5.73205 9.92820i 0.299619 0.518955i
\(367\) 29.4768 + 7.89829i 1.53868 + 0.412288i 0.925838 0.377920i \(-0.123360\pi\)
0.612840 + 0.790207i \(0.290027\pi\)
\(368\) 5.72620 + 1.53433i 0.298499 + 0.0799826i
\(369\) −1.13397 + 1.96410i −0.0590324 + 0.102247i
\(370\) 0 0
\(371\) −2.50000 0.866025i −0.129794 0.0449618i
\(372\) 5.27792 + 5.27792i 0.273647 + 0.273647i
\(373\) −6.72930 25.1141i −0.348430 1.30036i −0.888554 0.458772i \(-0.848289\pi\)
0.540124 0.841585i \(-0.318377\pi\)
\(374\) −3.73205 6.46410i −0.192980 0.334251i
\(375\) 0 0
\(376\) 1.03590 + 0.598076i 0.0534224 + 0.0308434i
\(377\) −28.0812 + 28.0812i −1.44626 + 1.44626i
\(378\) −1.48356 + 2.19067i −0.0763063 + 0.112676i
\(379\) 3.92820i 0.201778i −0.994898 0.100889i \(-0.967831\pi\)
0.994898 0.100889i \(-0.0321687\pi\)
\(380\) 0 0
\(381\) 4.33013 2.50000i 0.221839 0.128079i
\(382\) −0.757875 + 2.82843i −0.0387762 + 0.144715i
\(383\) −21.2318 + 5.68904i −1.08489 + 0.290696i −0.756599 0.653879i \(-0.773141\pi\)
−0.328294 + 0.944575i \(0.606474\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −22.7846 −1.15971
\(387\) 8.62398 2.31079i 0.438382 0.117464i
\(388\) 0.757875 2.82843i 0.0384753 0.143592i
\(389\) 31.7321 18.3205i 1.60888 0.928887i 0.619257 0.785188i \(-0.287434\pi\)
0.989622 0.143699i \(-0.0458996\pi\)
\(390\) 0 0
\(391\) 44.2487i 2.23775i
\(392\) 5.60609 4.19187i 0.283150 0.211722i
\(393\) −2.91636 + 2.91636i −0.147111 + 0.147111i
\(394\) −14.5981 8.42820i −0.735440 0.424607i
\(395\) 0 0
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) −7.45001 27.8038i −0.373905 1.39543i −0.854938 0.518730i \(-0.826405\pi\)
0.481033 0.876702i \(-0.340262\pi\)
\(398\) −8.86422 8.86422i −0.444323 0.444323i
\(399\) 3.92820 + 4.53590i 0.196656 + 0.227079i
\(400\) 0 0
\(401\) −0.964102 + 1.66987i −0.0481449 + 0.0833895i −0.889094 0.457725i \(-0.848664\pi\)
0.840949 + 0.541115i \(0.181998\pi\)
\(402\) 1.93185 + 0.517638i 0.0963520 + 0.0258174i
\(403\) 41.3268 + 11.0735i 2.05863 + 0.551609i
\(404\) 0.535898 0.928203i 0.0266619 0.0461798i
\(405\) 0 0
\(406\) −3.46410 18.0000i −0.171920 0.893325i
\(407\) −2.77766 2.77766i −0.137683 0.137683i
\(408\) 1.93185 + 7.20977i 0.0956409 + 0.356937i
\(409\) −14.3923 24.9282i −0.711654 1.23262i −0.964236 0.265045i \(-0.914613\pi\)
0.252582 0.967575i \(-0.418720\pi\)
\(410\) 0 0
\(411\) −16.3923 9.46410i −0.808573 0.466830i
\(412\) 13.0053 13.0053i 0.640726 0.640726i
\(413\) 13.2456 + 27.2862i 0.651771 + 1.34266i
\(414\) 5.92820i 0.291355i
\(415\) 0 0
\(416\) 4.96410 2.86603i 0.243385 0.140518i
\(417\) −2.68973 + 10.0382i −0.131716 + 0.491573i
\(418\) 2.19067 0.586988i 0.107149 0.0287105i
\(419\) 11.0526 0.539953 0.269976 0.962867i \(-0.412984\pi\)
0.269976 + 0.962867i \(0.412984\pi\)
\(420\) 0 0
\(421\) −13.8564 −0.675320 −0.337660 0.941268i \(-0.609635\pi\)
−0.337660 + 0.941268i \(0.609635\pi\)
\(422\) −19.1105 + 5.12063i −0.930283 + 0.249269i
\(423\) 0.309587 1.15539i 0.0150526 0.0561772i
\(424\) 0.866025 0.500000i 0.0420579 0.0242821i
\(425\) 0 0
\(426\) 8.92820i 0.432573i
\(427\) 25.1141 + 17.0077i 1.21536 + 0.823062i
\(428\) 10.5558 10.5558i 0.510235 0.510235i
\(429\) 4.96410 + 2.86603i 0.239669 + 0.138373i
\(430\) 0 0
\(431\) 16.8564 + 29.1962i 0.811945 + 1.40633i 0.911501 + 0.411297i \(0.134924\pi\)
−0.0995567 + 0.995032i \(0.531742\pi\)
\(432\) −0.258819 0.965926i −0.0124524 0.0464731i
\(433\) 11.3137 + 11.3137i 0.543702 + 0.543702i 0.924612 0.380910i \(-0.124389\pi\)
−0.380910 + 0.924612i \(0.624389\pi\)
\(434\) −14.9282 + 12.9282i −0.716577 + 0.620574i
\(435\) 0 0
\(436\) 8.46410 14.6603i 0.405357 0.702099i
\(437\) −12.9867 3.47979i −0.621240 0.166461i
\(438\) −3.86370 1.03528i −0.184615 0.0494674i
\(439\) 10.0000 17.3205i 0.477274 0.826663i −0.522387 0.852709i \(-0.674958\pi\)
0.999661 + 0.0260459i \(0.00829161\pi\)
\(440\) 0 0
\(441\) −5.50000 4.33013i −0.261905 0.206197i
\(442\) 30.2533 + 30.2533i 1.43900 + 1.43900i
\(443\) 7.20977 + 26.9072i 0.342546 + 1.27840i 0.895452 + 0.445157i \(0.146852\pi\)
−0.552906 + 0.833244i \(0.686481\pi\)
\(444\) 1.96410 + 3.40192i 0.0932121 + 0.161448i
\(445\) 0 0
\(446\) 8.07180 + 4.66025i 0.382211 + 0.220669i
\(447\) −0.656339 + 0.656339i −0.0310438 + 0.0310438i
\(448\) −0.189469 + 2.63896i −0.00895155 + 0.124679i
\(449\) 13.9282i 0.657313i −0.944450 0.328656i \(-0.893404\pi\)
0.944450 0.328656i \(-0.106596\pi\)
\(450\) 0 0
\(451\) −1.96410 + 1.13397i −0.0924859 + 0.0533968i
\(452\) −3.34607 + 12.4877i −0.157386 + 0.587371i
\(453\) −3.72500 + 0.998111i −0.175016 + 0.0468954i
\(454\) −3.46410 −0.162578
\(455\) 0 0
\(456\) −2.26795 −0.106206
\(457\) 15.3161 4.10394i 0.716458 0.191974i 0.117867 0.993029i \(-0.462394\pi\)
0.598591 + 0.801055i \(0.295728\pi\)
\(458\) 0.757875 2.82843i 0.0354132 0.132164i
\(459\) 6.46410 3.73205i 0.301718 0.174197i
\(460\) 0 0
\(461\) 38.6410i 1.79969i −0.436208 0.899846i \(-0.643679\pi\)
0.436208 0.899846i \(-0.356321\pi\)
\(462\) −2.38014 + 1.15539i −0.110734 + 0.0537538i
\(463\) −16.0604 + 16.0604i −0.746389 + 0.746389i −0.973799 0.227410i \(-0.926974\pi\)
0.227410 + 0.973799i \(0.426974\pi\)
\(464\) 6.00000 + 3.46410i 0.278543 + 0.160817i
\(465\) 0 0
\(466\) −0.928203 1.60770i −0.0429982 0.0744750i
\(467\) −1.65445 6.17449i −0.0765588 0.285721i 0.917023 0.398833i \(-0.130585\pi\)
−0.993582 + 0.113112i \(0.963918\pi\)
\(468\) −4.05317 4.05317i −0.187358 0.187358i
\(469\) −1.73205 + 5.00000i −0.0799787 + 0.230879i
\(470\) 0 0
\(471\) −2.33013 + 4.03590i −0.107367 + 0.185964i
\(472\) −11.0735 2.96713i −0.509698 0.136573i
\(473\) 8.62398 + 2.31079i 0.396531 + 0.106250i
\(474\) −1.53590 + 2.66025i −0.0705461 + 0.122190i
\(475\) 0 0
\(476\) −19.3923 + 3.73205i −0.888845 + 0.171058i
\(477\) −0.707107 0.707107i −0.0323762 0.0323762i
\(478\) −6.21166 23.1822i −0.284115 1.06033i
\(479\) −14.5359 25.1769i −0.664162 1.15036i −0.979512 0.201387i \(-0.935455\pi\)
0.315350 0.948976i \(-0.397878\pi\)
\(480\) 0 0
\(481\) 19.5000 + 11.2583i 0.889123 + 0.513336i
\(482\) 15.7458 15.7458i 0.717202 0.717202i
\(483\) 15.6443 + 1.12321i 0.711839 + 0.0511078i
\(484\) 10.0000i 0.454545i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) 1.51575 5.65685i 0.0686852 0.256337i −0.923042 0.384699i \(-0.874305\pi\)
0.991727 + 0.128362i \(0.0409720\pi\)
\(488\) −11.0735 + 2.96713i −0.501273 + 0.134316i
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −11.7128 −0.528592 −0.264296 0.964442i \(-0.585140\pi\)
−0.264296 + 0.964442i \(0.585140\pi\)
\(492\) 2.19067 0.586988i 0.0987631 0.0264635i
\(493\) −13.3843 + 49.9507i −0.602797 + 2.24967i
\(494\) −11.2583 + 6.50000i −0.506536 + 0.292449i
\(495\) 0 0
\(496\) 7.46410i 0.335148i
\(497\) 23.5612 + 1.69161i 1.05686 + 0.0758793i
\(498\) 7.34847 7.34847i 0.329293 0.329293i
\(499\) −24.2487 14.0000i −1.08552 0.626726i −0.153141 0.988204i \(-0.548939\pi\)
−0.932381 + 0.361478i \(0.882272\pi\)
\(500\) 0 0
\(501\) −3.40192 5.89230i −0.151987 0.263249i
\(502\) 1.89967 + 7.08965i 0.0847862 + 0.316427i
\(503\) 9.62209 + 9.62209i 0.429028 + 0.429028i 0.888297 0.459269i \(-0.151889\pi\)
−0.459269 + 0.888297i \(0.651889\pi\)
\(504\) 2.59808 0.500000i 0.115728 0.0222718i
\(505\) 0 0
\(506\) 2.96410 5.13397i 0.131770 0.228233i
\(507\) −19.1798 5.13922i −0.851806 0.228241i
\(508\) −4.82963 1.29410i −0.214280 0.0574162i
\(509\) 5.19615 9.00000i 0.230315 0.398918i −0.727586 0.686017i \(-0.759358\pi\)
0.957901 + 0.287099i \(0.0926909\pi\)
\(510\) 0 0
\(511\) 3.46410 10.0000i 0.153243 0.442374i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0.586988 + 2.19067i 0.0259162 + 0.0967205i
\(514\) 1.19615 + 2.07180i 0.0527600 + 0.0913830i
\(515\) 0 0
\(516\) −7.73205 4.46410i −0.340385 0.196521i
\(517\) 0.845807 0.845807i 0.0371986 0.0371986i
\(518\) −9.34967 + 4.53862i −0.410801 + 0.199416i
\(519\) 7.58846i 0.333096i
\(520\) 0 0
\(521\) 27.8205 16.0622i 1.21884 0.703697i 0.254169 0.967160i \(-0.418198\pi\)
0.964669 + 0.263463i \(0.0848647\pi\)
\(522\) 1.79315 6.69213i 0.0784841 0.292907i
\(523\) −5.93426 + 1.59008i −0.259487 + 0.0695293i −0.386217 0.922408i \(-0.626218\pi\)
0.126730 + 0.991937i \(0.459552\pi\)
\(524\) 4.12436 0.180173
\(525\) 0 0
\(526\) −29.8564 −1.30180
\(527\) 53.8144 14.4195i 2.34419 0.628125i
\(528\) 0.258819 0.965926i 0.0112637 0.0420365i
\(529\) −10.5167 + 6.07180i −0.457246 + 0.263991i
\(530\) 0 0
\(531\) 11.4641i 0.497500i
\(532\) 0.429705 5.98502i 0.0186301 0.259484i
\(533\) 9.19239 9.19239i 0.398167 0.398167i
\(534\) −6.00000 3.46410i −0.259645 0.149906i
\(535\) 0 0
\(536\) −1.00000 1.73205i −0.0431934 0.0748132i
\(537\) −2.32937 8.69333i −0.100520 0.375145i
\(538\) 17.9043 + 17.9043i 0.771909 + 0.771909i
\(539\) −2.59808 6.50000i −0.111907 0.279975i
\(540\) 0 0
\(541\) −15.4641 + 26.7846i −0.664854 + 1.15156i 0.314471 + 0.949267i \(0.398173\pi\)
−0.979325 + 0.202293i \(0.935161\pi\)
\(542\) 7.72741 + 2.07055i 0.331921 + 0.0889378i
\(543\) 13.9019 + 3.72500i 0.596588 + 0.159855i
\(544\) 3.73205 6.46410i 0.160010 0.277146i
\(545\) 0 0
\(546\) 11.4641 9.92820i 0.490618 0.424888i
\(547\) −18.1817 18.1817i −0.777394 0.777394i 0.201993 0.979387i \(-0.435258\pi\)
−0.979387 + 0.201993i \(0.935258\pi\)
\(548\) 4.89898 + 18.2832i 0.209274 + 0.781021i
\(549\) 5.73205 + 9.92820i 0.244638 + 0.423725i
\(550\) 0 0
\(551\) −13.6077 7.85641i −0.579707 0.334694i
\(552\) −4.19187 + 4.19187i −0.178418 + 0.178418i
\(553\) −6.72930 4.55721i −0.286159 0.193792i
\(554\) 22.0000i 0.934690i
\(555\) 0 0
\(556\) 9.00000 5.19615i 0.381685 0.220366i
\(557\) 1.25693 4.69093i 0.0532579 0.198761i −0.934171 0.356826i \(-0.883859\pi\)
0.987429 + 0.158065i \(0.0505256\pi\)
\(558\) −7.20977 + 1.93185i −0.305214 + 0.0817818i
\(559\) −51.1769 −2.16455
\(560\) 0 0
\(561\) 7.46410 0.315135
\(562\) −26.9766 + 7.22835i −1.13794 + 0.304910i
\(563\) 0.619174 2.31079i 0.0260951 0.0973881i −0.951650 0.307184i \(-0.900613\pi\)
0.977745 + 0.209796i \(0.0672800\pi\)
\(564\) −1.03590 + 0.598076i −0.0436192 + 0.0251836i
\(565\) 0 0
\(566\) 12.5359i 0.526923i
\(567\) −1.15539 2.38014i −0.0485220 0.0999565i
\(568\) −6.31319 + 6.31319i −0.264896 + 0.264896i
\(569\) 27.5263 + 15.8923i 1.15396 + 0.666240i 0.949849 0.312707i \(-0.101236\pi\)
0.204112 + 0.978948i \(0.434569\pi\)
\(570\) 0 0
\(571\) 6.92820 + 12.0000i 0.289936 + 0.502184i 0.973794 0.227431i \(-0.0730325\pi\)
−0.683858 + 0.729615i \(0.739699\pi\)
\(572\) −1.48356 5.53674i −0.0620309 0.231503i
\(573\) −2.07055 2.07055i −0.0864986 0.0864986i
\(574\) 1.13397 + 5.89230i 0.0473312 + 0.245940i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 20.3538 + 5.45378i 0.847339 + 0.227044i 0.656264 0.754531i \(-0.272136\pi\)
0.191076 + 0.981575i \(0.438802\pi\)
\(578\) 37.3937 + 10.0196i 1.55537 + 0.416761i
\(579\) 11.3923 19.7321i 0.473448 0.820036i
\(580\) 0 0
\(581\) 18.0000 + 20.7846i 0.746766 + 0.862291i
\(582\) 2.07055 + 2.07055i 0.0858272 + 0.0858272i
\(583\) −0.258819 0.965926i −0.0107192 0.0400046i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 0 0
\(586\) −1.50000 0.866025i −0.0619644 0.0357752i
\(587\) 15.0759 15.0759i 0.622248 0.622248i −0.323858 0.946106i \(-0.604980\pi\)
0.946106 + 0.323858i \(0.104980\pi\)
\(588\) 0.827225 + 6.95095i 0.0341142 + 0.286652i
\(589\) 16.9282i 0.697514i
\(590\) 0 0
\(591\) 14.5981 8.42820i 0.600485 0.346690i
\(592\) 1.01669 3.79435i 0.0417859 0.155947i
\(593\) −40.9478 + 10.9719i −1.68153 + 0.450563i −0.968181 0.250250i \(-0.919487\pi\)
−0.713344 + 0.700814i \(0.752820\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 0.928203 0.0380207
\(597\) 12.1087 3.24453i 0.495578 0.132790i
\(598\) −8.79487 + 32.8229i −0.359649 + 1.34223i
\(599\) 36.2487 20.9282i 1.48108 0.855103i 0.481312 0.876549i \(-0.340160\pi\)
0.999770 + 0.0214460i \(0.00682701\pi\)
\(600\) 0 0
\(601\) 28.7846i 1.17415i 0.809533 + 0.587074i \(0.199720\pi\)
−0.809533 + 0.587074i \(0.800280\pi\)
\(602\) 13.2456 19.5588i 0.539849 0.797155i
\(603\) −1.41421 + 1.41421i −0.0575912 + 0.0575912i
\(604\) 3.33975 + 1.92820i 0.135892 + 0.0784575i
\(605\) 0 0
\(606\) 0.535898 + 0.928203i 0.0217694 + 0.0377057i
\(607\) −4.93117 18.4034i −0.200150 0.746969i −0.990873 0.134796i \(-0.956962\pi\)
0.790724 0.612173i \(-0.209705\pi\)
\(608\) 1.60368 + 1.60368i 0.0650379 + 0.0650379i
\(609\) 17.3205 + 6.00000i 0.701862 + 0.243132i
\(610\) 0 0
\(611\) −3.42820 + 5.93782i −0.138690 + 0.240219i
\(612\) −7.20977 1.93185i −0.291438 0.0780905i
\(613\) −17.3173 4.64016i −0.699440 0.187414i −0.108460 0.994101i \(-0.534592\pi\)
−0.590980 + 0.806686i \(0.701259\pi\)
\(614\) −11.1962 + 19.3923i −0.451840 + 0.782610i
\(615\) 0 0
\(616\) 2.50000 + 0.866025i 0.100728 + 0.0348932i
\(617\) 2.17209 + 2.17209i 0.0874450 + 0.0874450i 0.749476 0.662031i \(-0.230305\pi\)
−0.662031 + 0.749476i \(0.730305\pi\)
\(618\) 4.76028 + 17.7656i 0.191486 + 0.714637i
\(619\) −5.79423 10.0359i −0.232890 0.403377i 0.725768 0.687940i \(-0.241485\pi\)
−0.958657 + 0.284563i \(0.908151\pi\)
\(620\) 0 0
\(621\) 5.13397 + 2.96410i 0.206019 + 0.118945i
\(622\) 14.5211 14.5211i 0.582242 0.582242i
\(623\) 10.2784 15.1774i 0.411797 0.608070i
\(624\) 5.73205i 0.229466i
\(625\) 0 0
\(626\) 27.0000 15.5885i 1.07914 0.623040i
\(627\) −0.586988 + 2.19067i −0.0234421 + 0.0874870i
\(628\) 4.50146 1.20616i 0.179628 0.0481311i
\(629\) 29.3205 1.16909
\(630\) 0 0
\(631\) 42.7846 1.70323 0.851614 0.524169i \(-0.175624\pi\)
0.851614 + 0.524169i \(0.175624\pi\)
\(632\) 2.96713 0.795040i 0.118026 0.0316250i
\(633\) 5.12063 19.1105i 0.203527 0.759573i
\(634\) −12.1244 + 7.00000i −0.481520 + 0.278006i
\(635\) 0 0
\(636\) 1.00000i 0.0396526i
\(637\) 24.0280 + 32.1344i 0.952025 + 1.27321i
\(638\) 4.89898 4.89898i 0.193952 0.193952i
\(639\) 7.73205 + 4.46410i 0.305875 + 0.176597i
\(640\) 0 0
\(641\) −15.9641 27.6506i −0.630544 1.09213i −0.987441 0.157991i \(-0.949498\pi\)
0.356897 0.934144i \(-0.383835\pi\)
\(642\) 3.86370 + 14.4195i 0.152488 + 0.569094i
\(643\) 29.2180 + 29.2180i 1.15225 + 1.15225i 0.986101 + 0.166144i \(0.0531318\pi\)
0.166144 + 0.986101i \(0.446868\pi\)
\(644\) −10.2679 11.8564i −0.404614 0.467208i
\(645\) 0 0
\(646\) −8.46410 + 14.6603i −0.333016 + 0.576800i
\(647\) −4.26122 1.14179i −0.167526 0.0448884i 0.174081 0.984731i \(-0.444305\pi\)
−0.341607 + 0.939843i \(0.610971\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) −5.73205 + 9.92820i −0.225003 + 0.389716i
\(650\) 0 0
\(651\) −3.73205 19.3923i −0.146271 0.760044i
\(652\) −8.48528 8.48528i −0.332309 0.332309i
\(653\) −6.39615 23.8707i −0.250301 0.934134i −0.970645 0.240518i \(-0.922683\pi\)
0.720344 0.693617i \(-0.243984\pi\)
\(654\) 8.46410 + 14.6603i 0.330973 + 0.573261i
\(655\) 0 0
\(656\) −1.96410 1.13397i −0.0766853 0.0442743i
\(657\) 2.82843 2.82843i 0.110347 0.110347i
\(658\) −1.38203 2.84701i −0.0538771 0.110988i
\(659\) 39.7128i 1.54699i 0.633801 + 0.773496i \(0.281494\pi\)
−0.633801 + 0.773496i \(0.718506\pi\)
\(660\) 0 0
\(661\) 7.85641 4.53590i 0.305579 0.176426i −0.339368 0.940654i \(-0.610213\pi\)
0.644946 + 0.764228i \(0.276880\pi\)
\(662\) −6.67355 + 24.9060i −0.259375 + 0.968000i
\(663\) −41.3268 + 11.0735i −1.60500 + 0.430058i
\(664\) −10.3923 −0.403300
\(665\) 0 0
\(666\) −3.92820 −0.152215
\(667\) −39.6723 + 10.6302i −1.53612 + 0.411602i
\(668\) −1.76097 + 6.57201i −0.0681338 + 0.254279i
\(669\) −8.07180 + 4.66025i −0.312074 + 0.180176i
\(670\) 0 0
\(671\) 11.4641i 0.442567i
\(672\) −2.19067 1.48356i −0.0845070 0.0572297i
\(673\) 17.5254 17.5254i 0.675553 0.675553i −0.283438 0.958991i \(-0.591475\pi\)
0.958991 + 0.283438i \(0.0914749\pi\)
\(674\) 9.58846 + 5.53590i 0.369334 + 0.213235i
\(675\) 0 0
\(676\) 9.92820 + 17.1962i 0.381854 + 0.661390i
\(677\) 12.9360 + 48.2777i 0.497170 + 1.85546i 0.517522 + 0.855670i \(0.326855\pi\)
−0.0203517 + 0.999793i \(0.506479\pi\)
\(678\) −9.14162 9.14162i −0.351082 0.351082i
\(679\) −5.85641 + 5.07180i −0.224748 + 0.194638i
\(680\) 0 0
\(681\) 1.73205 3.00000i 0.0663723 0.114960i
\(682\) −7.20977 1.93185i −0.276076 0.0739744i
\(683\) −13.6617 3.66063i −0.522749 0.140070i −0.0122111 0.999925i \(-0.503887\pi\)
−0.510538 + 0.859855i \(0.670554\pi\)
\(684\) 1.13397 1.96410i 0.0433586 0.0750993i
\(685\) 0 0
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 2.07055 + 2.07055i 0.0789965 + 0.0789965i
\(688\) 2.31079 + 8.62398i 0.0880980 + 0.328786i
\(689\) 2.86603 + 4.96410i 0.109187 + 0.189117i
\(690\) 0 0
\(691\) −34.8564 20.1244i −1.32600 0.765567i −0.341322 0.939947i \(-0.610875\pi\)
−0.984678 + 0.174380i \(0.944208\pi\)
\(692\) −5.36585 + 5.36585i −0.203979 + 0.203979i
\(693\) 0.189469 2.63896i 0.00719732 0.100246i
\(694\) 2.92820i 0.111153i
\(695\) 0 0
\(696\) −6.00000 + 3.46410i −0.227429 + 0.131306i
\(697\) 4.38134 16.3514i 0.165955 0.619353i
\(698\) −1.79315 + 0.480473i −0.0678718 + 0.0181862i
\(699\) 1.85641 0.0702157
\(700\) 0 0
\(701\) −4.14359 −0.156501 −0.0782507 0.996934i \(-0.524933\pi\)
−0.0782507 + 0.996934i \(0.524933\pi\)
\(702\) 5.53674 1.48356i 0.208971 0.0559935i
\(703\) −2.30581 + 8.60540i −0.0869653 + 0.324559i
\(704\) −0.866025 + 0.500000i −0.0326396 + 0.0188445i
\(705\) 0 0
\(706\) 6.92820i 0.260746i
\(707\) −2.55103 + 1.23835i −0.0959412 + 0.0465729i
\(708\) 8.10634 8.10634i 0.304655 0.304655i
\(709\) −23.3205 13.4641i −0.875820 0.505655i −0.00654213 0.999979i \(-0.502082\pi\)
−0.869278 + 0.494324i \(0.835416\pi\)
\(710\) 0 0
\(711\) −1.53590 2.66025i −0.0576007 0.0997673i
\(712\) 1.79315 + 6.69213i 0.0672012 + 0.250798i
\(713\) 31.2886 + 31.2886i 1.17177 + 1.17177i
\(714\) 6.46410 18.6603i 0.241913 0.698342i
\(715\) 0 0
\(716\) −4.50000 + 7.79423i −0.168173 + 0.291284i
\(717\) 23.1822 + 6.21166i 0.865756 + 0.231979i
\(718\) 4.89898 + 1.31268i 0.182828 + 0.0489887i
\(719\) −3.19615 + 5.53590i −0.119196 + 0.206454i −0.919449 0.393208i \(-0.871365\pi\)
0.800253 + 0.599662i \(0.204698\pi\)
\(720\) 0 0
\(721\) −47.7846 + 9.19615i −1.77959 + 0.342483i
\(722\) 9.79796 + 9.79796i 0.364642 + 0.364642i
\(723\) 5.76337 + 21.5092i 0.214342 + 0.799935i
\(724\) −7.19615 12.4641i −0.267443 0.463225i
\(725\) 0 0
\(726\) 8.66025 + 5.00000i 0.321412 + 0.185567i
\(727\) −10.8468 + 10.8468i −0.402287 + 0.402287i −0.879038 0.476751i \(-0.841814\pi\)
0.476751 + 0.879038i \(0.341814\pi\)
\(728\) −15.1266 1.08604i −0.560631 0.0402515i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −57.7128 + 33.3205i −2.13459 + 1.23240i
\(732\) 2.96713 11.0735i 0.109668 0.409287i
\(733\) 14.5397 3.89589i 0.537034 0.143898i 0.0198997 0.999802i \(-0.493665\pi\)
0.517135 + 0.855904i \(0.326999\pi\)
\(734\) 30.5167 1.12639
\(735\) 0 0
\(736\) 5.92820 0.218516
\(737\) −1.93185 + 0.517638i −0.0711607 + 0.0190674i
\(738\) −0.586988 + 2.19067i −0.0216073 + 0.0806397i
\(739\) −17.2583 + 9.96410i −0.634858 + 0.366535i −0.782631 0.622486i \(-0.786123\pi\)
0.147773 + 0.989021i \(0.452789\pi\)
\(740\) 0 0
\(741\) 13.0000i 0.477567i
\(742\) −2.63896 0.189469i −0.0968792 0.00695561i
\(743\) −5.50455 + 5.50455i −0.201942 + 0.201942i −0.800832 0.598889i \(-0.795609\pi\)
0.598889 + 0.800832i \(0.295609\pi\)
\(744\) 6.46410 + 3.73205i 0.236985 + 0.136824i
\(745\) 0 0
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) 2.68973 + 10.0382i 0.0984119 + 0.367278i
\(748\) −5.27792 5.27792i −0.192980 0.192980i
\(749\) −38.7846 + 7.46410i −1.41716 + 0.272732i
\(750\) 0 0
\(751\) 6.92820 12.0000i 0.252814 0.437886i −0.711486 0.702701i \(-0.751977\pi\)
0.964299 + 0.264814i \(0.0853107\pi\)
\(752\) 1.15539 + 0.309587i 0.0421329 + 0.0112895i
\(753\) −7.08965 1.89967i −0.258361 0.0692277i
\(754\) −19.8564 + 34.3923i −0.723128 + 1.25249i
\(755\) 0 0
\(756\) −0.866025 + 2.50000i −0.0314970 + 0.0909241i
\(757\) −26.6670 26.6670i −0.969228 0.969228i 0.0303124 0.999540i \(-0.490350\pi\)
−0.999540 + 0.0303124i \(0.990350\pi\)
\(758\) −1.01669 3.79435i −0.0369280 0.137817i
\(759\) 2.96410 + 5.13397i 0.107590 + 0.186351i
\(760\) 0 0
\(761\) 41.8923 + 24.1865i 1.51859 + 0.876761i 0.999760 + 0.0218864i \(0.00696721\pi\)
0.518834 + 0.854875i \(0.326366\pi\)
\(762\) 3.53553 3.53553i 0.128079 0.128079i
\(763\) −40.2915 + 19.5588i −1.45865 + 0.708074i
\(764\) 2.92820i 0.105939i
\(765\) 0 0
\(766\) −19.0359 + 10.9904i −0.687795 + 0.397099i
\(767\) 17.0077 63.4737i 0.614113 2.29190i
\(768\) 0.965926 0.258819i 0.0348548 0.00933933i
\(769\) 10.8038 0.389597 0.194798 0.980843i \(-0.437595\pi\)
0.194798 + 0.980843i \(0.437595\pi\)
\(770\) 0 0
\(771\) −2.39230 −0.0861568
\(772\) −22.0082 + 5.89709i −0.792094 + 0.212241i
\(773\) 9.41404 35.1337i 0.338600 1.26367i −0.561314 0.827603i \(-0.689704\pi\)
0.899914 0.436068i \(-0.143629\pi\)
\(774\) 7.73205 4.46410i 0.277923 0.160459i
\(775\) 0 0
\(776\) 2.92820i 0.105116i
\(777\) 0.744272 10.3664i 0.0267006 0.371891i
\(778\) 25.9091 25.9091i 0.928887 0.928887i
\(779\) 4.45448 + 2.57180i 0.159598 + 0.0921442i
\(780\) 0 0
\(781\) 4.46410 + 7.73205i 0.159738 + 0.276675i
\(782\) 11.4524 + 42.7410i 0.409537 + 1.52841i