Properties

Label 1050.2.bc.a.607.1
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 607.1
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.a.493.1

$q$-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 \(-0.957527\pi\)
−0.133037 0.991111i \(-0.542473\pi\)
\(14\) −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 −0.764294 0.644868i \(-0.776912\pi\)
−0.984332 + 0.176325i \(0.943579\pi\)
\(18\) 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 \(-0.871253\pi\)
0.599381 0.800464i \(-0.295414\pi\)
\(24\) 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 −0.556849 0.830614i \(-0.687990\pi\)
−0.0669387 + 0.997757i \(0.521323\pi\)
\(38\) 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 −0.0365779 0.999331i \(-0.511646\pi\)
0.999331 + 0.0365779i \(0.0116457\pi\)
\(44\) −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 0.939664 0.342098i \(-0.111138\pi\)
−0.984822 + 0.173566i \(0.944471\pi\)
\(48\) −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 0.191868 0.981421i \(-0.438546\pi\)
−0.324548 + 0.945869i \(0.605212\pi\)
\(54\) 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 −0.990310 0.138874i \(-0.955652\pi\)
0.927071 + 0.374887i \(0.122318\pi\)
\(68\) −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 −0.878504 0.477734i \(-0.841458\pi\)
0.999674 + 0.0255221i \(0.00812481\pi\)
\(74\) 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 0.984118 0.177518i \(-0.0568069\pi\)
−0.177518 + 0.984118i \(0.556807\pi\)
\(84\) −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 −0.804366 0.594134i \(-0.797495\pi\)
0.594134 + 0.804366i \(0.297495\pi\)
\(98\) −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 −0.984732 0.174077i \(-0.944306\pi\)
−0.765765 + 0.643121i \(0.777639\pi\)
\(104\) 5.73205 0.562074
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) −14.4195 + 3.86370i −1.39399 + 0.373518i −0.876183 0.481979i \(-0.839918\pi\)
−0.517807 + 0.855498i \(0.673251\pi\)
\(108\) −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 −0.131363 0.991334i \(-0.541935\pi\)
0.991334 + 0.131363i \(0.0419354\pi\)
\(114\) −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 0.846352 0.532624i \(-0.178794\pi\)
−0.532624 + 0.846352i \(0.678794\pi\)
\(128\) 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 \(-0.616907\pi\)
0.777621 0.628733i \(-0.216426\pi\)
\(138\) 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 0.0746765 0.997208i \(-0.476208\pi\)
−0.433932 + 0.900946i \(0.642874\pi\)
\(158\) −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 \(0.0723970\pi\)
−0.730979 + 0.682400i \(0.760936\pi\)
\(164\) −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 −0.496021 0.868311i \(-0.665206\pi\)
0.868311 + 0.496021i \(0.165206\pi\)
\(168\) 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 0.0308241 0.999525i \(-0.490187\pi\)
0.526457 + 0.850202i \(0.323520\pi\)
\(174\) −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 0.940219 0.340570i \(-0.110620\pi\)
0.643969 + 0.765052i \(0.277287\pi\)
\(194\) 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 0.990035 0.140822i \(-0.0449744\pi\)
−0.140822 + 0.990035i \(0.544974\pi\)
\(198\) −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 0.451123 0.892462i \(-0.351024\pi\)
−0.892462 + 0.451123i \(0.851024\pi\)
\(224\) −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 0.368146 0.929768i \(-0.379993\pi\)
−0.146060 + 0.989276i \(0.546659\pi\)
\(228\) 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 0.979877 0.199603i \(-0.0639654\pi\)
−0.948400 + 0.317077i \(0.897299\pi\)
\(234\) −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 0.943922 0.330169i \(-0.107106\pi\)
−0.982545 + 0.186026i \(0.940439\pi\)
\(258\) 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 0.990271 0.139154i \(-0.0444383\pi\)
0.788023 + 0.615646i \(0.211105\pi\)
\(264\) 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 \(0.313170\pi\)
−0.895940 + 0.444174i \(0.853497\pi\)
\(278\) −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 \(0.204864\pi\)
−0.992809 + 0.119712i \(0.961803\pi\)
\(284\) −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 0.741976 0.670426i \(-0.233889\pi\)
−0.670426 + 0.741976i \(0.733889\pi\)
\(294\) −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 −0.0920724 0.995752i \(-0.529349\pi\)
0.995752 + 0.0920724i \(0.0293491\pi\)
\(308\) −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 −0.973486 0.228746i \(-0.926538\pi\)
−0.728691 + 0.684843i \(0.759871\pi\)
\(314\) 4.66025 0.262993
\(315\) 0 0
\(316\) 3.07180 0.172802
\(317\) 13.5230 3.62347i 0.759525 0.203514i 0.141786 0.989897i \(-0.454715\pi\)
0.617739 + 0.786383i \(0.288049\pi\)
\(318\) 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 0.460954 0.887424i \(-0.347507\pi\)
−0.887424 + 0.460954i \(0.847507\pi\)
\(338\) −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 −0.983280 0.182099i \(-0.941711\pi\)
0.942595 + 0.333937i \(0.108377\pi\)
\(348\) 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 −0.901646 0.432475i \(-0.857640\pi\)
0.997086 + 0.0762887i \(0.0243071\pi\)
\(354\) 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 −0.612840 0.790207i \(-0.709973\pi\)
−0.925838 + 0.377920i \(0.876640\pi\)
\(368\) −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 \(0.151711\pi\)
−0.540124 + 0.841585i \(0.681623\pi\)
\(374\) −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 0.328294 0.944575i \(-0.393526\pi\)
0.756599 + 0.653879i \(0.226859\pi\)
\(384\) 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 \(0.173595\pi\)
−0.481033 + 0.876702i \(0.659738\pi\)
\(398\) 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 0.380910 0.924612i \(-0.375611\pi\)
−0.924612 + 0.380910i \(0.875611\pi\)
\(434\) −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 \(-0.853148\pi\)
0.552906 0.833244i \(-0.313519\pi\)
\(444\) 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 −0.598591 0.801055i \(-0.704272\pi\)
−0.117867 + 0.993029i \(0.537606\pi\)
\(458\) −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 −0.227410 0.973799i \(-0.573026\pi\)
0.973799 + 0.227410i \(0.0730257\pi\)
\(464\) 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 0.993582 0.113112i \(-0.0360819\pi\)
−0.917023 + 0.398833i \(0.869415\pi\)
\(468\) 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 −0.991727 0.128362i \(-0.959028\pi\)
0.923042 + 0.384699i \(0.125695\pi\)
\(488\) 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 0.459269 0.888297i \(-0.348111\pi\)
−0.888297 + 0.459269i \(0.848111\pi\)
\(504\) 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 −0.126730 0.991937i \(-0.540448\pi\)
0.386217 + 0.922408i \(0.373782\pi\)
\(524\) 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 0.979387 0.201993i \(-0.0647419\pi\)
−0.201993 + 0.979387i \(0.564742\pi\)
\(548\) −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 −0.987429 0.158065i \(-0.949474\pi\)
0.934171 + 0.356826i \(0.116141\pi\)
\(558\) 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 −0.977745 0.209796i \(-0.932720\pi\)
0.951650 + 0.307184i \(0.0993867\pi\)
\(564\) −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 −0.191076 0.981575i \(-0.561198\pi\)
−0.656264 + 0.754531i \(0.727864\pi\)
\(578\) −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 −0.946106 0.323858i \(-0.895020\pi\)
0.323858 + 0.946106i \(0.395020\pi\)
\(588\) −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 0.713344 0.700814i \(-0.247180\pi\)
0.968181 + 0.250250i \(0.0805129\pi\)
\(594\) −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 \(0.0430379\pi\)
−0.790724 + 0.612173i \(0.790295\pi\)
\(608\) −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 0.590980 0.806686i \(-0.298741\pi\)
0.108460 + 0.994101i \(0.465408\pi\)
\(614\) −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 0.662031 0.749476i \(-0.269695\pi\)
−0.749476 + 0.662031i \(0.769695\pi\)
\(618\) −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 \(-0.946868\pi\)
−0.166144 0.986101i \(-0.553132\pi\)
\(644\) −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 0.341607 0.939843i \(-0.389029\pi\)
−0.174081 + 0.984731i \(0.555695\pi\)
\(648\) −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 \(0.0773172\pi\)
−0.720344 + 0.693617i \(0.756016\pi\)
\(654\) 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 −0.958991 0.283438i \(-0.908525\pi\)
0.283438 + 0.958991i \(0.408525\pi\)
\(674\) 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 \(-0.673145\pi\)
0.0203517 0.999793i \(-0.493521\pi\)
\(678\) 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 0.510538 0.859855i \(-0.329446\pi\)
0.0122111 + 0.999925i \(0.496113\pi\)
\(684\) 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 −0.476751 0.879038i \(-0.658186\pi\)
0.879038 + 0.476751i \(0.158186\pi\)
\(728\) 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 −0.517135 0.855904i \(-0.673001\pi\)
−0.0198997 + 0.999802i \(0.506335\pi\)
\(734\) 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 −0.598889 0.800832i \(-0.704391\pi\)
0.800832 + 0.598889i \(0.204391\pi\)
\(744\) 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 0.999540 0.0303124i \(-0.00965021\pi\)
−0.0303124 + 0.999540i \(0.509650\pi\)
\(758\) 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 \(0.310296\pi\)
−0.899914 + 0.436068i \(0.856371\pi\)
\(774\) 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