Properties

Label 1050.2.o.j.499.2
Level $1050$
Weight $2$
Character 1050.499
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
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.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 499.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.499
Dual form 1050.2.o.j.949.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.866025 + 0.500000i) q^{12} +7.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.500000 - 2.59808i) q^{21} +1.00000i q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.50000 + 6.06218i) q^{26} -1.00000i q^{27} +(2.59808 + 0.500000i) q^{28} +8.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.866025 + 0.500000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(-2.59808 - 1.50000i) q^{37} +(0.866025 - 0.500000i) q^{38} +(3.50000 + 6.06218i) q^{39} +9.00000 q^{41} +(1.73205 - 2.00000i) q^{42} -4.00000i q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-2.59808 - 1.50000i) q^{47} +1.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{51} +(-6.06218 + 3.50000i) q^{52} +(-0.866025 + 0.500000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.00000 + 1.73205i) q^{56} -1.00000i q^{57} +(6.92820 + 4.00000i) q^{58} +(6.00000 + 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{61} -6.00000i q^{62} +(-0.866025 - 2.50000i) q^{63} -1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(-10.3923 + 6.00000i) q^{67} +(3.46410 + 2.00000i) q^{68} -1.00000 q^{69} -14.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-12.1244 + 7.00000i) q^{73} +(-1.50000 - 2.59808i) q^{74} +1.00000 q^{76} +(2.59808 + 0.500000i) q^{77} +7.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{82} +12.0000i q^{83} +(2.50000 - 0.866025i) q^{84} +(2.00000 - 3.46410i) q^{86} +(6.92820 - 4.00000i) q^{87} +(-0.866025 + 0.500000i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(14.0000 + 12.1244i) q^{91} -1.00000i q^{92} +(-5.19615 - 3.00000i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-0.500000 + 0.866025i) q^{96} +16.0000i q^{97} +(2.59808 - 6.50000i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + 2q^{11} + 10q^{14} - 2q^{16} + 2q^{19} + 2q^{21} + 2q^{24} - 14q^{26} + 32q^{29} - 12q^{31} + 16q^{34} + 4q^{36} + 14q^{39} + 36q^{41} - 2q^{44} - 2q^{46} - 4q^{49} + 8q^{51} + 2q^{54} + 8q^{56} + 24q^{59} + 8q^{61} - 4q^{64} + 2q^{66} - 4q^{69} - 56q^{71} - 6q^{74} + 4q^{76} + 8q^{79} - 2q^{81} + 10q^{84} + 8q^{86} - 4q^{89} + 56q^{91} - 6q^{94} - 2q^{96} + 4q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 1.73205 2.00000i 0.654654 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) 7.00000i 1.94145i 0.240192 + 0.970725i \(0.422790\pi\)
−0.240192 + 0.970725i \(0.577210\pi\)
\(14\) 2.50000 0.866025i 0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.46410 2.00000i 0.840168 0.485071i −0.0171533 0.999853i \(-0.505460\pi\)
0.857321 + 0.514782i \(0.172127\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 0.500000 2.59808i 0.109109 0.566947i
\(22\) 1.00000i 0.213201i
\(23\) −0.866025 0.500000i −0.180579 0.104257i 0.406986 0.913434i \(-0.366580\pi\)
−0.587565 + 0.809177i \(0.699913\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −3.50000 + 6.06218i −0.686406 + 1.18889i
\(27\) 1.00000i 0.192450i
\(28\) 2.59808 + 0.500000i 0.490990 + 0.0944911i
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i \(-0.985539\pi\)
0.460152 0.887840i \(-0.347795\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0.866025 + 0.500000i 0.150756 + 0.0870388i
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.59808 1.50000i −0.427121 0.246598i 0.270998 0.962580i \(-0.412646\pi\)
−0.698119 + 0.715981i \(0.745980\pi\)
\(38\) 0.866025 0.500000i 0.140488 0.0811107i
\(39\) 3.50000 + 6.06218i 0.560449 + 0.970725i
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 1.73205 2.00000i 0.267261 0.308607i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −2.59808 1.50000i −0.378968 0.218797i 0.298401 0.954441i \(-0.403547\pi\)
−0.677369 + 0.735643i \(0.736880\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) 0 0
\(51\) 2.00000 3.46410i 0.280056 0.485071i
\(52\) −6.06218 + 3.50000i −0.840673 + 0.485363i
\(53\) −0.866025 + 0.500000i −0.118958 + 0.0686803i −0.558298 0.829640i \(-0.688546\pi\)
0.439340 + 0.898321i \(0.355212\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) 1.00000i 0.132453i
\(58\) 6.92820 + 4.00000i 0.909718 + 0.525226i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 6.00000i 0.762001i
\(63\) −0.866025 2.50000i −0.109109 0.314970i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0.500000 + 0.866025i 0.0615457 + 0.106600i
\(67\) −10.3923 + 6.00000i −1.26962 + 0.733017i −0.974916 0.222571i \(-0.928555\pi\)
−0.294706 + 0.955588i \(0.595222\pi\)
\(68\) 3.46410 + 2.00000i 0.420084 + 0.242536i
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) −14.0000 −1.66149 −0.830747 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) −12.1244 + 7.00000i −1.41905 + 0.819288i −0.996215 0.0869195i \(-0.972298\pi\)
−0.422833 + 0.906208i \(0.638964\pi\)
\(74\) −1.50000 2.59808i −0.174371 0.302020i
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 2.59808 + 0.500000i 0.296078 + 0.0569803i
\(78\) 7.00000i 0.792594i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 7.79423 + 4.50000i 0.860729 + 0.496942i
\(83\) 12.0000i 1.31717i 0.752506 + 0.658586i \(0.228845\pi\)
−0.752506 + 0.658586i \(0.771155\pi\)
\(84\) 2.50000 0.866025i 0.272772 0.0944911i
\(85\) 0 0
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 6.92820 4.00000i 0.742781 0.428845i
\(88\) −0.866025 + 0.500000i −0.0923186 + 0.0533002i
\(89\) −1.00000 + 1.73205i −0.106000 + 0.183597i −0.914146 0.405385i \(-0.867138\pi\)
0.808146 + 0.588982i \(0.200471\pi\)
\(90\) 0 0
\(91\) 14.0000 + 12.1244i 1.46760 + 1.27098i
\(92\) 1.00000i 0.104257i
\(93\) −5.19615 3.00000i −0.538816 0.311086i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 16.0000i 1.62455i 0.583272 + 0.812277i \(0.301772\pi\)
−0.583272 + 0.812277i \(0.698228\pi\)
\(98\) 2.59808 6.50000i 0.262445 0.656599i
\(99\) 1.00000 0.100504
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 3.46410 2.00000i 0.342997 0.198030i
\(103\) −13.8564 8.00000i −1.36531 0.788263i −0.374987 0.927030i \(-0.622353\pi\)
−0.990325 + 0.138767i \(0.955686\pi\)
\(104\) −7.00000 −0.686406
\(105\) 0 0
\(106\) −1.00000 −0.0971286
\(107\) −15.5885 9.00000i −1.50699 0.870063i −0.999967 0.00813215i \(-0.997411\pi\)
−0.507026 0.861931i \(-0.669255\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) −5.00000 8.66025i −0.478913 0.829502i 0.520794 0.853682i \(-0.325636\pi\)
−0.999708 + 0.0241802i \(0.992302\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) 0.866025 + 2.50000i 0.0818317 + 0.236228i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0.500000 0.866025i 0.0468293 0.0811107i
\(115\) 0 0
\(116\) 4.00000 + 6.92820i 0.371391 + 0.643268i
\(117\) 6.06218 + 3.50000i 0.560449 + 0.323575i
\(118\) 12.0000i 1.10469i
\(119\) 2.00000 10.3923i 0.183340 0.952661i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 3.46410 2.00000i 0.313625 0.181071i
\(123\) 7.79423 4.50000i 0.702782 0.405751i
\(124\) 3.00000 5.19615i 0.269408 0.466628i
\(125\) 0 0
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) 5.00000i 0.443678i −0.975083 0.221839i \(-0.928794\pi\)
0.975083 0.221839i \(-0.0712060\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) 0 0
\(131\) 6.50000 11.2583i 0.567908 0.983645i −0.428865 0.903369i \(-0.641086\pi\)
0.996773 0.0802763i \(-0.0255803\pi\)
\(132\) 1.00000i 0.0870388i
\(133\) −0.866025 2.50000i −0.0750939 0.216777i
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) 1.73205 1.00000i 0.147979 0.0854358i −0.424182 0.905577i \(-0.639438\pi\)
0.572161 + 0.820141i \(0.306105\pi\)
\(138\) −0.866025 0.500000i −0.0737210 0.0425628i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) −12.1244 7.00000i −1.01745 0.587427i
\(143\) −6.06218 + 3.50000i −0.506945 + 0.292685i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) −14.0000 −1.15865
\(147\) −4.33013 5.50000i −0.357143 0.453632i
\(148\) 3.00000i 0.246598i
\(149\) −2.00000 + 3.46410i −0.163846 + 0.283790i −0.936245 0.351348i \(-0.885723\pi\)
0.772399 + 0.635138i \(0.219057\pi\)
\(150\) 0 0
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) 0.866025 + 0.500000i 0.0702439 + 0.0405554i
\(153\) 4.00000i 0.323381i
\(154\) 2.00000 + 1.73205i 0.161165 + 0.139573i
\(155\) 0 0
\(156\) −3.50000 + 6.06218i −0.280224 + 0.485363i
\(157\) −12.9904 + 7.50000i −1.03675 + 0.598565i −0.918910 0.394468i \(-0.870929\pi\)
−0.117836 + 0.993033i \(0.537596\pi\)
\(158\) 3.46410 2.00000i 0.275589 0.159111i
\(159\) −0.500000 + 0.866025i −0.0396526 + 0.0686803i
\(160\) 0 0
\(161\) −2.50000 + 0.866025i −0.197028 + 0.0682524i
\(162\) 1.00000i 0.0785674i
\(163\) −6.92820 4.00000i −0.542659 0.313304i 0.203497 0.979076i \(-0.434769\pi\)
−0.746156 + 0.665771i \(0.768103\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 5.00000i 0.386912i 0.981109 + 0.193456i \(0.0619696\pi\)
−0.981109 + 0.193456i \(0.938030\pi\)
\(168\) 2.59808 + 0.500000i 0.200446 + 0.0385758i
\(169\) −36.0000 −2.76923
\(170\) 0 0
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) 3.46410 2.00000i 0.264135 0.152499i
\(173\) 18.1865 + 10.5000i 1.38270 + 0.798300i 0.992478 0.122422i \(-0.0390662\pi\)
0.390218 + 0.920722i \(0.372399\pi\)
\(174\) 8.00000 0.606478
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 10.3923 + 6.00000i 0.781133 + 0.450988i
\(178\) −1.73205 + 1.00000i −0.129823 + 0.0749532i
\(179\) 6.50000 + 11.2583i 0.485833 + 0.841487i 0.999867 0.0162823i \(-0.00518305\pi\)
−0.514035 + 0.857769i \(0.671850\pi\)
\(180\) 0 0
\(181\) −12.0000 −0.891953 −0.445976 0.895045i \(-0.647144\pi\)
−0.445976 + 0.895045i \(0.647144\pi\)
\(182\) 6.06218 + 17.5000i 0.449359 + 1.29719i
\(183\) 4.00000i 0.295689i
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) 0 0
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) 3.46410 + 2.00000i 0.253320 + 0.146254i
\(188\) 3.00000i 0.218797i
\(189\) −2.00000 1.73205i −0.145479 0.125988i
\(190\) 0 0
\(191\) 5.00000 8.66025i 0.361787 0.626634i −0.626468 0.779447i \(-0.715500\pi\)
0.988255 + 0.152813i \(0.0488333\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 22.5167 13.0000i 1.62078 0.935760i 0.634074 0.773272i \(-0.281381\pi\)
0.986710 0.162488i \(-0.0519520\pi\)
\(194\) −8.00000 + 13.8564i −0.574367 + 0.994832i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 3.00000i 0.213741i 0.994273 + 0.106871i \(0.0340831\pi\)
−0.994273 + 0.106871i \(0.965917\pi\)
\(198\) 0.866025 + 0.500000i 0.0615457 + 0.0355335i
\(199\) −6.00000 10.3923i −0.425329 0.736691i 0.571122 0.820865i \(-0.306508\pi\)
−0.996451 + 0.0841740i \(0.973175\pi\)
\(200\) 0 0
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) 0 0
\(203\) 13.8564 16.0000i 0.972529 1.12298i
\(204\) 4.00000 0.280056
\(205\) 0 0
\(206\) −8.00000 13.8564i −0.557386 0.965422i
\(207\) −0.866025 + 0.500000i −0.0601929 + 0.0347524i
\(208\) −6.06218 3.50000i −0.420336 0.242681i
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) −15.0000 −1.03264 −0.516321 0.856395i \(-0.672699\pi\)
−0.516321 + 0.856395i \(0.672699\pi\)
\(212\) −0.866025 0.500000i −0.0594789 0.0343401i
\(213\) −12.1244 + 7.00000i −0.830747 + 0.479632i
\(214\) −9.00000 15.5885i −0.615227 1.06561i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −15.5885 3.00000i −1.05821 0.203653i
\(218\) 10.0000i 0.677285i
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) 0 0
\(221\) 14.0000 + 24.2487i 0.941742 + 1.63114i
\(222\) −2.59808 1.50000i −0.174371 0.100673i
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) −0.500000 + 2.59808i −0.0334077 + 0.173591i
\(225\) 0 0
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 17.3205 10.0000i 1.14960 0.663723i 0.200812 0.979630i \(-0.435642\pi\)
0.948790 + 0.315906i \(0.102309\pi\)
\(228\) 0.866025 0.500000i 0.0573539 0.0331133i
\(229\) −11.0000 + 19.0526i −0.726900 + 1.25903i 0.231287 + 0.972886i \(0.425707\pi\)
−0.958187 + 0.286143i \(0.907627\pi\)
\(230\) 0 0
\(231\) 2.50000 0.866025i 0.164488 0.0569803i
\(232\) 8.00000i 0.525226i
\(233\) −22.5167 13.0000i −1.47512 0.851658i −0.475509 0.879711i \(-0.657736\pi\)
−0.999606 + 0.0280525i \(0.991069\pi\)
\(234\) 3.50000 + 6.06218i 0.228802 + 0.396297i
\(235\) 0 0
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) 4.00000i 0.259828i
\(238\) 6.92820 8.00000i 0.449089 0.518563i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) 8.66025 5.00000i 0.556702 0.321412i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) 4.00000 0.256074
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) 6.06218 + 3.50000i 0.385727 + 0.222700i
\(248\) 5.19615 3.00000i 0.329956 0.190500i
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 0 0
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 1.73205 2.00000i 0.109109 0.125988i
\(253\) 1.00000i 0.0628695i
\(254\) 2.50000 4.33013i 0.156864 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.92820 4.00000i −0.432169 0.249513i 0.268101 0.963391i \(-0.413604\pi\)
−0.700270 + 0.713878i \(0.746937\pi\)
\(258\) 4.00000i 0.249029i
\(259\) −7.50000 + 2.59808i −0.466027 + 0.161437i
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) 11.2583 6.50000i 0.695542 0.401571i
\(263\) −13.8564 + 8.00000i −0.854423 + 0.493301i −0.862141 0.506669i \(-0.830877\pi\)
0.00771799 + 0.999970i \(0.497543\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 0 0
\(266\) 0.500000 2.59808i 0.0306570 0.159298i
\(267\) 2.00000i 0.122398i
\(268\) −10.3923 6.00000i −0.634811 0.366508i
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 18.1865 + 3.50000i 1.10070 + 0.211830i
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) −0.500000 0.866025i −0.0300965 0.0521286i
\(277\) 1.73205 1.00000i 0.104069 0.0600842i −0.447062 0.894503i \(-0.647530\pi\)
0.551131 + 0.834419i \(0.314196\pi\)
\(278\) 3.46410 + 2.00000i 0.207763 + 0.119952i
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) −2.59808 1.50000i −0.154713 0.0893237i
\(283\) −1.73205 + 1.00000i −0.102960 + 0.0594438i −0.550596 0.834772i \(-0.685599\pi\)
0.447636 + 0.894216i \(0.352266\pi\)
\(284\) −7.00000 12.1244i −0.415374 0.719448i
\(285\) 0 0
\(286\) −7.00000 −0.413919
\(287\) 15.5885 18.0000i 0.920158 1.06251i
\(288\) 1.00000i 0.0589256i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 8.00000 + 13.8564i 0.468968 + 0.812277i
\(292\) −12.1244 7.00000i −0.709524 0.409644i
\(293\) 9.00000i 0.525786i 0.964825 + 0.262893i \(0.0846766\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(294\) −1.00000 6.92820i −0.0583212 0.404061i
\(295\) 0 0
\(296\) 1.50000 2.59808i 0.0871857 0.151010i
\(297\) 0.866025 0.500000i 0.0502519 0.0290129i
\(298\) −3.46410 + 2.00000i −0.200670 + 0.115857i
\(299\) 3.50000 6.06218i 0.202410 0.350585i
\(300\) 0 0
\(301\) −8.00000 6.92820i −0.461112 0.399335i
\(302\) 2.00000i 0.115087i
\(303\) 0 0
\(304\) 0.500000 + 0.866025i 0.0286770 + 0.0496700i
\(305\) 0 0
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) 8.00000i 0.456584i −0.973593 0.228292i \(-0.926686\pi\)
0.973593 0.228292i \(-0.0733141\pi\)
\(308\) 0.866025 + 2.50000i 0.0493464 + 0.142451i
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) −8.00000 13.8564i −0.453638 0.785725i 0.544970 0.838455i \(-0.316541\pi\)
−0.998609 + 0.0527306i \(0.983208\pi\)
\(312\) −6.06218 + 3.50000i −0.343203 + 0.198148i
\(313\) 20.7846 + 12.0000i 1.17482 + 0.678280i 0.954810 0.297218i \(-0.0960589\pi\)
0.220006 + 0.975499i \(0.429392\pi\)
\(314\) −15.0000 −0.846499
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 8.66025 + 5.00000i 0.486408 + 0.280828i 0.723083 0.690761i \(-0.242724\pi\)
−0.236675 + 0.971589i \(0.576058\pi\)
\(318\) −0.866025 + 0.500000i −0.0485643 + 0.0280386i
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) −2.59808 0.500000i −0.144785 0.0278639i
\(323\) 4.00000i 0.222566i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 0 0
\(326\) −4.00000 6.92820i −0.221540 0.383718i
\(327\) −8.66025 5.00000i −0.478913 0.276501i
\(328\) 9.00000i 0.496942i
\(329\) −7.50000 + 2.59808i −0.413488 + 0.143237i
\(330\) 0 0
\(331\) 4.50000 7.79423i 0.247342 0.428410i −0.715445 0.698669i \(-0.753776\pi\)
0.962788 + 0.270259i \(0.0871094\pi\)
\(332\) −10.3923 + 6.00000i −0.570352 + 0.329293i
\(333\) −2.59808 + 1.50000i −0.142374 + 0.0821995i
\(334\) −2.50000 + 4.33013i −0.136794 + 0.236934i
\(335\) 0 0
\(336\) 2.00000 + 1.73205i 0.109109 + 0.0944911i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −31.1769 18.0000i −1.69580 0.979071i
\(339\) −3.00000 5.19615i −0.162938 0.282216i
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 1.00000i 0.0540738i
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) 29.4449 17.0000i 1.58068 0.912608i 0.585923 0.810366i \(-0.300732\pi\)
0.994760 0.102241i \(-0.0326014\pi\)
\(348\) 6.92820 + 4.00000i 0.371391 + 0.214423i
\(349\) 28.0000 1.49881 0.749403 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) 0 0
\(351\) 7.00000 0.373632
\(352\) −0.866025 0.500000i −0.0461593 0.0266501i
\(353\) −6.92820 + 4.00000i −0.368751 + 0.212899i −0.672913 0.739722i \(-0.734957\pi\)
0.304162 + 0.952620i \(0.401624\pi\)
\(354\) 6.00000 + 10.3923i 0.318896 + 0.552345i
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) −3.46410 10.0000i −0.183340 0.529256i
\(358\) 13.0000i 0.687071i
\(359\) 18.0000 31.1769i 0.950004 1.64545i 0.204595 0.978847i \(-0.434412\pi\)
0.745409 0.666608i \(-0.232254\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −10.3923 6.00000i −0.546207 0.315353i
\(363\) 10.0000i 0.524864i
\(364\) −3.50000 + 18.1865i −0.183450 + 0.953233i
\(365\) 0 0
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) −16.4545 + 9.50000i −0.858917 + 0.495896i −0.863649 0.504093i \(-0.831827\pi\)
0.00473247 + 0.999989i \(0.498494\pi\)
\(368\) 0.866025 0.500000i 0.0451447 0.0260643i
\(369\) 4.50000 7.79423i 0.234261 0.405751i
\(370\) 0 0
\(371\) −0.500000 + 2.59808i −0.0259587 + 0.134885i
\(372\) 6.00000i 0.311086i
\(373\) −22.5167 13.0000i −1.16587 0.673114i −0.213165 0.977016i \(-0.568377\pi\)
−0.952703 + 0.303902i \(0.901711\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) 0 0
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) 56.0000i 2.88415i
\(378\) −0.866025 2.50000i −0.0445435 0.128586i
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) −2.50000 4.33013i −0.128079 0.221839i
\(382\) 8.66025 5.00000i 0.443097 0.255822i
\(383\) −11.2583 6.50000i −0.575274 0.332134i 0.183979 0.982930i \(-0.441102\pi\)
−0.759253 + 0.650796i \(0.774435\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 26.0000 1.32337
\(387\) −3.46410 2.00000i −0.176090 0.101666i
\(388\) −13.8564 + 8.00000i −0.703452 + 0.406138i
\(389\) −7.00000 12.1244i −0.354914 0.614729i 0.632189 0.774814i \(-0.282157\pi\)
−0.987103 + 0.160085i \(0.948823\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 6.92820 1.00000i 0.349927 0.0505076i
\(393\) 13.0000i 0.655763i
\(394\) −1.50000 + 2.59808i −0.0755689 + 0.130889i
\(395\) 0 0
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) 15.5885 + 9.00000i 0.782362 + 0.451697i 0.837267 0.546795i \(-0.184152\pi\)
−0.0549046 + 0.998492i \(0.517485\pi\)
\(398\) 12.0000i 0.601506i
\(399\) −2.00000 1.73205i −0.100125 0.0867110i
\(400\) 0 0
\(401\) 8.50000 14.7224i 0.424470 0.735203i −0.571901 0.820323i \(-0.693794\pi\)
0.996371 + 0.0851195i \(0.0271272\pi\)
\(402\) −10.3923 + 6.00000i −0.518321 + 0.299253i
\(403\) 36.3731 21.0000i 1.81187 1.04608i
\(404\) 0 0
\(405\) 0 0
\(406\) 20.0000 6.92820i 0.992583 0.343841i
\(407\) 3.00000i 0.148704i
\(408\) 3.46410 + 2.00000i 0.171499 + 0.0990148i
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 0 0
\(411\) 1.00000 1.73205i 0.0493264 0.0854358i
\(412\) 16.0000i 0.788263i
\(413\) 31.1769 + 6.00000i 1.53412 + 0.295241i
\(414\) −1.00000 −0.0491473
\(415\) 0 0
\(416\) −3.50000 6.06218i −0.171602 0.297223i
\(417\) 3.46410 2.00000i 0.169638 0.0979404i
\(418\) 0.866025 + 0.500000i 0.0423587 + 0.0244558i
\(419\) −11.0000 −0.537385 −0.268693 0.963226i \(-0.586592\pi\)
−0.268693 + 0.963226i \(0.586592\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) −12.9904 7.50000i −0.632362 0.365094i
\(423\) −2.59808 + 1.50000i −0.126323 + 0.0729325i
\(424\) −0.500000 0.866025i −0.0242821 0.0420579i
\(425\) 0 0
\(426\) −14.0000 −0.678302
\(427\) −3.46410 10.0000i −0.167640 0.483934i
\(428\) 18.0000i 0.870063i
\(429\) −3.50000 + 6.06218i −0.168982 + 0.292685i
\(430\) 0 0
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 40.0000i 1.92228i 0.276066 + 0.961139i \(0.410969\pi\)
−0.276066 + 0.961139i \(0.589031\pi\)
\(434\) −12.0000 10.3923i −0.576018 0.498847i
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) −0.866025 + 0.500000i −0.0414276 + 0.0239182i
\(438\) −12.1244 + 7.00000i −0.579324 + 0.334473i
\(439\) 8.00000 13.8564i 0.381819 0.661330i −0.609503 0.792784i \(-0.708631\pi\)
0.991322 + 0.131453i \(0.0419644\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 28.0000i 1.33182i
\(443\) 31.1769 + 18.0000i 1.48126 + 0.855206i 0.999774 0.0212481i \(-0.00676401\pi\)
0.481486 + 0.876454i \(0.340097\pi\)
\(444\) −1.50000 2.59808i −0.0711868 0.123299i
\(445\) 0 0
\(446\) 2.00000 3.46410i 0.0947027 0.164030i
\(447\) 4.00000i 0.189194i
\(448\) −1.73205 + 2.00000i −0.0818317 + 0.0944911i
\(449\) 25.0000 1.17982 0.589911 0.807468i \(-0.299163\pi\)
0.589911 + 0.807468i \(0.299163\pi\)
\(450\) 0 0
\(451\) 4.50000 + 7.79423i 0.211897 + 0.367016i
\(452\) 5.19615 3.00000i 0.244406 0.141108i
\(453\) 1.73205 + 1.00000i 0.0813788 + 0.0469841i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) 8.66025 + 5.00000i 0.405110 + 0.233890i 0.688686 0.725059i \(-0.258188\pi\)
−0.283577 + 0.958950i \(0.591521\pi\)
\(458\) −19.0526 + 11.0000i −0.890268 + 0.513996i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) 2.59808 + 0.500000i 0.120873 + 0.0232621i
\(463\) 33.0000i 1.53364i 0.641862 + 0.766820i \(0.278162\pi\)
−0.641862 + 0.766820i \(0.721838\pi\)
\(464\) −4.00000 + 6.92820i −0.185695 + 0.321634i
\(465\) 0 0
\(466\) −13.0000 22.5167i −0.602213 1.04306i
\(467\) 10.3923 + 6.00000i 0.480899 + 0.277647i 0.720791 0.693153i \(-0.243779\pi\)
−0.239892 + 0.970799i \(0.577112\pi\)
\(468\) 7.00000i 0.323575i
\(469\) −6.00000 + 31.1769i −0.277054 + 1.43962i
\(470\) 0 0
\(471\) −7.50000 + 12.9904i −0.345582 + 0.598565i
\(472\) −10.3923 + 6.00000i −0.478345 + 0.276172i
\(473\) 3.46410 2.00000i 0.159280 0.0919601i
\(474\) 2.00000 3.46410i 0.0918630 0.159111i
\(475\) 0 0
\(476\) 10.0000 3.46410i 0.458349 0.158777i
\(477\) 1.00000i 0.0457869i
\(478\) 5.19615 + 3.00000i 0.237666 + 0.137217i
\(479\) 13.0000 + 22.5167i 0.593985 + 1.02881i 0.993689 + 0.112168i \(0.0357796\pi\)
−0.399704 + 0.916644i \(0.630887\pi\)
\(480\) 0 0
\(481\) 10.5000 18.1865i 0.478759 0.829235i
\(482\) 7.00000i 0.318841i
\(483\) −1.73205 + 2.00000i −0.0788110 + 0.0910032i
\(484\) 10.0000 0.454545
\(485\) 0 0
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 6.92820 4.00000i 0.313947 0.181257i −0.334744 0.942309i \(-0.608650\pi\)
0.648691 + 0.761052i \(0.275317\pi\)
\(488\) 3.46410 + 2.00000i 0.156813 + 0.0905357i
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 7.79423 + 4.50000i 0.351391 + 0.202876i
\(493\) 27.7128 16.0000i 1.24812 0.720604i
\(494\) 3.50000 + 6.06218i 0.157472 + 0.272750i
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) −24.2487 + 28.0000i −1.08770 + 1.25597i
\(498\) 12.0000i 0.537733i
\(499\) 12.0000 20.7846i 0.537194 0.930447i −0.461860 0.886953i \(-0.652818\pi\)
0.999054 0.0434940i \(-0.0138489\pi\)
\(500\) 0 0
\(501\) 2.50000 + 4.33013i 0.111692 + 0.193456i
\(502\) −2.59808 1.50000i −0.115958 0.0669483i
\(503\) 28.0000i 1.24846i 0.781241 + 0.624229i \(0.214587\pi\)
−0.781241 + 0.624229i \(0.785413\pi\)
\(504\) 2.50000 0.866025i 0.111359 0.0385758i
\(505\) 0 0
\(506\) 0.500000 0.866025i 0.0222277 0.0384995i
\(507\) −31.1769 + 18.0000i −1.38462 + 0.799408i
\(508\) 4.33013 2.50000i 0.192118 0.110920i
\(509\) 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 0 0
\(511\) −7.00000 + 36.3731i −0.309662 + 1.60905i
\(512\) 1.00000i 0.0441942i
\(513\) −0.866025 0.500000i −0.0382360 0.0220755i
\(514\) −4.00000 6.92820i −0.176432 0.305590i
\(515\) 0 0
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 3.00000i 0.131940i
\(518\) −7.79423 1.50000i −0.342459 0.0659062i
\(519\) 21.0000 0.921798
\(520\) 0 0
\(521\) 10.5000 + 18.1865i 0.460013 + 0.796766i 0.998961 0.0455727i \(-0.0145113\pi\)
−0.538948 + 0.842339i \(0.681178\pi\)
\(522\) 6.92820 4.00000i 0.303239 0.175075i
\(523\) 12.1244 + 7.00000i 0.530161 + 0.306089i 0.741082 0.671414i \(-0.234313\pi\)
−0.210921 + 0.977503i \(0.567646\pi\)
\(524\) 13.0000 0.567908
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) −20.7846 12.0000i −0.905392 0.522728i
\(528\) −0.866025 + 0.500000i −0.0376889 + 0.0217597i
\(529\) −11.0000 19.0526i −0.478261 0.828372i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 1.73205 2.00000i 0.0750939 0.0867110i
\(533\) 63.0000i 2.72883i
\(534\) −1.00000 + 1.73205i −0.0432742 + 0.0749532i
\(535\) 0 0
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 11.2583 + 6.50000i 0.485833 + 0.280496i
\(538\) 0 0
\(539\) 5.50000 4.33013i 0.236902 0.186512i
\(540\) 0 0
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) −13.8564 + 8.00000i −0.595184 + 0.343629i
\(543\) −10.3923 + 6.00000i −0.445976 + 0.257485i
\(544\) −2.00000 + 3.46410i −0.0857493 + 0.148522i
\(545\) 0 0
\(546\) 14.0000 + 12.1244i 0.599145 + 0.518875i
\(547\) 36.0000i 1.53925i −0.638497 0.769624i \(-0.720443\pi\)
0.638497 0.769624i \(-0.279557\pi\)
\(548\) 1.73205 + 1.00000i 0.0739895 + 0.0427179i
\(549\) −2.00000 3.46410i −0.0853579 0.147844i
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 1.00000i 0.0425628i
\(553\) −3.46410 10.0000i −0.147309 0.425243i
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −38.9711 + 22.5000i −1.65126 + 0.953356i −0.674705 + 0.738087i \(0.735729\pi\)
−0.976555 + 0.215268i \(0.930937\pi\)
\(558\) −5.19615 3.00000i −0.219971 0.127000i
\(559\) 28.0000 1.18427
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 2.59808 + 1.50000i 0.109593 + 0.0632737i
\(563\) 12.1244 7.00000i 0.510981 0.295015i −0.222256 0.974988i \(-0.571342\pi\)
0.733237 + 0.679974i \(0.238009\pi\)
\(564\) −1.50000 2.59808i −0.0631614 0.109399i
\(565\) 0 0
\(566\) −2.00000 −0.0840663
\(567\) −2.59808 0.500000i −0.109109 0.0209980i
\(568\) 14.0000i 0.587427i
\(569\) −18.5000 + 32.0429i −0.775560 + 1.34331i 0.158919 + 0.987292i \(0.449199\pi\)
−0.934479 + 0.356018i \(0.884134\pi\)
\(570\) 0 0
\(571\) 4.00000 + 6.92820i 0.167395 + 0.289936i 0.937503 0.347977i \(-0.113131\pi\)
−0.770108 + 0.637913i \(0.779798\pi\)
\(572\) −6.06218 3.50000i −0.253472 0.146342i
\(573\) 10.0000i 0.417756i
\(574\) 22.5000 7.79423i 0.939132 0.325325i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 12.1244 7.00000i 0.504744 0.291414i −0.225927 0.974144i \(-0.572541\pi\)
0.730670 + 0.682730i \(0.239208\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) 13.0000 22.5167i 0.540262 0.935760i
\(580\) 0 0
\(581\) 24.0000 + 20.7846i 0.995688 + 0.862291i
\(582\) 16.0000i 0.663221i
\(583\) −0.866025 0.500000i −0.0358671 0.0207079i
\(584\) −7.00000 12.1244i −0.289662 0.501709i
\(585\) 0 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) 42.0000i 1.73353i −0.498721 0.866763i \(-0.666197\pi\)
0.498721 0.866763i \(-0.333803\pi\)
\(588\) 2.59808 6.50000i 0.107143 0.268055i
\(589\) −6.00000 −0.247226
\(590\) 0 0
\(591\) 1.50000 + 2.59808i 0.0617018 + 0.106871i
\(592\) 2.59808 1.50000i 0.106780 0.0616496i
\(593\) −10.3923 6.00000i −0.426761 0.246390i 0.271205 0.962522i \(-0.412578\pi\)
−0.697966 + 0.716131i \(0.745911\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) −4.00000 −0.163846
\(597\) −10.3923 6.00000i −0.425329 0.245564i
\(598\) 6.06218 3.50000i 0.247901 0.143126i
\(599\) 3.00000 + 5.19615i 0.122577 + 0.212309i 0.920783 0.390075i \(-0.127551\pi\)
−0.798206 + 0.602384i \(0.794218\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) −3.46410 10.0000i −0.141186 0.407570i
\(603\) 12.0000i 0.488678i
\(604\) −1.00000 + 1.73205i −0.0406894 + 0.0704761i
\(605\) 0 0
\(606\) 0 0
\(607\) 21.6506 + 12.5000i 0.878772 + 0.507359i 0.870253 0.492604i \(-0.163955\pi\)
0.00851879 + 0.999964i \(0.497288\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 4.00000 20.7846i 0.162088 0.842235i
\(610\) 0 0
\(611\) 10.5000 18.1865i 0.424785 0.735748i
\(612\) 3.46410 2.00000i 0.140028 0.0808452i
\(613\) −12.9904 + 7.50000i −0.524677 + 0.302922i −0.738846 0.673874i \(-0.764629\pi\)
0.214169 + 0.976797i \(0.431296\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) 0 0
\(616\) −0.500000 + 2.59808i −0.0201456 + 0.104679i
\(617\) 8.00000i 0.322068i −0.986949 0.161034i \(-0.948517\pi\)
0.986949 0.161034i \(-0.0514829\pi\)
\(618\) −13.8564 8.00000i −0.557386 0.321807i
\(619\) −3.50000 6.06218i −0.140677 0.243659i 0.787075 0.616858i \(-0.211595\pi\)
−0.927752 + 0.373198i \(0.878261\pi\)
\(620\) 0 0
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) 16.0000i 0.641542i
\(623\) 1.73205 + 5.00000i 0.0693932 + 0.200321i
\(624\) −7.00000 −0.280224
\(625\) 0 0
\(626\) 12.0000 + 20.7846i 0.479616 + 0.830720i
\(627\) 0.866025 0.500000i 0.0345857 0.0199681i
\(628\) −12.9904 7.50000i −0.518373 0.299283i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 14.0000 0.557331 0.278666 0.960388i \(-0.410108\pi\)
0.278666 + 0.960388i \(0.410108\pi\)
\(632\) 3.46410 + 2.00000i 0.137795 + 0.0795557i
\(633\) −12.9904 + 7.50000i −0.516321 + 0.298098i
\(634\) 5.00000 + 8.66025i 0.198575 + 0.343943i
\(635\) 0 0
\(636\) −1.00000 −0.0396526
\(637\) 48.4974 7.00000i 1.92154 0.277350i
\(638\) 8.00000i 0.316723i
\(639\) −7.00000 + 12.1244i −0.276916 + 0.479632i
\(640\) 0 0
\(641\) 11.5000 + 19.9186i 0.454223 + 0.786737i 0.998643 0.0520757i \(-0.0165837\pi\)
−0.544420 + 0.838812i \(0.683250\pi\)
\(642\) −15.5885 9.00000i −0.615227 0.355202i
\(643\) 26.0000i 1.02534i 0.858586 + 0.512670i \(0.171344\pi\)
−0.858586 + 0.512670i \(0.828656\pi\)
\(644\) −2.00000 1.73205i −0.0788110 0.0682524i
\(645\) 0 0
\(646\) 2.00000 3.46410i 0.0786889 0.136293i
\(647\) 12.9904 7.50000i 0.510705 0.294855i −0.222419 0.974951i \(-0.571395\pi\)
0.733123 + 0.680096i \(0.238062\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −6.00000 + 10.3923i −0.235521 + 0.407934i
\(650\) 0 0
\(651\) −15.0000 + 5.19615i −0.587896 + 0.203653i
\(652\) 8.00000i 0.313304i
\(653\) −25.1147 14.5000i −0.982816 0.567429i −0.0796966 0.996819i \(-0.525395\pi\)
−0.903119 + 0.429390i \(0.858728\pi\)
\(654\) −5.00000 8.66025i −0.195515 0.338643i
\(655\) 0 0
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) 14.0000i 0.546192i
\(658\) −7.79423 1.50000i −0.303851 0.0584761i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −4.00000 6.92820i −0.155582 0.269476i 0.777689 0.628649i \(-0.216392\pi\)
−0.933271 + 0.359174i \(0.883059\pi\)
\(662\) 7.79423 4.50000i 0.302931 0.174897i
\(663\) 24.2487 + 14.0000i 0.941742 + 0.543715i
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −3.00000 −0.116248
\(667\) −6.92820 4.00000i −0.268261 0.154881i
\(668\) −4.33013 + 2.50000i −0.167538 + 0.0967279i
\(669\) −2.00000 3.46410i −0.0773245 0.133930i
\(670\) 0 0
\(671\) 4.00000 0.154418
\(672\) 0.866025 + 2.50000i 0.0334077 + 0.0964396i
\(673\) 12.0000i 0.462566i −0.972887 0.231283i \(-0.925708\pi\)
0.972887 0.231283i \(-0.0742923\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −18.0000 31.1769i −0.692308 1.19911i
\(677\) 0.866025 + 0.500000i 0.0332841 + 0.0192166i 0.516550 0.856257i \(-0.327216\pi\)
−0.483266 + 0.875474i \(0.660549\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 32.0000 + 27.7128i 1.22805 + 1.06352i
\(680\) 0 0
\(681\) 10.0000 17.3205i 0.383201 0.663723i
\(682\) 5.19615 3.00000i 0.198971 0.114876i
\(683\) 10.3923 6.00000i 0.397650 0.229584i −0.287819 0.957685i \(-0.592930\pi\)
0.685470 + 0.728101i \(0.259597\pi\)
\(684\) 0.500000 0.866025i 0.0191180 0.0331133i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 22.0000i 0.839352i
\(688\) 3.46410 + 2.00000i 0.132068 + 0.0762493i
\(689\) −3.50000 6.06218i −0.133339 0.230951i
\(690\) 0 0
\(691\) −6.00000 + 10.3923i −0.228251 + 0.395342i −0.957290 0.289130i \(-0.906634\pi\)
0.729039 + 0.684472i \(0.239967\pi\)
\(692\) 21.0000i 0.798300i
\(693\) 1.73205 2.00000i 0.0657952 0.0759737i
\(694\) 34.0000 1.29062
\(695\) 0 0
\(696\) 4.00000 + 6.92820i 0.151620 + 0.262613i
\(697\) 31.1769 18.0000i 1.18091 0.681799i
\(698\) 24.2487 + 14.0000i 0.917827 + 0.529908i
\(699\) −26.0000 −0.983410
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 6.06218 + 3.50000i 0.228802 + 0.132099i
\(703\) −2.59808 + 1.50000i −0.0979883 + 0.0565736i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) −8.00000 −0.301084
\(707\) 0 0
\(708\) 12.0000i 0.450988i
\(709\) 2.00000 3.46410i 0.0751116 0.130097i −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) 0 0
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) −1.73205 1.00000i −0.0649113 0.0374766i
\(713\) 6.00000i 0.224702i
\(714\) 2.00000 10.3923i 0.0748481 0.388922i
\(715\) 0 0
\(716\) −6.50000 + 11.2583i −0.242916 + 0.420744i
\(717\) 5.19615 3.00000i 0.194054 0.112037i
\(718\) 31.1769 18.0000i 1.16351 0.671754i
\(719\) 13.0000 22.5167i 0.484818 0.839730i −0.515030 0.857172i \(-0.672219\pi\)
0.999848 + 0.0174426i \(0.00555244\pi\)
\(720\) 0 0
\(721\) −40.0000 + 13.8564i −1.48968 + 0.516040i
\(722\) 18.0000i 0.669891i
\(723\) −6.06218 3.50000i −0.225455 0.130166i
\(724\) −6.00000 10.3923i −0.222988 0.386227i
\(725\) 0 0
\(726\) 5.00000 8.66025i 0.185567 0.321412i
\(727\) 17.0000i 0.630495i −0.949009 0.315248i \(-0.897912\pi\)
0.949009 0.315248i \(-0.102088\pi\)
\(728\) −12.1244 + 14.0000i −0.449359 + 0.518875i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) 3.46410 2.00000i 0.128037 0.0739221i
\(733\) −32.0429 18.5000i −1.18353 0.683313i −0.226704 0.973964i \(-0.572795\pi\)
−0.956829 + 0.290651i \(0.906128\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −10.3923 6.00000i −0.382805 0.221013i
\(738\) 7.79423 4.50000i 0.286910 0.165647i
\(739\) 20.5000 + 35.5070i 0.754105 + 1.30615i 0.945818 + 0.324697i \(0.105262\pi\)
−0.191714 + 0.981451i \(0.561404\pi\)
\(740\) 0 0
\(741\) 7.00000 0.257151
\(742\) −1.73205 + 2.00000i −0.0635856 + 0.0734223i
\(743\) 9.00000i 0.330178i −0.986279 0.165089i \(-0.947209\pi\)
0.986279 0.165089i \(-0.0527911\pi\)
\(744\) 3.00000 5.19615i 0.109985 0.190500i
\(745\) 0 0
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) 10.3923 + 6.00000i 0.380235 + 0.219529i
\(748\) 4.00000i 0.146254i
\(749\) −45.0000 + 15.5885i −1.64426 + 0.569590i
\(750\) 0 0
\(751\) 13.0000 22.5167i 0.474377 0.821645i −0.525193 0.850983i \(-0.676007\pi\)
0.999570 + 0.0293387i \(0.00934013\pi\)
\(752\) 2.59808 1.50000i 0.0947421 0.0546994i
\(753\) −2.59808 + 1.50000i −0.0946792 + 0.0546630i
\(754\) −28.0000 + 48.4974i −1.01970 + 1.76617i
\(755\) 0 0
\(756\) 0.500000 2.59808i 0.0181848 0.0944911i
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) −0.866025 0.500000i −0.0314555 0.0181608i
\(759\) −0.500000 0.866025i −0.0181489 0.0314347i
\(760\) 0 0
\(761\) 8.50000 14.7224i 0.308125 0.533688i −0.669827 0.742517i \(-0.733632\pi\)
0.977952 + 0.208829i \(0.0669652\pi\)
\(762\) 5.00000i 0.181131i
\(763\) −25.9808 5.00000i −0.940567 0.181012i
\(764\) 10.0000 0.361787
\(765\) 0 0
\(766\) −6.50000 11.2583i −0.234855 0.406780i
\(767\) −72.7461 + 42.0000i −2.62671 + 1.51653i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) 29.0000 1.04577 0.522883 0.852404i \(-0.324856\pi\)
0.522883 + 0.852404i \(0.324856\pi\)
\(770\) 0 0
\(771\) −8.00000 −0.288113
\(772\) 22.5167 + 13.0000i 0.810392 + 0.467880i
\(773\) 37.2391 21.5000i 1.33940 0.773301i 0.352679 0.935744i \(-0.385271\pi\)
0.986718 + 0.162443i \(0.0519374\pi\)
\(774\) −2.00000 3.46410i −0.0718885 0.124515i
\(775\) 0 0
\(776\) −16.0000 −0.574367
\(777\) −5.19615 + 6.00000i −0.186411 + 0.215249i
\(778\) 14.0000i 0.501924i
\(779\) 4.50000 7.79423i 0.161229 0.279257i
\(780\) 0 0
\(781\) −7.00000 12.1244i −0.250480 0.433844i
\(782\) −3.46410 2.00000i −0.123876 0.0715199i
\(783\) 8.00000i 0.285897i
\(784\) 6.50000 + 2.59808i 0.232143 + 0.0927884i
\(785\) 0 0
\(786\) 6.50000 11.2583i 0.231847 0.401571i
\(787\) 19.0526 11.0000i 0.679150 0.392108i −0.120384 0.992727i \(-0.538413\pi\)
0.799535 + 0.600620i \(0.205079\pi\)
\(788\) −2.59808 + 1.50000i −0.0925526 + 0.0534353i
\(789\) −8.00000 + 13.8564i −0.284808 + 0.493301i
\(790\) 0 0
\(791\) −12.0000 10.3923i −0.426671 0.369508i
\(792\) 1.0000